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Basic Physics of Nuclear Medicine/Atomic & Nuclear Structure

You will have encountered much of what we will cover here in your high school physics. We are going to review this material again below so as to set the context for subsequent chapters. This chapter will also provide you with an opportunity to check your understanding of this topic.

The chapter covers atomic structure, nuclear structure, the classification of nuclei, binding energy and nuclear stability.

Atomic Structure
The atom is considered to be the basic building block of all matter. Simple atomic theory tells us that it consists of two components:  a nucleus surrounded by an electron cloud. The situation can be considered as being similar in some respects to planets orbiting the sun.

From an electrical point of view, the nucleus is said to be positively charged and the electrons negatively charged.

From a size point of view, the radius of an atom is about 10-10 m while the radius of a nucleus is about 10-14 m, i.e. about ten thousand times smaller. The situation could be viewed as something like a cricket ball, representing the nucleus, in the middle of a sporting arena with the electrons orbiting somewhere around where the spectators would sit. This perspective tells us that the atom should be composed mainly of empty space. However, the situation is far more complex than this simple picture portrays in that we must also take into account the physical forces which bind the atom together.

Chemical phenomena can be thought of as interactions between the electrons of individual atoms. Radioactivity on the other hand can be thought of as changes which occur within the nuclei of atoms.

The Nucleus
A simple description of the nucleus tells us that it is composed of protons and neutrons. These two particle types are collectively called nucleons, i.e. particles which inhabit the nucleus.

From a mass point of view the mass of a proton is roughly equal to the mass of a neutron and each of these is about 2,000 times the mass of an electron. So most of the mass of an atom is concentrated in the small region at its core.

From an electrical point of view the proton is positively charged and the neutron has no charge. An atom all on its own (if that were possible to achieve!) is electrically neutral. The number of protons in the nucleus of such an atom must therefore equal the number of electrons orbiting that atom.

Classification of Nuclei
The term Atomic Number is defined in nuclear physics as the number of protons in a nucleus and is given the symbol Z. From your chemistry you will remember that this number also defines the position of an element in the Periodic Table of Elements.

The term Mass Number is defined as the number of nucleons in a nucleus, that is the number of protons plus the number of neutrons, and is given the symbol A.

Note that the symbols here are a bit odd, in that it would prevent some confusion if the Atomic Number were given the symbol A, and the Mass Number were given another symbol, such as M, but its not a simple world!

It is possible for nuclei of a given element to have the same number of protons but differing numbers of neutrons, that is to have the same Atomic Number but different Mass Numbers. Such nuclei are referred to as Isotopes. All elements have isotopes and the number ranges from three for hydrogen to over 30 for elements such as caesium and barium.

Chemistry has a relatively simple way of classifying the different elements by the use of symbols such as H for hydrogen, He for helium and so on. The classification scheme used to identify different isotopes is based on this approach with the use of a superscript before the chemical symbol to denote the Mass Number along with a subscript before the chemical symbol to denote the Atomic Number. In other words an isotope is identified as:

$${}_{\mathbf{Z}}^{\mathbf{A}}\mathbf{X}$$

where X is the chemical symbol of the element; A is the "Mass Number," (protons+ neutrons); Z is the "Atomic Number," (number identifying the element on the periodic chart).

Let us take the case of hydrogen as an example. It has three isotopes:

 * the most common one consisting of a single proton orbited by one electron,
 * a second isotope consisting of a nucleus containing a proton and a neutron orbited by one electron,
 * a third whose nucleus consists of one proton and two neutrons, again orbited by a single electron.

A simple illustration of these isotopes is shown below. Remember though that this is a simplified illustration given what we noted earlier about the size of a nucleus compared with that of an atom. But the illustration is nevertheless useful for showing how isotopes are classified.

The first isotope commonly called hydrogen has a Mass Number of 1, an Atomic Number of 1 and hence is identified as:

$${}_1^1\mathbf{H}$$

The second isotope commonly called deuterium has a Mass Number of 2, an Atomic Number of 1 and is identified as:

$${}_1^2\mathbf{H}$$

The third isotope commonly called tritium is identified as:

$${}_1^3\mathbf{H}$$

The same classification scheme is used for all isotopes. For example, you should now be able to figure out that the uranium isotope, $${}_{92}^{236}\mathbf{U}$$, contains 92 protons and 144 neutrons.

A final point on classification is that we can also refer to individual isotopes by giving the name of the element followed by the Mass Number. For example, we can refer to deuterium as hydrogen-2 and we can refer to $${}_{92}^{236}\mathbf{U}$$ as uranium-236.

Before we leave this classification scheme let us further consider the difference between chemistry and nuclear physics. You will remember that the water molecule is made up of two hydrogen atoms bonded with an oxygen atom. Theoretically if we were to combine atoms of hydrogen and oxygen in this manner many, many of billions of times we could make a glass of water. We could also make our glass of water using deuterium instead of hydrogen. This second glass of water would theoretically be very similar from a chemical perspective. However, from a physics perspective our second glass would be heavier than the first since each deuterium nucleus is about twice the mass of each hydrogen nucleus. Indeed water made in this fashion is called heavy water.

Atomic Mass Unit
The conventional unit of mass, the kilogram, is rather large for use in describing characteristics of nuclei. For this reason, a special unit called the Atomic Mass Unit (amu) is often used. This unit is sometimes defined as 1/12th of the mass of the stable most commonly occurring isotope of carbon, i.e. 12C. In terms of grams, 1 amu is equal to 1.66 x 10-24 g, that is, just over one million, million, million millionth of a gram.

The masses of the proton, mp and neutron, mn on this basis are:

mp	=	1.00783 amu

and

mn	=	1.00866 amu

while that of the electron is just 0.00055 amu.

Binding Energy
We are now in a position to consider the subject of nuclear stability. From what we have covered so far, we have seen that the nucleus is a tiny region in the centre of an atom and that it is composed of neutrally and positively charged particles. So, in a large nucleus such as that of uranium (Z=92) we have a large number of positively charged protons concentrated into a tiny region in the centre of the atom. An obvious question which arises is that with all these positive charges in close proximity, why doesn't the nucleus fly apart? How can a nucleus remain as an entity with such electrostatic repulsion between the components? Should the orbiting negatively-charged electrons not attract the protons away from the atoms centre?

Let us take the case of the helium-4 nucleus as an example. This nucleus contains two protons and two neutrons so that in terms of amu we can figure out from what we covered earlier that the

mass of 2 protons	=	2.01566 amu, and the mass of 2 neutrons	=	2.01732 amu.

Therefore we would expect the total mass of the nucleus to be 4.03298 amu.

The experimentally determined mass of a helium-4 nucleus is a bit less - just 4.00260 amu. In other words there is a difference of 0.03038 amu between what we might expect as the mass of this nucleus and what we actually measure. You might think of this difference as very small at just 0.75%. But remember that since the mass of one electron is 0.00055 amu the difference is actually equivalent to the mass of about 55 electrons. Therefore it is significant enough to wonder about.

It is possible to consider that this missing mass is converted to energy which is used to hold the nucleus together; it is converted to a form of energy called Binding Energy. You could say, as with all relationships, energy must be expended in order to maintain them!

Like the gram in terms of the mass of nuclei, the common unit of energy, the joule is rather cumbersome when we consider the energy needed to bind a nucleus together. The unit used to express energies on the atomic scale is the electron volt, symbol: eV.

One electron volt is defined as the amount of energy gained by an electron as it falls through a potential difference of one volt. This definition on its own is not of great help to us here and it is stated purely for the sake of completeness. So do not worry about it for the time being. Just appreciate that it is a unit representing a tiny amount of energy which is useful on the atomic scale. It is a bit too small in the case of binding energies however and the mega-electron volt (MeV) is often used.

Albert Einstein introduced us to the equivalence of mass, m, and energy, E, at the atomic level using the following equation:

E = m c2 ,

where c is the velocity of light.

It is possible to show that 1 amu is equivalent to 931.48 MeV. Therefore, the mass difference we discussed earlier between the expected and measured mass of the helium-4 nucleus of 0.03038 amu is equivalent to about 28 MeV. This represents about 7 MeV for each of the four nucleons contained in the nucleus.

Nuclear Stability
In most stable isotopes the binding energy per nucleon lies between 7 and 9 MeV. There are two competing forces in the nuclei, electrostatic repulsion between protons and the attractive nuclear force between nucleons (protons and neutrons). The electrostatic force is a long range force that becomes more difficult to compensate for as more protons are added to the nucleus. The nuclear force, which arises as the residual strong force (the strong force binds the quarks together within a nucleon), is a short range force that only operates on a very short distance scale (~ 1.5 fm) as it arises from a Yukawa potential. (Electromagnetism is a long range force as the force carrier, the photon, is massless; the nuclear force is a short range force as the force carrier, the pion, is massive). Therefore, larger nuclei tend to be less stable, and require a larger ratio of neutrons to protons (which contribute to the attractive strong force, but not the long-range electrostatic repulsion). For the low Z nuclides the ratio of neutrons to protons is approximately 1, though it gradually increases to about 1.5 for the higher Z nuclides as shown below on the Nuclear Stability Curve.

In other words to combat the effect of the increase in electrostatic repulsion when the number of protons increases the number of neutrons must increase more rapidly to contribute sufficient energy to bind the nucleus together.

As we noted earlier there are a number of isotopes for each element of the Periodic Table. It has been found that the most stable isotope for each element has a specific number of neutrons in its nucleus. Plotting a graph of the number of protons against the number of neutrons for these stable isotopes generates what is called the Nuclear Stability Curve:

Note that the number of protons equals the number of neutrons for small nuclei. But notice also that the number of neutrons increases more rapidly than the number of protons as the size of the nucleus gets bigger so as to maintain the stability of the nucleus. In other words more neutrons need to be there to contribute to the binding energy used to counteract the electrostatic repulsion between the protons.

Radioactivity
There are about 2,450 known isotopes of the approximately one hundred elements in the Periodic Table. You can imagine the size of a table of isotopes relative to that of the Periodic Table! The unstable isotopes lie above or below the Nuclear Stability Curve. These unstable isotopes attempt to reach the stability curve by splitting into fragments, in a process called Fission, or by emitting particles and/or energy in the form of radiation. This latter process is called Radioactivity.

It is useful to dwell for a few moments on the term radioactivity. For example what has nuclear stability to do with radio? From a historical perspective remember that when these radiations were discovered about 100 years ago we did not know exactly what we were dealing with. When people like Henri Becquerel and Marie Curie were working initially on these strange emanations from certain natural materials it was thought that the radiations were somehow related to another phenomenon which also was not well understood at the time - that of radio communication. It seems reasonable on this basis to appreciate that some people considered that the two phenomena were somehow related and hence that the materials which emitted radiation were termed radio-active.

We know today that the two phenomena are not directly related but we nevertheless hold onto the term radioactivity for historical purposes. But it should be quite clear to you having reached this stage of this chapter that the term radioactive refers to the emission of particles and/or energy from unstable isotopes. Unstable isotopes for instance those that have too many protons to remain a stable entity are called radioactive isotopes - and called radioisotopes for short. The term radionuclide is also sometimes used.

Finally about 300 of the 2,450-odd isotopes mentioned above are found in nature. The rest are man-made, that is they are produced artificially. These 2,150 or so artificial isotopes have been made during the last 100 years or so with most having been made since the second world war.

We will return to the production of radioisotopes in a later chapter of this wikibook and will proceed for the time being with a description of the types of radiation emitted by radioisotopes.

Multiple Choice Questions
Click here to access multiple choice questions on atomic and nuclear structure.


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Basic Physics of Nuclear Medicine/Radioactive Decay

We saw in the last chapter that radioactivity is a process used by unstable nuclei to achieve a more stable situation. It is said that such nuclei decay in an attempt to achieve stability. So, an alternative title for this chapter is Nuclear Decay Processes.

We also saw in the previous chapter that we can use the Nuclear Stability Curve as a means of describing what is going on. So a second alternative title for this chapter is Methods of Getting onto the Nuclear Stability Curve.

We are going to follow a descriptive or phenomenological approach to the topic here by describing in a fairly simple fashion what is known about each of the major decay mechanisms. Once again you may have already covered this material in high school physics. But bear with us because the treatment here will help us set the scene for subsequent chapters.

Methods of Radioactive Decay
Rather than considering what happens to individual nuclei it is perhaps easier to consider a hypothetical nucleus that can undergo many of the major forms of radioactive decay. This hypothetical nucleus is shown below:

Firstly we can see two protons and two neutrons being emitted together in a process called alpha-decay. Secondly, we can see that a proton can release a positron in a process called beta-plus decay, and that a neutron can emit an electron in a process called beta-minus decay. We can also see an electron being captured by a proton. Thirdly we can see some energy (a photon) being emitted which results from a process called gamma-decay as well as an electron being attracted into the nucleus and being ejected again. Finally there is the rather catastrophic process where the nucleus cracks in half called spontaneous fission.

We will now describe each of these decay processes in turn.

Spontaneous Fission
This is a very destructive process which occurs in some heavy nuclei which split into 2 or 3 fragments plus some neutrons. These fragments form new nuclei which are usually radioactive. Nuclear reactors exploit this phenomenon for the production of radioisotopes. Its also used for nuclear power generation and in nuclear weaponry. The process is not of great interest to us here and we will say no more about it for the time being.

Alpha Decay
In this decay process two protons and two neutrons leave the nucleus together in an assembly known as an alpha particle. Note that an alpha particle is really a helium-4 nucleus.

So why not call it a helium nucleus? Why give it another name? The answer to this question lies in the history of the discovery of radioactivity. At the time when these radiations were discovered we didn't know what they really were. We found out that one type of these radiations had a double positive charge and it was not until sometime later that we learned that they were in fact nuclei of helium-4. In the initial period of their discovery this form of radiation was given the name alpha rays (and the other two were called beta and gamma rays), these terms being the first three letters of the Greek alphabet. We still call this form of radiation by the name alpha particle for historical purposes. Calling it by this name also contributes to the specific jargon of the field and leads outsiders to think that the subject is quite specialized!

But notice that the radiation really consists of a helium-4 nucleus emitted from an unstable larger nucleus. There is nothing strange about helium since it is quite an abundant element on our planet. So why is this radiation dangerous to humans? The answer to this question lies with the energy with which they are emitted and the fact that they are quite massive and have a double positive charge. So when they interact with living matter they can cause substantial destruction to molecules which they encounter in their attempt to slow down and to attract two electrons to become a neutral helium atom.

An example of this form of decay occurs in the uranium-238 nucleus. The equation which represents what occurs is:

$${}_{\mathbf{92}}^{\mathbf{238}}\mathbf{U}$$ → $${}_{\mathbf{90}}^{\mathbf{234}}\mathbf{Th}$$ + $${}_{\mathbf{2}}^{\mathbf{4}}\mathbf{He}$$

Here the uranium-238 nucleus emits a helium-4 nucleus (the alpha particle) and the parent nucleus becomes thorium-234. Note that the Mass Number of the parent nucleus has been reduced by 4 and the Atomic Number is reduced by 2 which is a characteristic of alpha decay for any nucleus in which it occurs.

Beta Decay
There are three common forms of beta decay:

(a)	Electron Emission

 * Certain nuclei which have an excess of neutrons may attempt to reach stability by converting a neutron into a proton with the emission of an electron. The electron is called a beta-minus particle – the minus indicating that the particle is negatively charged.

 * We can represent what occurs as follows:

n0 → p+ + e-

 * where a neutron converts into a proton and an electron. Notice that the total electrical charge is the same on both sides of this equation.  We say that the electric charge is conserved.

 * We can consider that the electron cannot exist inside the nucleus and therefore is ejected.

 * Once again there is nothing strange or mysterious about an electron. What is important though from a radiation safety point of view is the energy with which it is emitted and the chemical damage it can cause when it interacts with living matter.

 * An example of this type of decay occurs in the iodine-131 nucleus which decays into xenon-131 with the emission of an electron, that is

$${}_{\mathbf{53}}^{\mathbf{131}}\mathbf{I}$$ → $${}_{\mathbf{54}}^{\mathbf{131}}\mathbf{Xe}$$ + $${}_{\mathbf{-1}}^{\mathbf{0}}\mathbf{e}$$

 * The electron is what is called a beta-minus particle. Note that the Mass Number in the above equation remains the same and that the Atomic Number increases by 1 which is characteristic of this type of decay.

 * You may be wondering how an electron can be produced inside a nucleus given that the simple atomic description we gave in the previous chapter indicated that the nucleus consists of protons and neutrons only. This is one of the limitations of the simple treatment presented so far and can be explained by considering that the two particles which we call protons and neutrons are themselves formed of smaller particles called quarks.  We are not going to consider these in any way here other than to note that some combinations of different types of quark produce protons and another combination produces neutrons.  The message here is to appreciate that a simple picture is the best way to start in an introductory text such as this and that the real situation is a lot more complex than what has been described.  The same can be said about the treatment of beta-decay given above as we will see in subsequent chapters.

(b)	Positron Emission

 * When the number of protons in a nucleus is too large for the nucleus to be stable it may attempt to reach stability by converting a proton into a neutron with the emission of a positively-charged electron.

 * That is not a typographical error! An electron with a positive charge also called a positron is emitted. The positron is the beta-plus particle.

 * The history here is quite interesting. A brilliant Italian physicist, Enrico Fermi developed a theory of beta decay and his theory predicted that positively-charged as well as negatively-charged electrons could be emitted by unstable nuclei.  These particles could be called pieces of anti-matter and they were subsequently discovered by experiment.  They do not exist for very long as they quickly combine with a normal electron and the subsequent reaction called annihilation gives rise to the emission of two gamma rays.

 * Science fiction writers had a great time following the discovery of anti-matter and speculated along with many scientists that parts of our universe may contain negatively-charged protons forming nuclei which are orbited by positively-charged electrons. But this is taking us too far away from the topic at hand!

 * The reaction in our unstable nucleus which contains one too many protons can be represented as follows:

p+ → n0 + e+

 * Notice, once again, that electric charge is conserved on each side of this equation.

 * An example of this type of decay occurs in sodium-22 which decays into neon-22 with the emission of a positron:

$${}_{\mathbf{11}}^{\mathbf{22}}\mathbf{Na}$$ → $${}_{\mathbf{10}}^{\mathbf{22}}\mathbf{Ne}$$ + $${}_{\mathbf{+1}}^{\mathbf{0}}\mathbf{e}$$

 * Note that the Mass Number remains the same and that the Atomic Number decreases by 1.

(c)	Electron Capture

 * In this third form of beta decay an inner orbiting electron is attracted into an unstable nucleus where it combines with a proton to form a neutron. The reaction can be represented as:

e- + p+ → n0

 * This process is also known as K-capture since the electron is often attracted from the K-shell of the atom.

 * How do we know that a process like this occurs given that no radiation is emitted? In other words the event occurs within the atom itself and no information about it leaves the atom.  Or does it?  The signature of this type of decay can be obtained from effects in the electron cloud surrounding the nucleus when the vacant site left in the K-shell is filled by an electron from an outer shell.  The filling of the vacancy is associated with the emission of an X-ray from the electron cloud and it is this X-ray which provides a signature for this type of beta decay.

 * This form of decay can also be recognised by the emission of gamma-rays from the new nucleus.

 * An example of this type of radioactive decay occurs in iron-55 which decays into manganese-55 following the capture of an electron. The reaction can be represented as follows:

$${}_{\mathbf{26}}^{\mathbf{55}}\mathbf{Fe}$$ + $${}_{\mathbf{-1}}^{\mathbf{0}}\mathbf{e}$$ → $${}_{\mathbf{25}}^{\mathbf{55}}\mathbf{Mn}$$

 * Note that the Mass Number once again is unchanged in this form of decay and that the Atomic Number is decreased by 1.

Gamma Decay
Gamma decay involves the emission of energy from an unstable nucleus in the form of electromagnetic radiation.

You should remember from your high school physics that electromagnetic radiation is the biggest physical phenomenon we have so far discovered. The radiation can be characterised in terms of its frequency, its wavelength and its energy. Thinking about it in terms of the energy of the radiation we have very low energy electromagnetic radiation called radio waves, infra-red radiation at a slightly higher energy, visible light at a higher energy still, then ultra-violet radiation and the higher energy forms of this radiation are called X-rays and gamma-rays. You should also remember that these radiations form what is called the Electromagnetic Spectrum.

Before proceeding it is useful to pause for a moment to consider the difference between X-rays and gamma-rays. These two forms of radiation are high energy electromagnetic rays and are therefore virtually the same. The difference between them is not what they consist of but where they come from. In general we can say that if the radiation emerges from a nucleus it is called a gamma-ray and if it emerges from outside the nucleus from the electron cloud for example, it is called an X-ray.

One final point is of relevance before we consider the different forms of gamma-decay and that is what such a high energy ray really is. It has been found in experiments that gamma-rays (and X-rays for that matter!) sometimes manifest themselves as waves and other times as particles. This wave-particle duality can be explained using the equivalence of mass and energy at the atomic level. When we describe a gamma ray as a wave it has been found useful to use terms such as frequency and wavelength just like any other wave. In addition when we describe a gamma ray as a particle we use terms such as mass and electric charge. Furthermore the term electromagnetic photon is used for these particles. The interesting feature about these photons however is that they have neither mass nor charge!

There are two common forms of gamma decay:

(a)	Isomeric Transition

 * A nucleus in an excited state may reach its ground or unexcited state by the emission of a gamma-ray.

 * An example of this type of decay is that of technetium-99m – which by the way is the most common radioisotope used for diagnostic purposes today in medicine. The reaction can be expressed as:

$${}_{\mathbf{43}}^{\mathbf{99m}}\mathbf{Tc}$$ → $${}_{\mathbf{43}}^{\mathbf{99}}\mathbf{Tc}$$ +  $$\gamma$$

 * Here a nucleus of technetium-99 is in an excited state, that is, it has excess energy. The excited state in this case is called a metastable state and the nucleus is therefore called technetium-99m (m for metastable).  The excited nucleus looses its excess energy by emitting a gamma-ray to become technetium-99.

(b)	Internal Conversion

 * Here the excess energy of an excited nucleus is given to an atomic electron, e.g. a K-shell electron.

Decay Schemes
Decay schemes are widely used to give a visual representation of radioactive decay. A scheme for a relatively straight-forward decay is shown below:

This scheme is for hydrogen-3 which decays to helium-3 with a half-life of 12.3 years through the emission of a beta-minus particle with an energy of 0.0057 MeV.

A scheme for a more complicated decay is that of caesium-137.

This isotope can decay through through two beta-minus processes. In one which occurs in 5% of disintegrations a beta-minus particle is emitted with an energy of 1.17 MeV to produce barium-137. In the second which occurs more frequently (in the remaining 95% of disintegrations) a beta-minus particle of energy 0.51 MeV is emitted to produce barium-137m – in other words a barium-137 nucleus in a metastable state. The barium-137m then decays via isomeric transition with the emission of a gamma-ray of energy 0.662 MeV.

The general method used for decay schemes is illustrated in the diagram on the right.

The energy is plotted on the vertical axis and atomic number on the horizontal axis – although these axes are rarely displayed in actual schemes. The isotope from which the scheme originates is displayed at the top – X in the case above. This isotope is referred to as the parent. The parent loses energy when it decays and hence the products of the decay referred to as daughters are plotted at a lower energy level.

The diagram illustrates the situation for common forms of radioactive decay. Alpha-decay is illustrated on the left where the mass number is reduced by 4 and the atomic number is reduced by 2 to produce daughter A. To its right the scheme for beta-plus decay is shown to produce daughter B. The situation for beta-minus decay followed by gamma-decay is shown on the right side of the diagram where daughters C and D respectively are produced.

Multiple Choice Questions
Click here to access multiple choice questions on radioactive decay.

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Wooden Boats: Building and Repair/Additional Resources/Books

Plank on Frame
Building Small Boats by Greg Rossel Hardcover: 288 pages Publisher: Wooden Boat Publications (December 15, 1998) ISBN: 0937822507

Wooden Boats to Build & Use by John Gardner Paperback: 261 pages Publisher: Mystic Seaport Museum (November 1996) ISBN: 0913372781

Building Classic Small Craft : Complete Plans and Instructions for 47 Boats by John Gardner Paperback: 560 pages Publisher: International Marine/Ragged Mountain Press; 2 edition (August 12, 2003) ISBN: 007142797X

More Building Classic Small Craft: How to Build 23 Traditional Boats by John Gardner Paperback: 241 pages Publisher: Intl Marine Pub; Reprint edition (March 1990) ISBN: 0877422745

Dory Book by John Gardner Paperback: 275 pages Publisher: Mystic Seaport Museum (June 1987) ISBN: 0913372447

Traditional boatbuilding made easy: Building Heidi, a 12 foot skiff for oar and sail by Richard Kolin Unknown Binding: 85 pages Publisher: WoodenBoat Books; 2nd [ed] edition (January 1, 1999) ASIN: B0006RA0TS

Plywood
Devlin's Boatbuilding: How to Build Any Boat the Stitch-and-Glue Way by Samual Devlin Paperback: 198 pages Publisher: International Marine/Ragged Mountain Press; 1 edition (October 25, 1995) ISBN: 0071579907

Clinker Plywood Boatbuilding Manual by Iain Oughtred Paperback: 174 pages Publisher: Wooden Boat Publications (March 1, 2000) ISBN: 0937822612

Repair
Boatowner's Mechanical & Electrical Manual: How to Maintain, Repair, and Improve Your Boat's Essential Systems by Nigel Calder, Charlie Wing Hardcover: 592 pages ; Dimensions (in inches): 1.08 x 11.12 x 8.74 Publisher: International Marine/Ragged Mountain Press; 2nd edition (November 1, 1995) ISBN: 007009618X

Marine Diesel Engines: Maintenance, Troubleshooting, and Repair by Nigel Calder Hardcover: 224 pages ; Dimensions (in inches): 0.81 x 9.54 x 7.54 Publisher: International Marine/Ragged Mountain Press; 2nd edition (December 1, 1991) ISBN: 0070096120

Wooden Boat Renovation: New Life for Old Boats Using Modern Methods by Jim Trefethen, Clint Trefethen (Illustrator) Hardcover: 302 pages ; Dimensions (in inches): 1.06 x 9.57 x 7.64 Publisher: International Marine/Ragged Mountain Press; (January 1, 1993) ISBN: 0070652392

Frame, Stem & Keel Repair (The WoodenBoat Series) Edited by Peter H Spectre Paperback: 133 pages Publisher: Wooden Boat Publications (September 1996) ISBN: 0937822426

Planking and Fastening (The WoodenBoat Series) by Peter Spectre & Maynard Bray Paperback: 170 pages Publisher: Wooden Boat Publications (September 1996) ISBN: 0937822418

Painting and Varnishing (The Woodenboat Series) Edited by Peter H. Spectre Paperback: 146 pages Publisher: Wooden Boat Publications (October 1995) ISBN: 0937822337

The Boatwright's Companion: Repairs Below the Waterline by Allen Taub Paperback: 161 pages Publisher: International Marine Publishing (January 1986) ISBN: 0877421986

Repairs by Walter Simmons

Guidance on Inspection, Repair, and Maintenance of Wooden Hulls - U.S. Coast Guard


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Basic Physics of Nuclear Medicine/The Radioactive Decay Law

We covered radioactive decay from a phenomenological perspective in the last chapter. In this chapter we consider the topic from a more general analytical perspective.

The reason for doing this is so that we can develop a form of thinking which will help us to understand what is going on in a quantitative, mathematical sense. We will be introduced to concepts such as the Decay Constant and the Half Life as well as units used for the measurement of radioactivity. You will also have a chance to develop your understanding by being brought through three questions on this subject.

Assumptions
The usual starting point in most forms of analysis in physics is to make some assumptions which simplify the situation. By simplifying the situation we can dispose of irrelevant effects which tend to complicate matters but in doing so we sometimes make the situation so simple that it becomes a bit too abstract and apparently hard to understand.

For this reason we will try here to relate the subject of radioactive decay to a more common situation which we will use as an analogy and hopefully we will be able to overcome the abstract feature of the subject matter. The analogy we will use here is that of making popcorn.

So think about putting some oil in a pot, adding the corn, heating the pot on the cooker and watching what happens. You might also like to try this out while considering the situation!

For our radioactive decay situation we first of all consider that we have a sample containing a large number of radioactive nuclei all of the same kind. This is our unpopped corn in the pot for example.

Secondly we assume that all of the radioactive nuclei decay by the same process be it alpha, beta or gamma-decay. In other words our unpopped corn goes pop at some stage during the heating process.

Thirdly take a few moments to ponder on the fact that we can only really consider what is going on from a statistical perspective. If you look at an individual piece of corn, can you figure out when it is going to pop? Not really. You can however figure out that a large number of them will have popped after a period of time. But its rather more difficult to figure out the situation for an individual piece of corn. So instead of dealing with individual entities we consider what happens on a larger scale and this is where statistics comes in. We can say that the radioactive decay is a statistical one-shot process, that is when a nucleus has decayed it cannot repeat the process again. In other words when a piece of corn has popped it cannot repeat the process. Simple!

In addition as long as a radioactive nucleus has not decayed the probability for it doing so in the next moment remains the same. In other words if a piece of corn has not popped at a certain time the chance of it popping in the next second is the same as in the previous second. The bets are even!

Let us not push this popcorn analogy too far though in that we know that we can control the rate of popping by the heat we apply to the pot for example. However as far as our radioactive nuclei are concerned there is nothing we can do to control what is going on. The rate at which nuclei go pop (or decay, in other words) cannot be influenced by heating up the sample. Nor by cooling it for that matter or by putting it under greater pressures, by changing the gravitational environment by taking it out into space for instance, or by changing any other aspect of its physical environment. The only thing that determines whether an individual nucleus will decay seems to be the nucleus itself. But on the average we can say that it will decay at some stage.

The Radioactive Decay Law
Let us now use some symbols to reduce the amount of writing we have to do to describe what is going on and to avail ourselves of some mathematical techniques to simplify the situation even further than we have been able to do so far.

Let us say that in the sample of radioactive material there are N nuclei which have not decayed at a certain time, t. So what happens in the next brief period of time? Some nuclei will decay for sure. But how many?

On the basis of our reasoning above we can say that the number which will decay will depend on overall number of nuclei, N, and also on the length of the brief period of time. In other words the more nuclei there are the more will decay and the longer the time period the more nuclei will decay. Let us denote the number which will have decayed as dN and the small time interval as dt.

So we have reasoned that the number of radioactive nuclei which will decay during the time interval from t to t+dt must be proportional to N and to dt. In symbols therefore:

$$-dN \propto N \cdot dt\,\!$$

the minus sign indicating that N is decreasing.

Turning the proportionality in this equation into an equality we can write:

$$-dN = \lambda N \cdot dt\,\!$$

where the constant of proportionality, λ (named lambda) is called the Decay Constant.

Dividing across by N we can rewrite this equation as:

$$-\frac{dN}{N} = \lambda \cdot dt$$

So this equation describes the situation for any brief time interval, dt. To find out what happens for all periods of time we simply add up what happens in each brief time interval. In other words we integrate the above equation. Expressing this more formally we can say that for the period of time from t = 0 to any later time t, the number of radioactive nuclei will decrease from N0 to Nt, so that:

$$-\int_{N_0}^{N_t} \frac{dN}{N} = \lambda \int_{0}^t dt$$

$$\therefore \ln \left ( \frac{N_t}{N_0} \right ) = -\lambda t$$

$$\therefore \frac{N_t}{N_0} = \text{exp}\,(-\lambda t)$$

$$\therefore N_t = N_0 \text{exp}\,(-\lambda t)$$

This final expression is known as the Radioactive Decay Law. It tells us that the number of radioactive nuclei will decrease in an exponential fashion with time with the rate of decrease being controlled by the Decay Constant.

Before looking at this expression in further detail let us review the mathematics which we used above. First of all we used integral calculus to figure out what was happening over a period of time by integrating what we knew would occur in a brief interval of time. Secondly we used a calculus relationship that the

$$\int \frac{dx}{x} = \ln x$$

where ln x represents the natural logarithm of x. And thirdly we used the definition of logarithms that when

$$\ln x = y\,\!$$

then,

$$x = \text{exp}\ y\,\!$$

Now, to return to the Radioactive Decay Law. The Law tells us that the number of radioactive nuclei will decrease with time in an exponential fashion with the rate of decrease being controlled by the Decay Constant. The Law is shown in graphical form in the figure below:

The graph plots the number of radioactive nuclei at any time, Nt, against time, t. We can see that the number of radioactive nuclei decreases from N0 that is the number at t = 0 in a rapid fashion initially and then more slowly in the classic exponential manner.

The influence of the Decay Constant can be seen in the following figure:

All three curves here are exponential in nature, only the Decay Constant is different. Notice that when the Decay Constant has a low value the curve decreases relatively slowly and when the Decay Constant is large the curve decreases very quickly.

The Decay Constant is characteristic of individual radionuclides. Some like uranium-238 have a small value and the material therefore decays quite slowly over a long period of time. Other nuclei such as technetium-99m have a relatively large Decay Constant and they decay far more quickly.

It is also possible to consider the Radioactive Decay Law from another perspective by plotting the logarithm of Nt against time. In other words from our analysis above by plotting the expression:

$$\ln \left ( \frac{N_t}{N_0} \right ) = - \lambda t$$

in the form

$$\ln N_t = -\lambda t + \ln N_0\,\!$$

Notice that this expression is simply an equation of the form y = mx + c where m = -l and c = ln N0. As a result it is the equation of a straight line of slope -l as shown in the following figure. Such a plot is sometimes useful when we wish to consider a situation without the complication of the direct exponential behaviour.

Half-Life
Most of us have not been taught to think instinctively in terms of logarithmic or exponential terms even though many natural phenomena display exponential behaviours. Most of the forms of thinking which we have been taught in school are based on linear changes and as a result it is rather difficult for us to grasp the Radioactive Decay Law intuitively. For this reason an indicator is usually derived from the law which helps us think more clearly about what is going on.

This indicator is called the Half Life and it expresses the length of time it takes for the radioactivity of a radioisotope to decrease by a factor of two. From a graphical point of view we can say that when:

$$N_t = \frac{N_0}{2}$$

the time taken is the Half Life:

Note that the half-life does not express how long a material will remain radioactive but simply the length of time for its radioactivity to halve. Examples of the half lives of some radioisotopes are given in the following table. Notice that some of these have a relatively short half life. These tend to be the ones used for medical diagnostic purposes because they do not remain radioactive for very long following administration to a patient and hence result in a relatively low radiation dose.

But they do present a logistical problem when we wish to use them when there may not be a radioisotope production facility nearby. For example suppose we wish to use 99mTc for a patient study and the nearest nuclear facility for making this isotope is 5,000 km away. The production facility could be in Sydney and the patient could be in Perth for instance. After making the isotope at the nuclear plant it would be decaying with a half life of 6 hours. So we put the material on a truck and drive it to Sydney airport. The isotope would be decaying as the truck sits in Sydney traffic then decaying still more as it waits for a plane to take it to Perth. Then decaying more as it is flown across to Perth and so on. By the time it gets to our patient it will have substantially reduced in radioactivity possibly to the point of being useless for the patient's investigation. And what about the problem if we needed to use 81mKr instead of 99mTc for our patient? You will see in another chapter of this book that logistical challenges such as this have given rise to quite innovative solutions. More about that later!

You can appreciate from the table above that other isotopes have a very long half lives. For example 226Ra has a half life of over 1,500 years. This isotope has been used in the past for therapeutic applications in medicine. Think about the logistical problems here. They obviously do not relate to transporting the material from the point of production to the point of use. But they relate to how the material is kept following its arrival at the point of use. We must have a storage facility so that the material can be kept safely for a long period of time. But for how long? A general rule of thumb for the quantities of radioactivity used in medicine is that the radioactivity will remain significant for about 10 half lives. So we would have to have a safe environment for storage of the 226Ra for about 16,000 years! This storage facility would have to be secure from many unforeseeable events such as earthquakes, bombing etc. and be kept in a manner which our children's, children's children can understand. A very serious undertaking indeed!

Relationship between the Decay Constant and the Half Life
On the basis of the above you should be able to appreciate that there is a relationship between the Decay Constant and the Half Life. For example when the Decay Constant is small the Half Life should be long and correspondingly when the Decay Constant is large the Half Life should be short. But what exactly is the nature of this relationship?

We can easily answer this question by using the definition of Half Life and applying it to the Radioactive Decay Law.

Once again the law tells us that at any time, t:

$$N_t = N_0\ \text{exp}\,(-\lambda t)\,\!$$

and the definition of Half Life tells us that:

$$N_t = \frac{N_0}{2}$$

when

$$t = t_{\frac{1}{2}}$$

We can therefore re-write the Radioactive Decay Law by substituting for Nt and t as follows:

$$\frac{N_0}{2} = N_0\ \text{exp}\,(-\lambda t_{\frac{1}{2}})$$

Therefore

$$\frac{1}{2} = \text{exp}\,(-\lambda t_{\frac{1}{2}})$$

$$\therefore 2^{-1} = \text{exp}\,(-\lambda t_{\frac{1}{2}})$$

$$\therefore \ln 2^{-1} = -\lambda t_{\frac{1}{2}}$$

$$\therefore \ln 2 = \lambda t_{\frac{1}{2}}$$

$$\therefore 0.693 = \lambda t_{\frac{1}{2}}$$

$$t_{\frac{1}{2}} = \frac{0.693}{\lambda}$$

and

$$\lambda = \frac{0.693}{t_{\frac{1}{2}}}$$

These last two equations express the relationship between the Decay Constant and the Half Life. They are very useful as you will see when solving numerical questions relating to radioactivity and usually form the first step in solving a numerical problem.

Units of Radioactivity
The SI or metric unit of radioactivity is named after Henri Becquerel, in honour of his discovery of radioactivity, and is called the becquerel with the symbol Bq. The becquerel is defined as the quantity of radioactive substance that gives rise to a decay rate of 1 decay per second.

In medical diagnostic work 1 Bq is a rather small amount of radioactivity. Indeed it is easy to remember its definition if you think of it as a buggerall amount of radioactivity. For this reason the kilobecquerel (kBq) and megabecquerel (MBq) are more frequently used.

The traditional unit of radioactivity is named after Marie Curie and is called the curie, with the symbol Ci. The curie is defined as the amount of radioactive substance which gives rise to a decay rate of 3.7 x 1010 decays per second. In other words 37 thousand, million decays per second which as you might appreciate is a substantial amount of radioactivity. For medical diagnostic work the millicurie (mCi) and the microcurie (µCi) are therefore more frequently used.

Why two units? It in essence like all other units of measurement depends on what part of the world you are in. For example the kilometer is widely used in Europe and Australia as a unit of distance and the mile is used in the USA. So if you are reading an American textbook you are likely to find the curie used as the unit of radioactivity, if you are reading an Australian book it will most likely refer to becquerels and both units might be used if you are reading a European book. You will therefore find it necessary to know and understand both units.

Multiple Choice Questions
Click here to access an MCQ on the Radioactive Decay Law.

Questions
Three questions are given below to help you develop your understanding of the material presented in this chapter. The first one is relatively straight-forward and will exercise your application of the Radioactive Decay Law as well as your understanding of the concept of Half Life. The second question is a lot more challenging and will help you relate the Radioactive Decay Law to the number of radioactive nuclei which are decaying in a sample of radioactive material. The third question will help you understand the approach used in the second question by asking a similar question from a slightly different perspective.

Question 1

(a)	The half-life of 99mTc is 6 hours. After how much time will 1/16th of the radioisotope remain?

(b)	Verify your answer by another means.

Answer:

 * (a)	Starting with the relationship we established earlier between the Decay Constant and the Half Life we can calculate the Decay Constant as follows:

$$\lambda = \frac{0.693}{t_{\frac{1}{2}}} = \frac{0.693}{6} = 0.1155\ \text{hr}^{-1}$$

 * Now applying the Radioactive Decay Law,

$$N_t = N_0\ \text{exp}\,(-\lambda t)\,\!$$

 * we can re-write it in the form:

$$\frac{N_t}{N_0} = \text{exp}\,(-\lambda t)$$

 * The question tells us that N0 has reduced to 1/16th of its value, that is:

$$\frac{N_t}{N_0} = \frac{1}{16}$$

 * Therefore

$$\frac{1}{16} = \text{exp}\,(-0.1155t)$$

 * which we need to solve for t. One way of doing this is as follows:

$$16^{-1} = \text{exp}\,(-0.1155t)$$

$$\therefore -\ln 16 = -0.1155t\,\!$$

$$t = \frac{\ln 16}{0.1155} = 24\ \text{hours}$$

 * So it will take 24 hours until 1/16th of the radioactivity remains.

 * (b)	A way in which this answer can be verified is by using the definition of Half Life. We are told that the Half Life of 99mTc is 6 hours.  Therefore after six hours half of the radioactivity remains.

 * Therefore after 12 hours a quarter remains; after 18 hours an eighth remains and after 24 hours one sixteenth remains. And we arrive at the same answer as in part (a).  So we must be right!

 * Note that this second approach is useful if we are dealing with relatively simple situations where the radioactivity is halved, quartered and so on. But supposing the question asked how long would it take for the radioactivity to decrease to a tenth of its initial value.  Deduction from the definition of half life is rather more difficult in this case and the mathematical approach used for part (a) above will yield the answer more readily.

Question 2

Find the radioactivity of a 1 g sample of 226Ra given that t1/2: 1620 years and Avogadro's Number: 6.023 x 1023.

Answer:

 * We can start the answer like we did with Question 1(a) by calculating the Decay Constant from the Half Life using the following equation:

$$\lambda = \frac{0.693}{t_{\frac{1}{2}}} = \frac{0.693}{1620} = 4.28 \cdot 10^{-4}\ \text{year}^{-1}$$

$$\therefore \lambda = 1.36 \cdot 10^{-11} s^{-1}$$

 * Note that the length of a year used in converting from 'per year' to 'per second' above is 365.25 days to account for leap years. In addition the reason for converting to units of 'per second' is because the unit of radioactivity is expressed as the number of nuclei decaying per second.

 * Secondly we can calculate that 1 g of 226Ra contains:

$$N = \frac{(\text{Avogadro No.})(\text{Mass})}{\text{Mass Number}} = \frac{(6.023 \cdot 10^{23})(1g)}{226} = 2.7 \cdot 10^{21}\ \text{nuclei}$$

 * Thirdly we need to express the Radioactive Decay Law in terms of the number of nuclei decaying per unit time. We can do this by differentiating the equation as follows:

$$N = N_0\ \text{exp}\,(-\lambda t)$$

$$\therefore \frac{dN}{dt} = N_0 \cdot -\lambda\ \text{exp}\,(-\lambda t) = -\lambda N_0\ \text{exp}\,(-\lambda t)$$

$$\therefore \frac{dN}{dt} = -\lambda N$$

$$\therefore \left | \frac{dN}{dt} \right | = \lambda N$$

 * The reason for expressing the result above in absolute terms is to remove the minus sign in that we already know that the number is decreasing.

 * We can now enter the data we derived above for λ and N:

$$\left | \frac{dN}{dt} \right | = (1.36 \cdot 10^{-11})(2.7 \cdot 10^{21})$$

$$\therefore \left | \frac{dN}{dt} \right | = 3.6 \cdot 10^{10}\ \text{decays per second}$$

 * So the radioactivity of our 1 g sample of radium-226 is approximately 1 Ci.

 * This is not a surprising answer since the definition of the curie was originally conceived as the radioactivity of 1 g of radium-226!

Question 3

What is the minimum mass of 99mTc that can have a radioactivity of 1 MBq? Assume the half-life is 6 hours and that Avogadro's Number is 6.023 x 1023.

Answer

 * Starting again with the relationship between the Decay Constant and the Half Life:

$$\lambda = \frac{0.693}{6} = 0.1155\ \text{hour}^{-1} = 3.21 \cdot 10^{-5}$$

 * Secondly the question tells us that the radioactivity is 1 MBq. Therefore since 1 MBq = 1 x 106 decays per second,

$$\left | \frac{dN}{dt} \right | = \lambda N = 1 \cdot 10^6\ \text{dps}$$

$$\therefore N = \frac{\left | \frac{dN}{dt} \right |}{\lambda} = \frac{1 \cdot 10^6}{3.21 \cdot 10^{-5}} = 3.116 \cdot 10^{10}$$

 * Finally the mass of these nuclei can be calculated as follows:

$$\text{Mass of N nuclei} = \frac{(\text{No. of Nuclei})(\text{Mass No.})}{\text{Avogadro Number}}$$

$$= \frac{(3.116 \cdot 10^{10})(99)}{6.023 \cdot 10^{23}} = 5.122 \cdot 10^{-12}\ \text{g}$$

 * In other words a mass of just over five picograms of 99mTc can emit one million gamma-rays per second. The result reinforces an important point that you will learn about radiation protection which is that you should treat radioactive materials just like you would handle pathogenic bacteria!


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Basic Physics of Nuclear Medicine/Units of Radiation Measurement

Introduction
This is the fourth chapter of a wikibook entitled Basic Physics of Nuclear Medicine.

After that rather long and detailed chapter we have just finished we will now proceed at a more leisurely pace for a short treatment of some of the more common units of measurement used in this field.

Before we do so however it is useful to consider the typical radiation environment. By doing so we will gain an appreciation of the various quantities that can be measured before considering the units which are used to express such measurements. So, we will first of all consider a typical radiation situation and then go on to consider the various units of measurement.

A Typical Radiation Situation
A typical radiation set-up is shown in the figure below. Firstly there is a source of radiation, secondly a radiation beam and thirdly some material which absorbs the radiation. So the quantities which can be measured are associated with the source, the radiation beam and the absorber.

This type of environment could be one where the radiation from the source is used to irradiate a patient (that is the absorber) for diagnostic purposes where we would place a device behind the patient for producing an image or for therapeutic purposes where the radiation is intended to cause damage to a specific region of a patient. It is also a situation where we as an absorber may be working with a source of radiation.

The Radiation Source
When the radiation source is a radioactive one the quantity that is typically measured is the radioactivity of the source. We saw in the previous chapter that the units used to express radioactivity are the becquerel (SI unit) and the curie (traditional unit).

The Radiation Beam
The characteristic of a radiation beam that is typically measured is called the Radiation Exposure. This quantity expresses how much ionisation the beam causes in the air through which it travels.

We will see in the following chapter that one of the major things that happens when radiation encounters matter is that ions are formed – air being the form of matter it encounters in this case. So the radiation exposure produced by a radiation beam is expressed in terms of the amount of ionisation which occurs in air.

A straight-forward way of measuring such ionisation is to determine the amount of electric charge which is produced. You will remember from your high school physics that the SI unit of electric charge is the coulomb.

The SI unit of radiation exposure is the coulomb per kilogram – and is given the symbol C kg-1. It is defined as the quantity of X- or gamma-rays such that the associated electrons emitted per kilogram of air at standard temperature and pressure (STP) produce ions carrying 1 coulomb of electric charge.

The traditional unit of radiation exposure is the roentgen, named in honour of Wilhelm Roentgen (who discovered X-rays) and is given the symbol R. The roentgen is defined as the quantity of X- or gamma-rays such that the associated  electrons emitted per kilogram of air at STP produce ions carrying 2.58 x 10-4 coulombs of electric charge.

So 1 R is a small exposure relative to 1 C kg-1 – in fact it is 3,876 times smaller.

Note that this unit is confined to radiation beams consisting of X-rays or gamma-rays.

Often it is not simply the exposure that is of interest but the exposure rate, that is the exposure per unit time. The units which tend to be used in this case are the C kg-1 s-1 and the R hr-1.

The Absorber
Energy is deposited in the absorber when radiation interacts with it. It is usually quite a small amount of energy but energy nonetheless. The quantity that is measured is called the Absorbed Dose and it is of relevance to all types of radiation be they X- or gamma-rays, alpha- or beta-particles.

The SI unit of absorbed dose is called the gray, named after a famous radiobiologist, LH Gray, and is given the symbol Gy. The gray is defined as the absorption of 1 joule of radiation energy per kilogram of material. So when 1 joule of radiation energy is absorbed by a kilogram of the absorber material we say that the absorbed dose is 1 Gy.

The traditional unit of absorbed dose is called the rad, which supposedly stands for Radiation Absorbed Dose. It is defined as the absorption of 10-2 joules of radiation energy per kilogram of material.

As you can figure out 1 Gy is equal to 100 rad.

There are other quantities derived from the gray and the rad which express the biological effects of such absorbed radiation energy when the absorber is living matter – human tissue for example. These quantities include the Equivalent Dose, H, and the Effective Dose, E. The Equivalent Dose is based on estimates of the ionization capability of the different types of radiation which are called Radiation Weighting Factors, wR, such that

H = wR D

where D is the absorbed dose. The Effective Dose includes wR as well as estimates of the sensitivity of different tissues called Tissue Weighting Factors, wT, such that

E = Σ wT H

where the summation, Σ, is over all the tissue types involved. Both the Equivalent Dose and the Effective Dose are measured in derived SI units called sieverts (Sv).

Let us pause here for a bit to ponder on the use of the term dose. It usually has a medical connotation in that we can say that someone had a dose of the 'flu, or that the doctor prescribed a certain dose of a drug. What has it to do with the deposition of energy by a beam of radiation in an absorber? It could have something to do with the initial applications of radiation in the early part of the 20th century when it was used to treat numerous diseases. As a result we can speculate that the term has stayed in the vernacular of the field. It would be much easier to use a term like absorbed radiation energy since we are talking about the deposition of energy in an absorber. But this might make the subject just a little too simple!

Specific Gamma Ray Constant
A final quantity is worth mentioning with regard to radiation units. This is the Specific Gamma-Ray Constant for a radioisotope. This quantity is an amalgam of the quantities we have already covered and expresses the exposure rate produced by the gamma-rays emitted from a radioisotope.

It is quite a useful quantity from a practical viewpoint when we are dealing with a radioactive source which emits gamma-rays. Supposing you are using a gamma-emitting radioactive source (for example 99mTc or 137Cs) and you will be standing at a certain distance from this source while you are working. You most likely will be interested in the exposure rate produced by the source from a radiation safety point of view. This is where the Specific Gamma-Ray Constant comes in.

It is defined as the exposure rate per unit activity at a certain distance from a source. The SI unit is therefore the

C kg-1 s-1 Bq-1   at    1 m  ,

and the traditional unit is the

R hr-1 mCi-1   at    1 cm.

These units of measurement are quite cumbersome and a bit of a mouthful. It might have been better if they were named after some famous scientist so that we could call the SI unit 1 smith and the traditional unit 1 jones for example. But again things are not that simple!

The Inverse Square Law
Before we finish this chapter we are going to consider what happens as we move our absorber away from the radiation source. In other words we are going to think about the influence of distance on the intensity of the radiation beam. You will find that a useful result emerges from this that has a very important impact on radiation safety.

The radiation produced in a radioactive source is emitted in all directions. We can consider that spheres of equal radiation intensity exist around the source with the number of photons/particles spreading out as we move away from the source.

Consider an area on the surface of one of these spheres and assume that there are a certain number of photons/particles passing though it. If we now consider a sphere at a greater distance from the source the same number of photons/particles will now be spread out over a bigger area. Following this line of thought it is easy to appreciate that the radiation intensity, I will decrease with the square of the distance, r from the source, i.e. $$ I \propto \frac{1}{r^2} $$

This effect is known as the Inverse Square Law. As a result if we double the distance from a source, we reduce the intensity by a factor of two squared, that is 4. If we triple the distance the intensity is reduced by a factor of 9, that is three squared, and so on.

This is a very useful piece of information if you are working with a source of radiation and are interested in minimising the dose of radiation you will receive.


text:
Talk:European History

Jaw Dropping
This book is amazing. It is content rich, it has a massive amount of information and best of all, it is made by volunteers, thank you! Mitchturn (discuss • contribs) 04:51, 11 November 2011 (UTC)

What happened to the Portuguese?
Why are most of the important Portuguese explorers missing? I added them back. #Brandon Johnsonn 16:38, 17 June 2007 (UTC)

There is a sentence hidden behind the infobox, that you can see if you change your font size. I use a 130% fontsize, and I can see '..tion' appear on the right of the box in the upper left corner.

 * I updated the template so the text should be gone now. Can you still see it? --hagindaz 13:52, 5 June 2006 (UTC)

Misleading title
The subtitle is wrong: From Joan of Arc to Tony Blair. If you want to make a clear chronological statement here spanning the lifetime of European History from its beginning to its present ('Tony Blair' is associated with the present) then Joan of Arc is wrong in this perspective, since there were many important historical figures before her life time. I suggest to replace her name with "Charlemagne", which makes much more sense to me.

As a remark and personal opinion: Tony Blair does not fit into Europe's picture as other politicians would do today, because of his standpoint in questions of the European Union and the special state Great Britain has in Europe (of the big and old nations of Europe Great Britain's people show the least identification with Europe and what it stands for) I would replace his name as well with somebody like the Luxembourg president or Romano Prodi.

 * I've removed the subtitle. Mentioning Tony Blair is POV, suggesting he is somehow the most important person in Europe today. I don't see why that would be him.
 * I've also changed "complete survey" to just "survey". I'm not sure what a complete survey is, and I don't think we're ever going to agree on that. Qwertyus 14:56, 26 August 2006 (UTC)

 * I also think the earlier title is misleading because it says "from Rome to present day, yet the next page says "from hundred years war to present"

pictures in PDF version
i started reading the book on line and deceded to download the pdf version, and notice there isn't so many pictures as the on line and print-version. why is that?

PS: very good book!!!201.78.130.253 06:15, 5 January 2007 (UTC)

Well Done
I'm reading the book at the moment and I have honestly ound it to be one of the best books I have read on history for a long time. Well Done to everyony. --82.33.114.90 (talk) 08:39, 14 April 2008 (UTC)

Linking to Wikipedia?
How do contributors feel about linking to Wikipedia for some (for lack of a better word) events? For example, I would like to link to the Wikipedia article for "denazification" in the chapter "1918-1945", as we need not go through it in detail, but it would be nice if we placed links for further reading.

This policy applies to all chapters of this book. I believe it would entice the reader to read on, and being a free culture book, its purpose is nothing but informing the reader about European History as effectively as possible. Placing links to Wikipedia is a means to this end. What do you think? Johnanth (discuss • contribs) 14:37, 27 May 2012 (UTC)

Anyone want a copy edit?
Being greatly interested in European History, this book naturally caught my eye. However, I've noticed that it seems to have some run-on sentences and other grammar problems. Copy editing is one of my primary areas of work on the English Wikipedia (I'm actually a coordinator for the Guild of Copy Editors), so I think I can make some good grammatical improvements to this book. Since this is a featured book, however, I wanted to see if people would like a copy edit before I do too much. --Biblioworm (discuss • contribs) 23:28, 12 February 2015 (UTC)

Social science history
Why European colonised Africa Mobicel Astro (discuss • contribs) 18:25, 12 September 2019 (UTC)

title: Talk:European History


text:
Basic Physics of Nuclear Medicine/Interaction of Radiation with Matter

We have focussed in previous chapters on the source of radiation and the types of radiation. We are now in a position to consider what happens when this radiation interacts with matter. Our main reason for doing this is to find out what happens to the radiation as it passes through matter and also to set ourselves up for considering how it interacts with living tissue and how to detect radiation. Since all radiation detectors are made from some form of matter it is useful to first of all know how radiation interacts so that we can exploit the effects in the design of such detectors in subsequent chapters of this wikibook.

Before we do this let us first remind ourselves of the physical characteristics of the major types of radiation. We have covered this information in some detail earlier and it is summarised in the table below for convenience.

We will now consider the passage of each type of radiation through matter with most attention given to gamma-rays because they are the most common type used in nuclear medicine. One of the main effects that you will notice irrespective of the type of radiation is that ions are produced when radiation interacts with matter. It is for this reason that it is called ionizing radiation.

Before we start though you might find an analogy useful to help you with your thinking. This analogy works on the basis of thinking about matter as an enormous mass of atoms (that is nuclei with orbiting electrons) and that the radiation is a particle/photon passing through this type of environment. So the analogy to think about is a spaceship passing through a meteor storm like you might see in a science-fiction movie where the spaceship represents the radiation and the meteors represent the atoms of the material through which the radiation is passing. One added feature to bring on board however is that our spaceship sometimes has an electric charge depending on the type of radiation it represents.

Alpha Particles
We can see from the table above that alpha-particles have a double positive charge and we can therefore easily appreciate that they will exert considerable electrostatic attraction on the outer orbital electrons of atoms near which they pass. The result is that some electrons will be attracted away from their parent atoms and that ions will be produced. In other words ionizations occur.

We can also appreciate from the table that alpha-particles are quite massive relative to the other types of radiation and also to the electrons of atoms of the material through which they are passing. As a result they travel in straight lines through matter except for rare direct collisions with nuclei of atoms along their path.

A third feature of relevance here is the energy with which they are emitted. This energy in the case of alpha-particles is always distinct. For example 221Ra emits an alpha-particle with an energy of 6.71 MeV. Every alpha-particle emitted from this radionuclide has this energy. Another example is 230U which emits three alpha-particles with energies of 5.66, 5.82, 5.89 MeV.

Finally it is useful to note that alpha-particles are very damaging biologically and this is one reason why they are not used for in-vivo diagnostic studies. We will therefore not be considering them in any great detail in this wikibook.

Beta Particles
We can see from the table that beta-particles have a negative electric charge. Notice that positrons are not considered here since as we noted in chapter 2 these particles do not last for very long in matter before they are annihilated. Beta-minus particles last considerably longer and are therefore the focus of our attention here.

Because of their negative charge they are attracted by nuclei and repelled by electron clouds as they pass through matter. The result once again without going into great detail is ionization.

The path of beta-particles in matter is often described as being tortuous, since they tend to ricochet from atom to atom.

A final and important point to note is that the energy of beta-particles is never found to be distinct in contrast to the alpha-particles above. The energies of the beta-particles from a radioactive source forms a spectrum up to a maximum energy – see figure below. Notice from the figure that a range of energies is present and features such as the mean energy, Emean, or the maximum energy, Emax, are quoted.

The question we will consider here is: why should a spectrum of energies be seen? Surely if a beta-particle is produced inside a nucleus when a neutron is converted into a proton, a single distinct energy should result. The answer lies in the fact that two particles are actually produced in beta-decay. We did not cover this in our treatment in chapter 2 for fear of complicating things too much at that stage of this wikibook. But we will cover it here briefly for the sake of completeness.

The second particle produced in beta-decay is called a neutrino and was named by Enrico Fermi. It is quite a mysterious particle possessing virtually no mass and carrying no charge, though we are still researching its properties today. The difficulty with them is that they are very hard to detect and this has greatly limited our knowledge about them so far.

The beta-particle energy spectrum can be explained by considering that the energy produced when a neutron is converted to a proton is shared between the beta-particle and the anti-neutrino. Sometimes all the energy is given to the beta-particle and it receives the maximum energy, Emax. But more often the energy is shared between them so that for example the beta-particle has the mean energy, Emean and the neutrino has the remainder of the energy.

Finally it is useful to note that beta-particles are quite damaging biologically and this is one reason why they are not used for in-vivo diagnostic studies. We will therefore not consider them in any great detail in this wikibook.

Gamma Rays
Since we have been talking about energies above, let us first note that the energies of gamma-rays emitted from a radioactive source are always distinct. For example 99mTc emits gamma-rays which all have an energy of 140 keV and 51Cr emits gamma-rays which have an energy of 320 keV.

Gamma-rays have many modes of interaction with matter. Those which have little or no relevance to nuclear medicine imaging are:

 * Mössbauer Effect
 * Coherent Scattering
 * Pair Production

and will not be described here.

Those which are very important to nuclear medicine imaging, are the Photoelectric Effect and the Compton Effect. We will consider each of these in turn below. Note that the effects described here are also of relevance to the interaction of X-rays with matter since as we have noted before X-rays and gamma-rays are essentially the same entities. So the treatment below is also of relevance to radiography.

Photoelectric Effect

 * When a gamma-ray collides with an orbital electron of an atom of the material through which it is passing it can transfer all its energy to the electron and cease to exist – see figure below. On the basis of the Principle of Conservation of Energy we can deduce that the electron will leave the atom with a kinetic energy equal to the energy of the gamma-ray less that of the orbital binding energy.  This electron is called a photoelectron.

 * Note that an ion results when the photoelectron leaves the atom. Also note that the gamma-ray energy is totally absorbed in the process.

 * Two subsequent points should also be noted. Firstly the photoelectron can cause ionisations along its track in a similar manner to a beta-particle.  Secondly X-ray emission can occur when the vacancy left by the photoelectron is filled by an electron from an outer shell of the atom.  Remember that we came across this type of feature before when we dealt with Electron Capture in chapter 2.

Compton Effect

 * This type of effect is somewhat akin to a cue ball hitting a coloured ball on a pool table. Here a gamma-ray transfers only part of its energy to a valance electron which is essentially free – see figure below.  Notice that the electron leaves the atom and may act like a beta-particle and that the gamma-ray deflects off in a different direction to that with which it approached the atom.  This deflected or scattered gamma-ray can undergo further Compton Effects within the material.

 * Note that this effect is sometimes called Compton Scattering.

The two effects we have just described give rise to both absorption and scattering of the radiation beam. The overall effect is referred to as attenuation of gamma-rays. We will investigate this feature from an analytical perspective in the following chapter. Before we do so, we'll briefly consider the interaction of radiation with living matter.

Radiation Biology
It is well known that exposure to ionizing radiation can result in damage to living tissue. We've already described the initial atomic interactions. What's important in radiation biology is that these interactions may trigger complex chains of biomolecular events and consequent biological damage.

We've seen above that the primary means by which ionizing radiations lose their energy in matter is by ejection of orbital electrons. The loss of orbital electrons from the atom leaves it positively charged. Other interaction processes lead to excitation of the atom rather than ionization. Here, an outer valence electron receives sufficient energy to overcome the binding energy of its shell and moves further away from the nucleus to an orbit that is not normally occupied. This type of effect alters the chemical force that binds atoms into molecules and a regrouping of the affected atoms into different molecular structures can result. That is, excitation is an indirect method of inducing chemical change through the modification of individual atomic bonds.

Ionizations and excitations can give rise to unstable chemical species called free radicals. These are atoms and molecules in which there are unpaired electrons. They are chemically very reactive and seek stability by bonding with other atoms and molecules. Changes to nearby molecules can arise because of their production.

But, let's go back to the interactions themselves for the moment.....

In the case of X- and gamma-ray interactions, the energy of the photons is usually transferred by collisions with orbital electrons, e.g. via photoelectric and Compton effects. These radiations are capable of penetrating deeply into tissue since their interactions depend on chance collisions with electrons. Indeed, nuclear medicine imaging is only possible when the energy of the gamma-rays is sufficient for complete emission from the body, but low enough to be detected.

The interaction of charged particles (e.g. alpha and beta particles), on the other hand, can be by collisions with atomic electrons and also via attractive and repulsive electrostatic forces. The rate at which energy is lost along the track of a charged particle depends therefore on the square of the charge on that particle. That is, the greater the particle charge, the greater the probability of it generating ion pairs along its track. In addition, a longer period of time is available for electrostatic forces to act when a charged particle is moving slowly and the ionization probability is therefore increased as a result.

The situation is illustrated in the following figure where tracks of charged particles in water are depicted. Notice that the track of the relatively massive α-particle is a straight line, as we've discussed earlier in this chapter, with a large number of interactions (indicated by the asterisks) per unit length. Notice also that the tracks for electrons are tortuous, as we've also discussed earlier, and that the number of interactions per unit length is considerably less.

The Linear Energy Transfer (LET) is defined as the energy released per unit length of the track of an ionizing particle. A slowly moving, highly charged particle therefore has a substantially higher LET than a fast, singly charged particle. An alpha particle of 5 MeV energy and an electron of 1 MeV energy have LETs, for instance, of 95 and 0.25 keV/μm, respectively. The ionization density and hence the energy deposition pattern associated with the heavier charged particle is very much greater than that arising from electrons, as illustrated in the figure above.

The energy transferred along the track of a charged particle will vary because the velocity of the particle is likely to be continuously decreasing. Each interaction removes a small amount of energy from the particle so that the LET gradually increases along a particle track with a dramatic increase (called the Bragg Peak) occurring just before the particle comes to rest.

The International Commission on Radiation Units and Measurements (ICRU) suggest that lineal energy is a better indicator of relative biological effectiveness (RBE). Although lineal energy has the same units as LET (e.g. keV/μm), it is defined as the:

ratio of the energy deposited in a volume of tissue to the average diameter of that volume.

Since the microscopic deposition of energy may be quite anisotropic, lineal energy should be a more appropriate measure of potential damage than that of LET. The ICRU and the ICRP have accordingly recommended that the radiation effectiveness of a particular radiation type should be based on lineal energy in a 1 μm diameter sphere of tissue. The lineal energy can be calculated for any given radiation type and energy and a Radiation Weighting Factor, (wR) can then be determined based on the integrated values of lineal energy along the radiation track.

All living things on this planet have been exposed to ionizing radiation since the dawn of time. The current situation for humans is summarized in the following table:

The sum total of this Natural Background Radiation is about 2.5 mSv per year, with large variations depending on altitude and dietary intake as well as geological and geographical location.

Its generally considered that repair mechanisms exist in living matter and that these can be invoked following radiation damage at the biomolecular level. These mechanisms are likely to have an evolutionary basis arising as a response to radiation fluxes generated by natural background sources over the aeons. Its also known that quite considerable damage to tissues can arise at quite higher radiation fluxes, even at medical exposures. Cell death and transformations to malignant states can result leading to latent periods of many years before clinical signs of cancer or leukemia, for instance, become manifest. Further treatment of this vast field of radiation biology however is beyond our scope here.

Practical Radiation Safety
Radiation hazards arise since nuclear medicine involves the handling of radioactive materials. Although this risk may be small, it remains important to keep occupational exposures as low as reasonably achievable. Essential practices for achieving this aim include:

Administration
 * Maintaining a comprehensive record of all radioactive source purchases, usage, movement and storage.
 * Ensuring that any Codes of Safe Practice are adhered to and develop sensible written protocols and working rules for handling radioisotopes.
 * Protocols for dealing with minor contamination incidents of the environment or of staff members must be established. Remember that no matter how good work practices are, minor accidents or incidents involving spillage of radioisotopes can take place.

Facility
 * Storage of radioactive sources in a secure shielded environment. Specially dedicated facilities are required for the storage, safe handling, manipulation and dispensing of unsealed radioactive sources. Storage areas should be designed for both bulk radioisotope and radioactive waste. Furthermore, radioactive patients should be regarded as unsealed sources.
 * Adequate ventilation of any work area. This is particularly important to minimize the inhalation of Technigas and potentially volatile radioisotopes such as I-125 and I-131. It is preferable to use fume hoods when working with volatile materials.
 * Benches should be manufactured with smooth, hard impervious surfaces with appropriate splash-backs to allow ready decontamination following any spillage of radioisotopes. Laboratory work should be performed in stainless steel trays lined with absorbent paper.
 * Excretion of radioactive materials by patients may be via faeces, urine, saliva, blood, exhaled breath or the skin. Provision to deal with any or all of these potential pathways for contamination must be made.
 * Provision for collection and possible storage of both liquid and solid radioactive waste may be necessary in some circumstances. Most short-lived, water soluble liquid waste can be flushed into the sewers but longer lived isotopes such as I-131 may have to be stored for decay. Such waste must be adequately contained and labelled during storage.

Equipment
 * Ensure that appropriate survey monitors are available to determine if any contamination has occurred and to assist in decontamination procedures. Routine monitoring of potentially contaminated areas must be performed.
 * Ensure that all potentially exposed staff are issued with individual personnel monitors.
 * Protective clothing such as gowns, smocks, overboots and gloves should be provided and worn to prevent contamination of the personnel handling the radioactivity. In particular, gloves must be worn when administering radioactive materials orally or intravenously to patients. It should be noted that penetration of gloves may occur when handling some iodine compounds so that wearing a second pair of gloves is recommended. In any event, gloves should be changed frequently and discarded ones treated as radioactive waste.

Behaviours
 * Eating and drinking of food, smoking, and the application of cosmetics is prohibited in laboratories in which unsealed sources are utilized.
 * Mouth pipetting of any radioactive substance is totally prohibited.
 * Precautions should be taken to avoid punctures, cuts, abrasions and any other open skin wounds which otherwise might allow egress of radiopharmaceuticals into the blood stream.

Optimization
 * Always ensure that there is a net benefit resulting from the patient procedure. Can the diagnosis or treatment be made by recourse to an alternative means using non ionizing radiation?
 * Ensure that all staff, including physicians, technologists, nurses and interns and other students, who are involved in the practice of nuclear medicine receive the relevant level of training and education appropriate to their assigned tasks. The training program could be in the form of seminars, refresher courses and informal tutorials.
 * A substantive Quality Assurance (QA) program should be implemented to ensure that the function of the Dose Calibrator, Gamma Camera, computer and other ancillary equipment is optimized.

The potential hazards to staff in a nuclear medicine environment include:

 * Milking the 99mTc generator, drawing up and measuring the quantity of radioisotope prior to administration.
 * Delivering the activity to the patient by injection or other means and positioning the now radioactive patient in the imaging device.
 * Removing the patients from the imaging device and returning them to the ward where they may continue to represent a radiation hazard for some time. For Tc-99m, a short-lived radionuclide the hazard period will be only a few hours but for therapeutic isotopes the hazardous period may be several days.
 * Disposal of radioactive waste including body fluids, such as blood and urine, but also swabs, syringes, needles, paper towels etc.
 * Cleaning up the imaging area after the procedure.
 * Contamination.

The table below lists the dose rates from patients having nuclear medicine examinations. In general, the hazards from handling or dealing with radioactive patients arise in two parts:

 * External hazard: This will be the case when the radioisotope emits penetrating gamma-rays. Usually, this hazard can be minimised by employing shielding and sensible work practices.
 * Radioactive contamination: This is potentially of more concern as it may lead to the inhalation or ingestion of radioactive material by staff. Possible sources of contamination are radioactive blood, urine and saliva, emanating from a patient, or airborne radioactive vapour. Sensible work practices, which involve high levels of personal hygiene, should ensure that contamination is not a major issue.

One of the most common nuclear medicine diagnostic procedures is the bone scan using the isotope Tc-99m. The exposure rate at 1 metre from a typical patient will peak at approximately 3 μSv per hour immediately after injection dropping steadily because of radioactivity decay and through excretion so that after 2 hours it will be about 1.5 μSv per hour. Neglecting any further excretion, the total exposure received by an individual, should that person stand one meter from the patient for the whole of the first 24 hours, would be ~17 μSv. For a person at 3 meters from the patient this number would reduce to 1.7 μSv and for a distance of 5 metres it would be ~0.7 μSv. These values have been estimated on the basis of the inverse square law.

Patients should be encouraged to drink substantial quantities of liquid following their scan, as this will improve excretion and aid in minimizing not only their radiation dose but also that of nursing staff.


text:
User:Afkafka~enwikibooks

entry text onto my fourth newly created user page... others are wikisource, wikiquote, wikipedia; planning to finally get some work done on the guide for people on the autistic spectrum, and came across an "aspie book" that needs exactly the kind of harsh third person treatment I feel like giving it, lol. leave me a line... Afkafka 16:43, 5 June 2006 (UTC)

title: User:Afkafka~enwikibooks


text:
User:Typetive

 * Optimal_Classification

 * Half-Life_Computation

 * Analog_hole

 * Harvard Chart Method

 * Rapid sort

 * Simulation of Logical human thought

Tenets
I, like most everyone, have several tenets which guide my actions.

Logic and God
One tenet is that if logic were accepted as superior to God and put into place as the basis for any system then the system would eventually have to be turned over to the control of a computer since computers are known to be potentially superior to humans in the number of variables they can handle; depriving humans the right of autonomy and taking that right for themselves. The problem with doing that is a computer is limited in the number of variables it can handle compared not to humans but to God. A computer can not handle nearly quite so many. Therefore God remains the superior choice upon which to base any system.

Food and Exercise
The stomach and the heart(pump) are organs of the body under constant warfare with each other. In the end if the stomach wins you do not.

Smoking and the EARTH
In additions to stopping humans from smoking there is a need to stop the EARTH from smoking.

HIGH tech startup facilities necessary to produce commercial grades and volume of biochar, bio-oil and syngas from municipal and agricultural organic waste requires a minimum investment of at least $100,000 per unit. LOW tech production can be started for much less.

Finding individuals and funding in each city or town to help get a high tech system started in the local community will stop the EARTH from smoking.

Living within your means
Borrow less than you invest, invest less than you save, when possible, save more than you spend and always spend less than you earn.

title: User:Typetive


text:
User:CatherineMunro

Hi!

See my main user page at the English Wikipedia.

title: User:CatherineMunro


text:
Talk:French/Lessons/To be

The French File does not exist! 404 error!
http://upload.wikimedia.org/wikibooks/en/3/33/French_Verb_-_?tre.ogg

 * See Image:French Verb - être.ogg. --hagindaz 22:46, 5 June 2006 (UTC)

title: Talk:French/Lessons/To be


text:
User talk:AndyD

Tutorial Authors Wanted on Official Blender MediaWiki!
The main Blender documentation and tutorial authors are now working on the Official Blender MediaWiki. If you're considering helping write Blender tutorials or documentation, please consider helping us at the official wiki instead.--Popski 18:02, 18 July 2006 (UTC)

Blender screenshots
First of all, screenshots copyrights aren't in fact very difficult to understand. If you have a program released under GPL license, you simply give its screenshots GPL license (and this also applies to Blender, which is GPL-licensed software). However, if you create work using Blender, the work itself is your own property and you can give it whatever license you want. If there are any screenshots of Blender using other copyright tags than GPL, please correct them if you can.

By the way, you wrote that our articles about image copyrights confused you. Can you say which help articles from Wikibooks have you read? Regards, --Derbeth talk 18:49, 5 June 2006 (UTC)

title: User talk:AndyD


text: User talk:202.177.171.133

title: User talk:202.177.171.133


text:
Ada Programming/Platform/VM/Java

Ada and the JVM
The Ada→J-Code compilers translate Ada programs directly to Java bytecode for the Virtual Machine. Both Ada programmers and Java programmers can use each other's classes almost seamlessly, including inheritance. Ada adds desirable language features like a strong base type system and full generics, Java VMs add garbage collection and a rich set of libraries.

"“Almost every Ada 95 feature has a very direct mapping using J-code, and almost every capability of J-code is readily represented in some Ada 95 construct.”"

- Taft, 1996

There are (at least) two compilers that support this: AppletMagic and JGNAT. The following example assumes AppletMagic. Changes required to make them work with JGNAT should be minimal. Some are explained in due course.

Ada programs for JVMs (see for example Programming:J2ME) appear to be surprisingly smooth. Unlike creating, and sometimes using, a binding to some library, using Ada→J-code compilers will make binding issues disappear.

Naming Conventions
AppletMagic and JGNAT use naming conventions for deciding how to distribute compiled code across Java class files. When a (tagged) type together with its surrounding package should be mapped to one Java class file, AppletMagic requires the type name to have a known suffix, and otherwise to be the same as the package name:

Foo Foo_Obj  ...    ... Foo

Similarly, JGNAT has some conventions that effectively turn type names into key words. These names tend to be short, and general, here is Typ:

Foo Typ  ...    ... Foo

Java Uses References, So Does Ada, Then
The mapping of Java's primitive types to corresponding Ada types is straightforward. (The semantics of integer types differ between the languages when the values approach a subtype's limits. JVM integers can jump from positive to negative when adding in excess of the maximum integer, Ada programs should not permit this. The compiler docs will explain to what extent Ada semantics will be preserved on the JVM.)

For reference types—everything is allocated in the heap—there is another convention.

Foo Foo_Obj Foo_Ptr   Foo_Obj Opx Foo_Obj Foo

(JGNAT sources use Ref instead of Foo_Ptr.) The classwide pointers can be used just like Java references. Notice that primitive operations can have parameters. This is a natural choice when interfacing to Java.

When Ada programmers wish to use Java objects in their programs, they will see the Java classes as normal packages, and the objects following the conventions outlined above. The compilers offer tools for creating Ada packages from Java .class files. Given the Java class Foo, the Ada package will be as show below. java.lang java.lang Foo Foo_Obj  Object Foo_Ptr   Foo_Obj new_Foothis Foo_Ptr    Foo_Ptr opthis  Foo_Obj Java op       Java_Constructor new_Foo Foo

 * new_Foo : This is a constructor function corresponding to the default constructor of the Java type. (Usually you won't be concerned with default constructors.) There is a special convention identifier for constructors, Java_Constructor.
 * : As both the constructor and the op method are defined in the Java class, they will be imported just like when importing C, or Fortran functions, using convention identifiers Java_Constructor, and Java, respectively.

Constructors
To be continued.

title: Ada Programming/Platform/VM/Java


text:
User:Purpill

nice to hear from you. Anyweays give me a link and i'll see how it can fit in. I believe in fun applications of physics and how it relates to the rest of us. The thing which needs to be emphasized is about "creativity" and how it relates to solving problems in science. Generally you could do lesson like "okay, class. We learned about Force today. Now, this weekends homework is draw me a picture of how forces are involved in real life" etc. etc.

Anyways my mail is Compatta@yahoo.com and i also like this other site called:

www.makezine.com

Emphasizes how "creativity" can be used to solve common engineering problems (i call it the hobbyists physics of how to make stuff without knowing too much physics)

www.instructables.com

great site to make stuff.

I hope to collaborate with you in the future.

title: User:Purpill


text:
User:Muttley.meen~enwikibooks

Interested in Data structures and alghorithms.

title: User:Muttley.meen~enwikibooks


text:
Talk:High School Physics/Projectile motion

Please only put things highschoolers would likely understand.
 * Why don't you think highschoolers will understand this? Is the issue derivatives and calculus?  Trig identities and quadratic formulas should be fine. (If you want to contact me directly, see my Wikipedia account w:User:Samw) Samw 00:20, 8 June 2006 (UTC)

To the author of this article: I am not familiar with Wiki Books in general, but I also believe that this would be a difficult resource for high school students to use. I am looking for texts right now that would be suitable for high school physics students, and I am most likely not going to use this one. Honestly there was something I was confused about by the second sentence. The first problem I have with this is that the author makes reference to more complicated situations before the simple ones have been thoroughly conveyed. For example, clarifying that you are referring to flat ground isn't preferable when first introducing the physics of flat ground projectile motion. Only when readers are comfortable with flat ground situations will they want/need a distinction between flat and non-flat situations to be made. Another example is how in the derivation section polar coordinates are used. Students trying to understand projectile motion for the first time will often not be familiar with polar coordinates or at least will not be comfortable enough to utilize them while learning a new topic. Also, all of the derivations are highly mathematical with little physical interpretation. The way this system is mathematically modeled is confusing to a reader who doesn't already understand projectile motion. Someone who is good at math can read this article, be able to reproduce all of its results mathematically, yet still fail to understand how this relates to the real world uniform gravitational field that that we essentially live in. The title "High School Physics / Projectile Motion" implies that this article is written to be a resource for high school students learning projectile motion. If the goal of this article is to help students understand projectile motion, then it is not accomplishing that. May I ask what your credentials are as an educator of physics? (I ask this not in an attempt to discredit the article or your work, but because I find many well educated people have misconceptions about how students learn and thus need to have this pointed out to them). This article, as it is written, is probably fine if it's targeted at readers who already understand projectile motion physically (to some extent), and simply want to expand or reinforce on the mathematical background. I'll discuss this with you at a later date if you wish. --129.2.239.111 05:21, 10 December 2006 (UTC)
 * I don't claim any expertise in education. I think this is useful material.  However, if there is a better location for this in Wikibooks (e.g. an undergrad textbook), go ahead and move it there. (Maybe my age is showing, but when I went to high school, we did polar coordinates and calculus.)  By all means feel free to add physical descriptions or otherwise improve the article.  Samw 01:25, 13 December 2006 (UTC)