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Organic Chemistry/Foundational concepts of organic chemistry/Atomic structure

< History | Electronegativity >

Atomic Structure
Atoms are made up of a nucleus and electrons that orbit the nucleus. The nucleus consists of protons and neutrons. An atom in its natural, uncharged state has the same number of electrons as protons.

The nucleus
The nucleus is made up of protons, which are positively charged, and neutrons, which have no charge. Neutrons and protons have about the same mass, and together account for most of the mass of the atom.

Electrons
The electrons are negatively charged particles. The mass of an electron is about 2000 times smaller than that of a proton or neutron at 0.00055 amu. Electrons circle so fast that it cannot be determined where electrons are at any point in time. The image depicts the old Bohr model of the atom, in which the electrons inhabit discrete "orbitals" around the nucleus much like planets orbit the sun. This model is outdated. Current models of the atomic structure hold that electrons occupy fuzzy clouds around the nucleus of specific shapes, some spherical, some dumbbell shaped, some with even more complex shapes.

Electron shells
Electrons orbit atoms in clouds of distinct shapes and sizes. The electron clouds are layered one inside the other into units called shells, with the electrons occupying the simplest orbitals in the innermost shell having the lowest energy state and the electrons in the most complex orbitals in the outermost shell having the highest energy state. The higher the energy state, the more energy the electron has, just like a rock at the top of a hill has more potential energy than a rock at the bottom of a valley. The main reason why electrons exist in higher energy orbitals is because only two electrons can exist in any orbital. So electrons fill up orbitals, always taking the lowest energy orbitals available. An electron can also be pushed to a higher energy orbital, for example by a photon. Typically this is not a stable state and after a while the electron descends to lower energy states by emitting a photon spontaneously. These concepts will be important in understanding later concepts like optical activity of chiral compounds as well as many interesting phenomena outside the realm of organic chemistry (for example, how lasers work).

Electron orbitals
Each different shell is subdivided into one or more orbitals, which also have different energy levels, although the energy difference between orbitals is less than the energy difference between shells.

Longer wavelengths have less energy; the s orbital has the longest wavelength allowed for an electron orbiting a nucleus and this orbital is observed to have the lowest energy.

Each orbital has a characteristic shape which shows where electrons most often exist. The orbitals are named using letters of the alphabet. In order of increasing energy the orbitals are: s, p, d, and f orbitals.

As one progresses up through the shells (represented by the principal quantum number n) more types of orbitals become possible. The shells are designated by numbers. So the 2s orbital refers to the s orbital in the second shell.

S orbital
The s orbital is the orbital lowest in energy and is spherical in shape. Electrons in this orbital are in their fundamental frequency. This orbital can hold a maximum of two electrons.

P orbital
The next lowest-energy orbital is the p orbital. Its shape is often described as like that of a dumbbell. There are three p-orbitals each oriented along one of the 3-dimensional coordinates x, y or z. Each of these three "p" orbitals can hold a maximum of two electrons.

These three different p orbitals can be referred to as the px, py, and pz.

The s and p orbitals are important for understanding most of organic chemistry as these are the orbitals that are occupied in the type of atoms that are most common in organic compounds.

D and F orbitals
There are also D and F orbitals. D orbitals are present in transition metals. Sulphur and phosphorus have empty D orbitals. Compounds involving atoms with D orbitals do come into play, but are rarely part of an organic molecule. F are present in the elements of the lanthanide and actinide series. Lanthanides and actinides are mostly irrelevant to organic chemistry.

Filling electron shells
 On WP: Electron configuration

When an atom or ion receives electrons into its orbitals, the orbitals and shells fill up in a particular manner.

There are three principles that govern this process:
 * 1) the Pauli exclusion principle,
 * 2) the Aufbau (build-up) principle, and
 * 3) Hund's rule.

Pauli exclusion principle
 On WP: Pauli exclusion principle

No two electrons in an atom can have all four quantum numbers the same. What this translates to in terms of our pictures of orbitals is that each orbital can only hold two electrons, one "spin up" and one "spin down".

Hund's rule
This states that filled and half-filled shells tend to have additional stability. In some instances, then, for example, the 4s orbitals will be filled before the 3d orbitals.

 On WP: Hund's rule

This rule is applicable only for those elements that have d electrons, and so is less important in organic chemistry (though it is important in organometallic chemistry).

Octet rule
The octet rule states that atoms tend to prefer to have eight electrons in their valence shell, so will tend to combine in such a way that each atom can have eight electrons in its valence shell, similar to the electronic configuration of a noble gas. In simple terms, molecules are more stable when the outer shells of their constituent atoms are empty, full, or have eight electrons in the outer shell.

The main exception to the rule is helium, which is at lowest energy when it has two electrons in its valence shell.

Other notable exceptions are aluminum and boron, which can function well with six valence electrons; and some atoms beyond group three on the periodic table that can have over eight electrons, such as sulphur. Additionally, some noble gasses can form compounds when expanding their valence shell.

Hybridization
 On WP: Orbital hybridization

Hybridization refers to the combining of the orbitals of two or more covalently bonded atoms. Depending on how many free electrons a given atom has and how many bonds it is forming, the electrons in the s and the p orbitals will combine in certain manners to form the bonds.

It is easy to determine the hybridization of an atom given a Lewis structure. First, you count the number of pairs of free electrons and the number of sigma bonds (single bonds). Do not count double bonds, since they do not affect the hybridization of the atom. Once the total of these two is determined, the hybridization pattern is as follows:

Sigma Bonds + Electron Pairs    Hybridization 2                      sp               3                       sp2 4                      sp3

The pattern here is the same as that for the electron orbitals, which serves as a memory guide.

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Organic Chemistry/Foundational concepts of organic chemistry/Bonding

< Electronegativity | Electron dot structure >

Ionic Bonding

Ionic bonding is when positively and negatively charged ions stick to each other through electrostatic force. These bonds are  slightly weaker than covalent bonds and stronger than Van der Waals bonding or hydrogen bonding.

In ionic bonds the electronegativity of the negative ion is so much stronger than the electronegativity of the positive ion that the two ions do not share electrons. Rather, the more electronegative ion assumes full ownership of the electron(s).

Perhaps the most common example of an ionically bonded substance is NaCl, or table salt. In this, the sodium (Na) atom gives up an electron to the much more electronegative chlorine (Cl) atom, and the two atoms become ions, Na+ and Cl-.The electrostatic bonding force between the two oppositely charged ions extends outside the local area attracting other ions to form giant crystal structures. For this reason most ionically bonded materials are solid at room temperature.

Sodium chloride forms crystals with cubic symmetry. In these, the larger chloride ions are arranged in a cubic close-packing, while the smaller sodium ions fill the octahedral gaps between them. Each ion is surrounded by six of the other kind. This same basic structure is found in many other minerals, and is known as the halite structure.

Covalent Bonding
Covalent bonding is close to the heart of organic chemistry. This is where two atoms share electrons in a bond. The goal of each atom is to fill its octet as well as have a formal charge of zero. To do this, atomic nuclei share electrons in the space between them. This sharing also allows the atoms to reach a lower energy state, which stabilizes the molecule. Most reactions in chemistry are due to molecules achieving a lower energy state. Covalent bonds are most frequently seen between atoms with similar electronegativity. In molecules that only have one type of atom, e.g. H2 or O2, the electronegativity of the atoms is essentially identical, so they cannot form ionic bonds. They always form covalent bonds.

Carbon is especially good at covalent bonding because its electronegativity is intermediate relative to other atoms. That means it can give as well as take electrons as needs warrant.

Covalently bonded compounds have strong internal bonds but weak attractive forces between molecules. Because of these weak attractive forces, the melting and boiling points of these compounds are much lower than compounds with ionic bonds. Therefore, such compounds are much more likely to be liquids or gases at room temperature than ionically bonded compounds.

In molecules formed from two atoms of the same element, there is no difference in the electronegativity of the bonded atoms, so the electrons in the covalent bond are shared equally, resulting in a completely non-polar covalent bond. In covalent bonds where the bonded atoms are different elements, there is a difference in electronegativities between the two atoms. The atom that is more electronegative will attract the bonding electrons more toward itself than the less electronegative atom. The difference in charge on the two atoms because of the electrons causes the covalent bond to be polar. Greater differences in electronegativity result in more polar bonds. Depending on the difference in electronegativities, the polarity of a bond can range from non-polar covalent to ionic with varying degrees of polar covalent in between. An overall imbalance in charge from one side of a molecule to the other side is called a dipole moment. Such molecules are said to be polar. For a completely symmetrical covalently bonded molecule, the overall dipole moment of the molecule is zero. Molecules with larger dipole moments are more polar. The most common polar molecule is water.

Bond Polarity and Dipole Moment

The ideas of bond polarity and dipole moment play important roles in organic chemistry.

If you look at the image of methane on the right, the single most important aspect of it in terms of bond polarity is that it is a symmetric molecule. It has 4 hydrogens, all bonded at 109.5° from the other, and all with precisely the same bond angle. Each carbon-hydrogen bond is slightly polar (hydrogen has an electronegativity of 2.1, carbon 2.5), but because of this symmetry, the polarities cancel each other out and overall, methane is a non-polar molecule.

The distinction is between Bond Polarity and Molecular polarity. The total polarity of a molecule is measured as Dipole Moment. The actual calculation of dipole moment isn't really necessary so much as an understanding of what it means. Frequently, a guesstimate of dipole moment is pretty easy once you understand the concept and until you get into the more advanced organic chemistry, exact values are of little value.

Basically, the molecular polarity is, essentially, the summation of the vectors of all of the bond polarities in a molecule.

Van der Waals Bonding
Van der Waals bonding is the collective name for three types of interactions:

 * 1) Permanent Dipole interactions: these are the electrostatic attractive forces between two dipoles, these are responsible for fluromethane's (CH3F) high boiling point (about -15 deg C) compared to Nitrogen (about -180 deg C).
 * 2) Permanent dipole / induced dipole: these are the interactions between a permanent dipole and another molecule, causing the latter molecule's electron cloud to be distorted and thus have an induced dipole itself. These are much weaker than the permanent dipole / dipole interactions.  These forces occur in permanent dipole-molecules, and in mixtures of permanent dipole and dipole free molecules.
 * 3) Instantaneous dipole / induced dipole: At any specific moment the electron cloud is not necessarily symmetrical, this instantaneous dipole then induces a dipole in another molecule and they are attracted; this is the weakest of all molecular interactions.

A Dipole is caused by an atom or molecule fragment having a higher electronegativity (this is a measure of its effective nuclear charge, and thus the attraction of the nucleus by electrons) than one to which it is attached. This means that it pulls electrons closer to it, and has a higher share of the electrons in the bond. Dipoles can cancel out by symmetry, eg: Carbon dioxide (O=C=O) is linear so there is no dipole, but the charge distribution is asymmetric causing a quadrupole moment (this acts similarly to a dipole, but is much weaker).

Organometallic Compounds and Bonding
Organometallic chemistry combines aspects of inorganic chemistry and organic chemistry, because organometallic compounds are chemical compounds containing bonds between carbon and a metal or metalloid element. Organometallic bonds are different from other bonds in that they are not either truly covalent or truly ionic, but each type of metal has individual bond character. Cuprate (copper) compounds, for example, behave quite differently than Grignard reagents (magnesium), and so beginning organic chemists should concentrate on how to use the most basic compounds mechanistically, while leaving the explanation of exactly what occurs at the molecular level until later and more in-depth studies in the subject.

Basic organometallic interactions are discussed fully in a later chapter.

<< Foundational concepts | < Electronegativity | Bonding | Electron dot structures > | Alkanes >>


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Organic Chemistry/Foundational concepts of organic chemistry/Resonance

<< Electron dot structures | Acids and bases >>

Resonance
Resonance refers to structures that are not easily represented by a single electron dot structure but that are intermediates between two or more drawn structures.

Resonance is easily misunderstood in part because of the way certain chemistry textbooks attempt to explain the concept. In science, analogies can provide an aid to understanding, but analogies should not be taken too literally. It is sometimes best to use analogies to introduce a topic, but then explain the differences and inevitable complications as further details on a complicated subject. This is the case for resonance.

Just as entropic principles cannot be applied to individual molecules, it is impossible to say whether or not any given individual molecule with a resonance structure is literally in one configuration or another. The actual situation on the molecular scale is that each configuration of the molecule contributes a percentage to the possible configurations, resulting in a "blend" of the possible structures. Changes in molecular shape occur so rapidly, and on such a tiny scale, that the actual physical locations of individual electrons cannot be precisely known (due to Heisenberg's Uncertainty Principle). The result of all that complexity is simply this: molecules with resonance structures are treated as mixtures of their multiple forms, with a greater percentage of probability given to the most stable configurations.

The nuclei of the atoms are not moving when they are represented by resonance structure drawings. Rather, the electrons are portrayed as if they were moving instead. The true situation is that no one can say for certain exactly where any individual electron is at any specific moment, but rather electron location can be expressed as a probability only. What a dot structure is actually showing is where electrons almost certainly are located, therefore resonance structures indicate a split in those same probabilities. Chemists are absolutely certain where electrons are located when one carbon bonds four hydrogens (methane), but it is less certain where precisely any given electron is located when six carbons bond six hydrogens in a ring structrue (benzene). Resonance is an expression of this uncertainty, and is therefore the average of probable locations.

Resonance structures are stabilizing in molecules because they allow electrons to lengthen their wavelengths and thereby lower their energy. This is the reason that benzene (C6H6) has a lower heat of formation than organic chemists would predict, not accounting for resonance. Other aromatic molecules have a similar stability, which leads to an overall entropic preference for aromaticity (a subject that will be covered fully in a later chapter). Resonance stability plays a major role in organic chemistry due to resonant molecules' lower energy of formation, so students of organic chemistry should understand this effect and practice spotting molecules stabilized by resonant forms.

In the Lewis structures above, carbonate (CO32-) has a resonance structure. Using laboratory procedures to measure the bond length of each bond, we do not find that one bond is shorter than the two others (remember, double bonds are shorter than single bonds), but instead that all bonds are of the same length somewhere between the length of typical double and single bonds.

Resonance Structures

Resonance structures are diagrammatic tools used predominately in organic chemistry to symbolize resonant bonds between atoms in molecules. The electron density of these bonds is spread over the molecule, also known as the delocalization of electrons. Resonance contributors for the same molecule all have the same chemical formula and same sigma framework, but the pi electrons will be distributed differently among the atoms. Because Lewis dot diagrams often cannot represent the true electronic structure of a molecule, resonance structures are often employed to approximate the true electronic structure. Resonance structures of the same molecule are connected with a double-headed arrow. While organic chemists use resonance structures frequently, they are also used in inorganic structures, with nitrate as an example.

Key characteristics
The key elements of resonance are:
 * Resonance occurs because of the overlap of orbitals. Double bonds contain pi bonds, formed from the overlap of 2p orbitals. The electrons in these pi orbitals will be spread over more than two atoms, and hence are delocalized.
 * Both paired and unshared electrons may be delocalized, but all the electrons must be conjugated in a pi system.
 * If the orbitals do not overlap (such as in orthogonal orbitals) the structures are not true resonance structures and do not mix.
 * Molecules or species with resonance structures are generally considered to be more stable than those without them. The delocalization of the electrons lowers the orbital energies, imparting this stability.  The resonance in benzene gives rise to the property of aromaticity. The gain in stability is called the resonance energy.
 * All resonance structures for the same molecule must have the same sigma framework (sigma bonds form from the "head on" overlap of hybridized orbitals). Furthermore, they must be correct Lewis structures with the same number of electrons (and consequent charge) as well as the same number of unpaired electrons.  Resonance structures with arbitrary separation of charge are unimportant, as are those with fewer covalent bonds. These unimportant resonance structures only contribute minimally (or not at all) to the overall bonding description; however, they are important in some cases such as for a carbonyl group.
 * The hybrid structure is defined as the superposition of the resonance structures. A benzene ring is often shown with a circle inside a hexagon (in American texts) rather than alternating double bonds — the latter example misrepresents the electronic structure. Bonds with broken bond orders are often displayed as double bonds with one solid and one dashed line.

What resonance is not
Significantly, resonance structures do not represent different, isolatable structures or compounds. In the case of benzene, for example, there are two important resonance structures - which can be thought of as cyclohexa-1,3,5-trienes. There are other resonance forms possible, but because they are higher in energy than the triene structures (due to charge separation or other effects) they are less important and contribute less to the "real" electronic structure (average hybrid). However, this does not mean there are two different, interconvertable forms of benzene; rather, the true electronic structure of benzene is an average of the two structures. The six carbon-carbon bond lengths are identical when measured, which would be invalid for the cyclic triene. Resonance should also not be confused with a chemical equilibrium or tautomerism which are equilibria between compounds that have different sigma bonding patterns. Hyperconjugation is a special case of resonance.

History
The concept of resonance was introduced by Linus Pauling in 1928. He was inspired by the quantum mechanical treatment of the H2+ ion in which an electron is located between two hydrogen nuclei. The alternative term mesomerism popular in German and French publications with the same meaning was introduced by Christopher Ingold in 1938 but did not catch on in the English literature. The current concept of Mesomeric effect has taken on a related but different meaning. The double headed arrow was introduced by the German chemist Arndt (also responsible for the Arndt-Eistert synthesis) who preferred the German phrase zwischenstufe or intermediate phase.

Due to confusion with the physical meaning of the word resonance, as no elements do actually appear to be resonating, it is suggested to abandon the term resonance in favor of delocalization. Resonance energy would become delocalization energy and a resonance structure becomes contributing structure. The double headed arrows would get replaced by commas.

Examples

The ozone molecule is represented by two resonance structures in the top of scheme 2. In reality the two terminal oxygen atoms are equivalent and the hybrid structure is drawn on the right with a charge of -1/2 on both oxygen atoms and partial double bonds. The concept of benzene as a hybrid of two conventional structures (middle scheme 2) was a major breakthrough in chemistry made by Kekule, and the two forms of the ring which together represent the total resonance of the system are called Kekule structures. In the hybrid structure on the right the circle replaces three double bonds. The allyl cation (bottom scheme 2) has two resonance forms and in the hybrid structure the positive charge is delocalized over the terminal methylene groups.


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Organic Chemistry/Foundational concepts of organic chemistry/Acids and bases

<< Resonance | Nomenclature >>

Arrhenius Definition: Hydroxide and Hydronium Ions
The first and earliest definition of acids and bases was proposed in the 1800s by Swedish scientist Svante Arrhenius, who said that an acid was anything that dissolved in water to yield H+ ions (like stomach acid HCl, hydrochloric acid), and a base was anything that dissolved in water to give up OH- ions (like soda lye NaOH, sodium hydroxide). Acids and bases were already widely used in various occupations and activities of the time, so Arrhenius' definition merely attempted to explained well-known and long-observed phenomenon.

Although simple, at the time this definition of the two types of substances was significant. It allowed chemists to explain certain reactions as ion chemistry, and it also expanded the ability of scientists of the time to predict certain chemical reactions. The definition left a great deal wanting, however, in that many types of reactions that did not involve hydroxide or hydronium ions directly remained unexplained.

Many general chemistry classes (especially in the lower grades or introductory levels) still use this simple definition of acids and bases today, but modern organic chemists make further distinctions between acids and bases than the distinctions provided under Arrhenius's definition.

Brønsted-Lowry Acids and Bases: Proton donors and acceptors
A new definition for acids and bases, building upon the one already proposed by Arrhenius, was brought forth independently by Johannes Nicolaus Brønsted and Thomas Martin Lowry in 1923. The new definition did not depend on a substance's dissolution in water for definition, but instead suggested that a substance was acidic if it readily donated a proton (H+) to a reaction and a substance was basic if it accepted a proton in a reaction.

The major advantage of the updated definition was that it was not limited to aqueous solution. This definition of acids and bases allowed chemists to explain a great number of reactions that took place in protic or aprotic solvents that were not water, and it also allowed for gaseous and solid phase reactions (although those reactions are more rare).

For example, the hypothetical acid HA will disassociate into H+ and A-:

$HA \overrightarrow\longleftarrow H^+ + A^-$

The Brønsted-Lowry definition of acids and bases is one of two definitions still in common use by modern chemists.

Lewis Acids and Bases: Electron donors and acceptors
The second definition in widespread use deals not with a molecule's propensity for accepting or donating protons but rather with accepting or donating electrons, thereby demonstrating a slightly different emphasis and further broadening the explanatory and predictive powers of acid-base chemistry.

Probably the most important aspect of Lewis acids and bases is which types of atoms can donate electrons, and which types of atoms can receive them. Essentially atoms with lone pairs, i.e. unshared pairs of electrons in an outer shell, have the capability of using those lone pairs to attract electron-deficient atoms or ions. This is why ammonia can bond a fourth hydrogen ion to create the ammonium ion; its lone pair of electrons can attract and bond to a free H+ ion in solution and hold on to it. For the same reason, methane cannot become methanium ion under ordinary circumstances, because the carbon in methane does not have any unshared pairs of electrons orbiting its nucleus. Generally speaking, Lewis acid are in the nitrogen, oxygen or halogen groups of the periodic table.

Nucleophiles and Electrophiles
Whether or not an atom can donate or accept electrons it can be called a nucleophile or electrophile, respectively. Electrophiles (literally, "lovers of electrons") are attracted to electrons. Electrophiles therefore seek to pair with unshared electrons of other atoms. Nucleophiles, or "nucleus lovers", seek positively charged nuclei such as those available in acidic solutions as hydronium ions. It is important to note that electrophiles and nucleophiles are often ions, but sometimes they are not.

Understanding electrophiles and nucleophiles goes beyond simply ideas of acids and bases. They are, in a majority of cases, the major players in organic reactions. As we will, over and over again, find reactions that are the result of nucleophiles attacking electrophiles. Keep in mind that the idea of nucleophiles and electrophiles is very related to the ideas of acids and bases in the Lewis context.

But it is also important to understand that, while they are related, they are not exactly the same thing either. An ion or molecule can be a strong nucleophile and a weak base (e.g. N3-, RS-, I-, Br- and CN-). Another ion can be a poor nucleophile and a strong base ((CH3)3CO-, R2N-). And yet others are strong nucleophiles and strong bases (R3C-, RO-, HO-) and poor nucleophiles and poor bases (RCO2-, ROH, NH3).

This will all be discussed in greater detail as the topics of specific reactions and reaction mechanisms are covered. In the meantime, try to bear in mind that nucleophiles are basic and electrophiles are acidic.

pKa and Acidity
The acid dissociation constant of a substance is commonly called its pKa, and it is a measure of the negative log of the K value of an acid dissociation reaction. (The K value refers to the equilibrium calculations you learned how to perform in general chemistry—if you have forgotten your K's and Q's, now would be a good time to refresh your memory on the topic.)

 * $$pK_a = -\log(K_a)$$

The lower the pKa value is, the more acidic (and consequently, less basic) a substance is. There is also a pKb value for all relevant substances, but it is common in organic chemistry to use pKa exclusively, even when discussing bases. This is because extremely high pKa values correlate exactly to extremely low pKb values, so there is no need to use both kinds of measurements. Any pKa value higher than seven means that a substance is not acidic when placed in water, but it does not mean that substance cannot be an acid. Alcohols are a good example of this: they can donate a hydrogen ion in chemical reactions but they do not do so readily, which makes them acidic but only very weakly so. Many of the acids in organic chemistry are considerably weaker than acids used for inorganic chemistry, so discussion of acid-base chemistry in organic reactions may not necessarily relate well to your previous understanding of the topic.

<< Foundational concepts | << Resonance | Acids and bases | Nomenclature >> | Alkanes >>


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Organic Chemistry/Foundational concepts of organic chemistry/Electron dot structures

<< Bonding | Resonance >>

Electron Dot Structures
 On WP: Lewis structures Electron dot structures, also called Lewis structures, give a representation of the valence electrons surrounding an atom.

Each valence electron is represented by one dot, thus, a lone atom of hydrogen would be drawn as an H with one dot, whereas a lone atom of Helium would be drawn as an He with two dots, and so forth.

Representing two atoms joined by a covalent bond is done by drawing the atomic symbols near to each other, and drawing a single line to represent a shared pair of electrons. It is important to note: a single valence electron is represented by a dot, whereas a pair of electrons is represented by a line.

The covalent compound hydrogen fluoride, for example, would be represented by the symbol H joined to the symbol F by a single line, with three pairs (six more dots) surrounding the symbol F. The line represents the two electrons shared by both hydrogen and fluorine, whereas the six paired dots represent fluorine's remaining six valence electrons.

Dot structures are useful in illustrating simple covalent molecules, but the limitations of dot structures become obvious when diagramming even relatively simple organic molecules. The dot structures have no ability to represent the actual physical orientation of molecules, and they become overly cumbersome when more than three or four atoms are represented.

Lewis dot structures are useful for introducing the idea of covalence and bonding in small molecules, but other model types have much more capability to communicate chemistry concepts.

Drawing electron dot structures
Some examples of electron dot structures for a few commonly encountered molecules from inorganic chemistry.

A note about Gilbert N. Lewis
 On WP: Gilbert N. Lewisyo Lewis was born in Weymouth, Massachusetts as the son of a Dartmouth-graduated lawyer/broker. He attended the University of Nebraska at age 14, then three years later transferred to Harvard. After showing an initial interest in Economics, Gilbert Newton Lewis earned first a B.A. in Chemistry, and then a Ph.D. in Chemistry in 1899.

For a few years after obtaining his doctorate, Lewis worked and studied both in the United States and abroad (including Germany and the Philippines) and he was even a professor at M.I.T. from 1907 until 1911. He then went on to U.C. Berkeley in order to be Dean of the College of Chemistry in 1912.

In 1916 Dr. Lewis formulated the idea that a covalent bond consisted of a shared pair of electrons. His ideas on chemical bonding were expanded upon by Irving Langmuir and became the inspiration for the studies on the nature of the chemical bond by Linus Pauling.

In 1923, he formulated the electron-pair theory of acid-base reactions. In the so-called Lewis theory of acids and bases, a "Lewis acid" is an electron-pair acceptor and a "Lewis base" is an electron-pair donor.

In 1926, he coined the term "photon" for the smallest unit of radiant energy.

Lewis was also the first to produce a pure sample of deuterium oxide (heavy water) in 1933. By accelerating deuterons (deuterium nuclei) in Ernest O. Lawrence's cyclotron, he was able to study many of the properties of atomic nuclei.

During his career he published on many other subjects, and he died at age 70 of a heart attack while working in his laboratory in Berkeley. He had one daughter and two sons; both of his sons became chemistry professors themselves.

Formal Charge
 On WP: Formal charge

The formal charge of an atom is the charge that it would have if every bond were 100% covalent (non-polar). Formal charges are computed by using a set of rules and are useful for accounting for the electrons when writing a reaction mechanism, but they don't have any intrinsic physical meaning. They may also be used for qualitative comparisons between different resonance structures (see below) of the same molecule, and often have the same sign as the partial charge of the atom, but there are exceptions.

The formal charge of an atom is computed as the difference between the number of valence electrons that a neutral atom would have and the number of electrons that "belong" to it in the Lewis structure when one counts lone pair electrons as belonging fully to the atom, while electrons in covalent bonds are split equally between the atoms involved in the bond. The total of the formal charges on an ion should be equal to the charge on the ion, and the total of the formal charges on a neutral molecule should be equal to zero.

For example, in the hydronium ion, H3O+, the oxygen atom has 5 electrons for the purpose of computing the formal charge—2 from one lone pair, and 3 from the covalent bonds with the hydrogen atoms. The other 3 electrons in the covalent bonds are counted as belonging to the hydrogen atoms (one each). A neutral oxygen atom has 6 valence electrons (due to its position in group 16 of the periodic table); therefore the formal charge on the oxygen atom is 6 – 5 = +1. A neutral hydrogen atom has one electron. Since each of the hydrogen atoms in the hydronium atom has one electron from a covalent bond, the formal charge on the hydrogen atoms is zero. The sum of the formal charges is +1, which matches the total charge of the ion.

 * Formal Charge: number of valence electrons for an atom - (number of lone pair electrons + number electrons in bonds/2)
 * $$FC = N_{valence} - \left( N_{lone pairs} + \frac{N_{electrons}}{2} \right)$$

In chemistry, a formal charge (FC) on an atom in a molecule is defined as:

 * FC = number of valence electrons of the atom - ( number of lone pair electrons on this atom + total number of electrons participating in covalent bonds with this atom / 2).
 * $$FC = N_{valence} - \left( N_{lone pairs} + \frac{N_{participating electrons}}{2} \right)$$

When determining the correct Lewis structure (or predominant resonance structure) for a molecule, the structure is chosen such that the formal charge on each of the atoms is minimized.

Examples

 * carbon in methane : $$FC = 4 - \left( 0 + \frac{8}{2} \right) = 0$$
 * Nitrogen in $$NO_2^{-}$$ : $$FC = 5 - \left( 2 + \frac{6}{2} \right) = 0$$
 * double bonded oxygen in $$NO_2^{-}$$ : $$FC = 6 - \left( 4 + \frac{4}{2} \right) = 0$$
 * single bonded oxygen in $$NO_2^{-}$$ : $$FC = 6 - \left( 6 + \frac{2}{2} \right) = -1$$

<< Foundational concepts | << Bonding | Electron dot structures | Resonance >> | Alkanes >>


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Organic Chemistry/Introduction to reactions/Overview of addition, elimination, substitution and rearrangement reactions

<< Cycloalkanes | Next >>

The real heart of organic chemistry is the reactions. Everything that you study is geared to prepare you for organic syntheses and other chemical transformations performed in the lab. This chapter gives you the basic tools to begin looking at these reactions.

Some basic reaction types
One way to organize organic reactions places them into a few basic categories:

 * addition reactions
 * elimination reactions
 * substitution reactions
 * rearrangement reactions

Other categories include:
 * Oxidations
 * Reductions
 * Alkylations

Sometimes one reaction can fall into more than one category. These classifications are just a tool and are not rigid.

Addition reaction
Something is added to something else to produce a third thing.

 * A + B → C

Note: the letters A, B and C here represent any atomic, ionic or molecular species which can undergo this type of reaction.

Elimination reaction
Something comes off of a molecule, resulting in two products.

 * A → B + C

Substitution reactions
This involves the exchange of one group for another.

 * AB + CD → AC + BD

Common reaction types include
 * radical reactions and
 * nucleophilic substitutions
 * SN1, Unimolecular nucleophilic substitution
 * SN2, Bimolecular nucleophilic substitution

Rearrangement reactions
A molecule shifts or otherwise rearranges to form a different molecule.

 * A → B

This typically happens when one molecule changes into an isomer of itself.

<< Alkanes | << Cycloalkanes | Overview of reactions | Polar and radical reactions >> | Intro to functional groups >>


text:
Organic Chemistry/Introduction to reactions/Polar and radical reactions

<< Overview of reactions | Redox reactions >>

Homolytic vs heterolytic cleavage
Two bonded atoms can come apart from each other in one of two ways. Either
 * each atom gets away with half of the shared electrons, or
 * one of the atoms leaves with more of the shared electrons than the other.

In homolytic cleavage, each atom leaves with one-half of the shared electrons (one electron for a single bond, or two for double bonds).

A—B → A* + B*

A* and B* represent uncharged radicals. The "*" represents an unbonded, unpaired valence electron.

In heterolytic cleavage, one atom leaves with all of the previously shared electrons and the other atom gets none of them.

A—B → A− + B+

Homo (from the Greek for same) indicates that each atom leaves with the same number of electrons from the bond. Hetero (from the Greek for different) refers to the fact that one atom gets all of the bonding electrons, while the other gets none.

Polar reactions
Polar reactions occur when two bonded atoms come apart, one taking more of the shared electrons than the other. They involve heterolytic cleavage. The result is two charged species—one cation and one anion.

Radical reactions
Radical reactions don't deal with charged particles but with radicals. Radicals are uncharged atoms or molecules with an incomplete octet of valence electrons.

When a molecule comes apart by homolytic cleavage the result is two radicals. Although uncharged, radicals are usually very reactive because the unfilled octet is unstable and the radical can lower its energy by forming a bond in a way that allows it to fill its valence shell while avoiding any electrostatic charge..


text:
User:Cehjohnson

Problem
A rectangular pizza is placed on a tray. The sides of the tray extend by 4 units to the right and left and by 3 units (x) above and below. Calculate a value of x such that the area of the tray protruding is as small as possible.

Answer
The solution to this problem lies in differential calculus. Looking at the diagram below, we can see that the area of the tray extending from the pizza is given by

Substituting:

$${\mathrm y} = \frac{60}x$$

$$A = (\frac{60}x + 6)(x + 8) - 60$$

$$A = \frac{60x}x + 6x + \frac{480}{x} - 60$$

$$A = 6x + \frac{480}{x}$$

$$\frac{{\mathrm d}A}{{\mathrm d}x} = 6 - \frac{480}{x^2}$$

Since the area should be at a minimum:

$$0 = 6 - \frac{480}{x^2}$$

$$x = \sqrt80$$

title: User:Cehjohnson


text:
Organic Chemistry/Introduction to functional groups

 * 1) ../Overview of Functional Groups/
 * 2) ../Alcohols/
 * 3) ../Phenols/
 * 4) ../Ethers/
 * 5) ../Epoxides/
 * 6) ../Ketones and aldehydes/
 * 7) ../Carboxylic Acids/
 * 8) ../Carboxylic acid derivatives/

<< Introduction to reactions | Introduction to functional groups | Overview of Functional Groups >> | Alkenes >>


text:
Organic Chemistry/Foundational concepts of organic chemistry/History of organic chemistry/Vital force theory

<< Foundational concepts | Synthesis of urea >>

Long ago, people observed the differences between compounds that were derived from living things and those that were not. There seemed to be an impassable gap between the properties of the two groups. Someone proposed the vital force theory to explain the difference. The theory said that there was a something called a vital force that dwelled within the organic material that did not exist in the nonorganic materials. However, to echo the words of President Ronald Reagan, it was "only" a theory.

Synthesis of urea >>


text:
Organic Chemistry/Foundational concepts of organic chemistry/History of organic chemistry/Synthesis of urea

<< Vital force theory | Organic vs inorganic chemistry >>


text:
Organic Chemistry/Foundational concepts of organic chemistry/History of organic chemistry/Organic vs inorganic chemistry

<< Synthesis of urea | Atomic structure >>


text:
Organic Chemistry/Foundational concepts of organic chemistry/Atomic structure/Nucleus and electrons

<< Atomic structure | Shells and orbitals >>

Atoms are made up of a nucleus and electrons that orbit the nucleus. An atom in its natural, uncharged state has the same number of electrons as protons. If it gains or loses electrons, the atom is then referred to as an ion.

The nucleus
The nucleus is made up of protons, which each have a positive charge, and neutrons, which have no charge. Neutrons and protons have about the same mass, and together account for most of the mass of the atom. Each of these particles is made up of even smaller particles, though the existence of these particles do not come into play at the energies and time spans in which most chemical reactions occur.

Electrons
The electrons are negatively charged and fly around the nucleus of an atom at something like light speed. We cannot determine exactly where electrons are at any point in time, rather, we can only guess at the probability of finding an electron at a point in space relative to a nucleus at any point in time. The image depicts the Bohr model of the atom, in which the electrons inhabit discrete "orbitals" around the nucleus much like planets orbit the sun. Current models of the atomic structure hold that electrons occupy fuzzy clouds around the nucleus of specific shapes, some spherical, some dumbbell shaped, some with even more complex shapes. Even though the simpler Bohr model of atomic structure has been superseded, we still refer to these electron clouds as "orbitals". The number of electrons and the nature of the orbitals they occupy greatly influence the reactivity of atoms in organic chemistry.

<< Atomic structure | Nucleus and electrons | Shells and orbitals >>


text:
Organic Chemistry/Foundational concepts of organic chemistry/Atomic structure/Shells and orbitals

<< Nucleus and electrons | Filling electron shells >>

Electron orbitals
Electrons orbit atoms in clouds of distinct shapes and sizes. The electron clouds are layered one inside the other into units called shells (think nested Russian dolls), with the electrons occupying the smallest, innermost shell having the lowest energy state and the electrons in the largest, outermost shell having the highest energy state. The higher the energy state, the more potential energy the electron has, just like a rock at the top of a hill has more potential energy than a rock at the bottom of a valley. These concepts will be important in understanding later concepts like optical activity of chiral compounds as well as many interesting things outside the realm of organic chemistry (like how lasers work).

Wave nature of electrons
Electrons behave as particles but also as waves. (Work by Albert Einstein and others revealed that in fact, light and all matter behaves with this dual nature, and it is most clearly observed in the tiniest particles.) One of the results of this observation is that electrons are not just in simple orbit around the nucleus as we imagine the moon to circle the earth, but instead occupy space as if they were a wave on the surface of a sphere.

If you jump a jumprope you could imagine that the wave in the rope is in its fundamental frequency. The high and low points fall right in the middle, and the places where the rope doesn't move much (the nodes) occur only at the two ends. If you shake the rope fast enough in a rythmic way, using more energy than you would just jumping rope, you might be able to make the rope vibrate with a wavelength shorter than the fundamental. You them might see that the rope has more than one place along its length where it vibrates from its highest spot to its lowest spot. Furthermore, you'll see that there is one or more places (or nodes) along its length where the rope seems to move very little, if at all.

Or consider stringed musical instruments. The sound made by these instruments comes from the different ways, or modes the strings can vibrate. We can refer to these different patterns or modes of vibrations as linear harmonics. Going from there, we can recognize that a drum makes sound by vibrations that occur across the 2-dimensional surface of the drumhead. Extending this now into three dimensions, we think of the electron as vibrating across a 3-dimensional sphere, and the patterns or modes of vibration are referred to as spherical harmonics. The mathematical analysis of spherical harmonics were worked out by the French mathematician Legendre long before anyone started to think about the shapes of electron orbitals. The algebraic expressions he developed, known as Legendre polynomials, describe the three dimension shapes of electron orbitals in much the same way that the expression x2+y2 = z describes a circle (or, for that matter, a drumhead). Many organic chemists need never actually work with these equations, but it helps to understand where the pictures we use to think about the shapes of these orbitals come from.

Electron shells
Each different shell is subdivided into one or more orbitals, which also have different energy levels, although the energy difference between orbitals is less than the energy difference between shells.

Longer wavelengths have less energy; the s orbital has the longest wavelength allowed for an electron orbiting a nucleus and this orbital is observed to have the lowest energy.

Each sub-shell in the main electron shell has a characteristic shape, and are named by a letter. The sub-shells are: s, p, d, and f.

As one progresses up through the shells (represented by the principle quantum number n) more types of orbitals become possible.

S orbital
The s orbital is the orbital lowest in energy and is spherical in shape. Electrons in this orbital are in their fundamental frequency.

P orbital
The next lowest-energy orbital is the p orbital. Its shape is often described as like that of a dumbbell. There are three p-orbitals each oriented along one of the 3-dimensional coordinates x, y or z.

These three different p orbitals can be referred to as the px, py, and pz.

The s and p orbitals are important for understanding most of organic chemistry as these are the orbitals that are occupied by the type of atoms that are most common in organic compounds.

D orbital
[[Image

configuration 	species 	excited states Ca+2, Ti+4, Sc+3 	0 Ti+3 	1 V+3 	3 Cr+3 	3 Mn+3 	1 Mn+2, Fe+3 	0 Fe+2 	1 Co+2 	3 Ni+2 	3 Cu+2 	1 Zn+2 	0

 * Jahn-Teller distortion breaks the expected degeneracy. :]]

There are 5 types of d orbitals. Three of them are roughly X-shaped, as shown here, and might be viewed as being shaped like a crossed pair of dumbbells. They are referred to as dxy, dxz, and d yz. Like the p-orbitals, these three d orbitals have a node at the origin of the coordinate system where the three axes all come together. Unlike the p orbitals, however, these three d orbitals are not oriented along the x, y, or z axes, but instead are oriented in between them. The dxy orbital, for instance, lies in the xy plane, but the lobes of the orbital point out in between the x and y axes.

F orbital and beyond
There are 7 kinds of F orbitals, but we will not discuss their shapes here. F orbitals are filled in the elements of the lanthanide and actinide series, although electrons in these orbitals rarely come into play in organometallic reactions involving these elements.


text:
Organic Chemistry/Foundational concepts of organic chemistry/Atomic structure/Filling electron shells

<< Shells and orbitals | Octet rule and exceptions >>

When an atom or ion receives electrons into its orbitals, the orbitals and shells fill up in a particular manner.

There are three principles that govern this process: 1) the Aufbau (build-up) principle, 2) the Pauli exclusion principle, and 3) Hund's rule.

Exclusion principle
No more than one electron can have all four quantum numbers the same. What this translates to in terms of our pictures of orbitals is that each orbital can only hold two electrons, one "spin up" and one "spin down".

Build-up principle
You may consider an atom as being "built up" from a naked nucleus by gradually adding to it one electron after another, until all the electrons it will hold have been added. Much as one fills up a container with liquid from the bottom up, so also are the orbitals of an atom filled from the lowest energy orbitals to the highest energy orbitals.

However, the three p orbitals of a given shell all occur at the same energy level. So, how are they filled up? Is one of them filled full with the two electrons it can hold first? Or do each of the three orbitals receive one electron apiece before the any single orbital is double occupied. As it turns out, the latter situation occurs.

Hund's rule
This rule is applicable only for those elements that have d electrons, and so is less important in organic chemistry (though it is important in organometallic chemistry). It says that filled and half-filled shells tend to have additional stability. In some instances, then, for example, the 4s orbitals will be filled before the 3d orbitals.

Building atoms with quantum mechanics (advanced topic)
The equations (like the Legendre polynomials that describe spherical harmonics, and thus the shapes of orbitals) of quantum mechanics are distinguished by four types of numbers. The first of these quantum numbers is referred to as the principal quantum number, and is indicated by n. This merely represents which shell electrons occupy, and shows up in the periodic chart as the rows of the periodic chart. It has integral values, n=1,2,3. . . .  The highest energy electrons of the atoms in the first row all have n=1. Those in the atoms in the second row all have n=2. As one gets into n=3, Hund's rule mixes it up a little bit, but when one gets to the end of the third row, at least, the electrons with the highest energy have n=3.

The next quantum number is indicated by the letter m and indicates how many different types of shells an atom can have. Those elements in the first row can have just one, the s orbital. The elements in the second row can have two, the s and the p orbitals. The elements in the third row can have three, the s, p, and d orbitals. And so on. It may be funny to think of s, p and d as "numbers", but these are used as an historical and geometrical convenience.

The third kind of quantum number ml specifies, for those kinds of orbitals that can have different shapes, which of the possible shapes one is referring to. So, for example, a 2pz orbital indicates three quantum numbers, represented respectively by the 2, the p and the z.

Finally, the fourth quantum number is the spin of the electron. It has only two possible values, +1/2 or -1/2.

Pretty much only computational chemists have to treat quantum numbers as numbers per se is equations. But it helps to know that the wide variety of elements of the periodic table and the different shapes and other properties of electron orbitals have a unifying principle--the proliferation of different shapes is not completely arbitrary, but is instead bounded by very specific rules.

Afbau Principle (it means 'building up'):- It states that the orbitals should be filled according to their increasing energies Thus the lowest energy orbital which is available is filled first. The increasing order of energies of the various orbitals is:- 1s,2s,2p,3s,3p,4s,3d,4p,5s,4d,5p,6s,4f,5d,6p,7s,5f...... The order of increasing of energy of orbitals can be calc. from(n+l) rule or 'Bohr bury rule' According to this rule, the value of n+l is the energy of the orbital and such on orbital will be filled up first. e.g. 4s orbital having lower value of(n+l) has lower energy than 3d orbital and hence 4s orbital is filled up first. For 4s orbital, n+l=4+0=4 For 3d orbital, n+l=3+2=5,therefore 4s orbital will be filled first.


text:
Cell Biology

Contents

 * Glossary and Guide
 * Glossary Alphabetically
 * Glossary By Lesson
 * How to edit this book

Beginning Cell Biology

 * Introduction
 * Introduction to Cell Biology
 * What is living?
 * What is a cell?
 * Size of cells
 * The Great Ancestor
 * Cells Under Microscopes
 * Chemical elements necessary for life

 * Types of cells
 * Prokaryotes
 * Bacteria
 * Archaea
 * Eukaryotes

 * Preliminary Glimpse at Organelles
 * Nucleus
 * Mitochondria
 * Chloroplasts
 * Membranes
 * Other Organelles
 * Unique Properties of Plant Cells

 * Preliminary Glimpse at Cytoskeleton
 * Actin filaments
 * Intermediate filaments
 * Microtubules

 * Models for Cell Biology Research
 * How do we know how cells function
 * Escherichia coli
 * Yeasts (Saccharomyces cerevisae)
 * Worms (Caenorhabditis elegans)
 * Flies (Drosophila melanogaster)
 * Mice
 * Cress (Arabidopsis thaliana)
 * Human

 * Cell division
 * Cell cycle
 * Meiosis
 * Mitosis
 * Cell Mass and Growth Rate
 * Genes
 * Expression
 * Translation

Resources

 * Cell biology article at wikipedia
 * Cell biology category at wikipedia
 * Cooper textbook The Cell (online)
 * Lodish textbook Molecular Cell Biology (online)
 * Alberts textbook Molecular Biology of the Cell (online)
 * CellsAlive animations
 * The History of Cell Biology
 * Inside the cell - National Institute of General Medical Sciences
 * UCMP glossary
 * Landmark Papers in Cell Biology Gall JG, McIntosh JR, eds. (online in The American Society for Cell Biology's Image & Video Library)
 * Biology Internet Library - has a cellular biology section.

Meta

 * Cell Biology/Authors

Клетъчна биология Biologie für Mediziner Biología celular Biologie cellulaire 細胞生物学

title: Cell Biology


text:
Modern Physics

Table of contents

 * Introduction
 * Note For Contributors
 * Page List

Books and chapters

 * /Annus Mirabilis of Albert Einstein/
 * Vibrations
 * Waves
 * General Mechanics
 * Special Relativity
 * General Relativity
 * /Gravity/
 * Quantum Mechanics
 * Electrodynamics
 * Quantum Optics
 * Thermodynamics
 * Statistical Mechanics
 * Solid State Physics
 * Condensed Matter Physics
 * Nuclear Physics
 * Particle Physics
 * Plasma Physics
 * /Space Physics/
 * Astrophysics

Appendices

 * /Constants/
 * Table of nuclides

Recommended Readings

 * Feynman, R. P., Leighton, R., Leighton, R. B., Sands, M. L. (2017). The Feynman Lectures on Physics: New Millenium Edition. Pearson India Education Services Pvt Limited.

Σύγχρονη Φυσική

title: Modern Physics


text:
Talk:Modern Physics

I agree that this is a stunning piece of work! However, having found his email (raymond@kestrel.nmt.edu), I am loath to contact him personally. Perhaps we could construct a letter of appreciation and an invitation over here from all of us. Forgive me if I take the liberty of starting the ball rolling - I think it should include:
 * thanks for his work
 * request that we continue to publish it (just for politness sake, I know it's GNU FDL)
 * an invitation to visit Wikibooks, Wikipedia, Wikiversity etc. --Mark Lewis 23:55, 12 Jan 2005 (UTC)

This is great! Let's make sure we give this guy proper credit per the GNU FDL and also make him aware of what we are doing. Maveric149

Hey Mav, there are more things like this one here with the GNU FDL license and everything .. I started one up for Cell Bio but there are many more to harvest. Karl Wick

I've done an initial conversion of this page:

Beats
Suppose two sound waves of different frequency impinge on your ear at the same time. The displacement perceived by your ear is the superposition of these two waves, with time dependence $$ A(t) = \sin ( \omega_1 t) + \sin ( \omega_2 t) = 2 \sin ( \omega_0 t) \cos ( \Delta \omega t), $$ (2.19)

where we now have $$\omega_0 = ( \omega_1 + \omega_2 )/2$$ and $$\Delta \omega = ( \omega_2 - \omega_1 )/2$$. What you actually hear is a tone with angular frequency $$\omega_0$$ which fades in and out with period $$T_{beat} = \pi / \Delta \omega = 2 \pi / ( \omega_2 - \omega_1 ) = 1 / ( f_2 - f_1 ). $$ (2.20)

The beat frequency is simply $$ f_{beat} = 1/T_{beat} = f_2 - f_1. $$ (2.21)

Note how beats are the time analog of wave packets -- the mathematics are the same except that frequency replaces wavenumber and time replaces space.

Is this generally acceptable? -- Jimregan 18:41 17 Jul 2003 (UTC)

Why don't you add other sections of your textbook here? I'm more interested in editing the more "fun" section than elementary wave theory/geometric optics.

 * Why don't you help out and add some other sections yourself. dave 22:50, 11 Sep 2003 (UTC)

Do you realize the presence of a partially ported textbook which no one seems to bother to completely transfer is actually hampering the creation of a textbook? If you'd never thought of porting over a textbook, by now, I'm pretty sure we'd have more material!

 * Why don't you help out and add some other sections yourself. dave 22:50, 11 Sep 2003 (UTC)

Two questions:

 * 1) If we make changes to this textbook and the original author makes changes, there is no easy way to "merge" them like in CVS for example.  How complete is his work?  If it is 99% complete physics textbook then that's fine.  I guess we could also entice him to work on this "fork" of his textbook once we port it over.

 * We could try, but anyway I don't think it matters if they diverge.Theresa knott

 * 1) Should all the graphics be changed to have a white background?  The grey looks horrid.  dave 22:59, 11 Sep 2003 (UTC)
 * I agree, or why not make it transparent, that way if we ever change the colour of the page w wonlt have go and change all the graphics. Theresa knott

- About TeX/HTML:

Over at www.wikipedia.org, on a few articles I've helped out with, I've been pushing for italic HTML in the text regions, and TeX for indented formulas, so like the following:

So, a great physicist proved that a = b + c except when e < d. Here is the proof of that:

 * $$a < b,$$

so,

 * $$e + d + c + a > b$$

Sorry I was stumped for a good example. Anyways, TeX in the text looks really bad, unless the PNG is made smaller by a future version of wikipedia. dave 23:22, 11 Sep 2003 (UTC)

Great book ! I'll give a hand to porting it here. BTW, has anyone reached the author ? R 19:07, 13 Jan 2004 (UTC)

Aim of text
Popped on over here from Wikipedia and couldn't help but check out the books in my field. My question though is what type of course this is supposed to be a text for.

 * None, specifically. Textbooks don't have to be tied to courses. This text is based on http://kestrel.nmt.edu/~raymond/classes/ph13xbook/index.html. It should give an introduction to the basic principles and methods of physics, with emphasis on the underlying unity. Carandol

It seems like way too much material for one semester, but each chapter is too little material, too.

 * That depends quite a bit on the university, and the country - one of the reasons why this text is not being tailored for a specific course. Carandol

Specifically, I'm looking at the Quantum Mechanics. It looks like it's going to be on a level of what is usually (at the schools I've been at) called Quantum Physics, which is a second year undergraduate course. But if it solves the Hydrogen atom (there's a Hydrogen Atom section at least),

 * The source text doesn't give a full solution. It uses the uncertainty principle to estimate the ground state. Carandol

then it looks like it's trying to be a text for a junior/senior-level Quantum Mechanics course, in which case it needs many more sections on Dirac notation, spin, angular momentum, the harmonic oscillator, path integrals, and maybe time-independent perturbation theory.

 * I'd put all that into a separate undergraduate comprehensive QM book, which should also include time-dependant perturbations, scattering and quantum thermodynamics, everything short of postgrad. Carandol 05:43, 3 Sep 2004 (UTC)

The latter is the stuff I think is interesting and would be into working on. So yeah, what is this textbook trying to be? -Laura Scudder

I got the same feeling as Laura above. If all the topics mentioned on Modern Physics covered with any reasonable depth, it should actually cover the full 4 year of physics major education (taking UC Berkeley as example, Intro (mere skimming surface, except for mechanics and E&M) to each of those topics would cover the first 3 semesters (7A - C), Quantum mechanics would cover 137A and B, E&M would cover 110A and B, Mechanics would cover 105. Nuclear physics and relativity (special and general) would cover a year (or two courses) of electives. The only thing it's missing is statistical mechanics and a lab course! I think Modern Physics needs to be clear (on the front page somewhere) regarding its aims, esp. whether it actually intends to cover all mentioned topics in depth (essentially forming what is comparable to Landau's course on theoretical physics), or whether it intends to simply give the student a quick taste of each without going into details.

I'm making this request because people seem to be suggesting often that other advanced textbooks be merged into this project, and if this project doesn't intend to cover all these topics in depth (and essentially forming a *complete* physics education for physics majors) ... well, it should be clearly out in the open. novakyu (talk) 11:57, 24 December 2007 (UTC)

Thanks to Flonejek
Flonejek, you are doing a great service in working on this book. It may not be overtly glamorous work at the onset but the result will be very helpful to many people. Thank you. --Karl Wick

Cool, thanks --flonejek 07:49, 22 Mar 2004 (UTC)

--- The various contents pages have some of the subsections in a different order to the source book.

If we're keeping this as a single coherent course (even if possibly in multiple volumes) many of them will need returning to the original order, to preserve logical dependance.

If we're going to convert the source book into a set of stand-alone books, most of the chapters will need considerably more expansion and some reordering.

I'll do it the first way, unless anyone objects. Carandol ---

I'm Back :)
Had some tough times at school, but now i'm back, and hope to be making at least one edit/addition a week --flonejek 04:38, 24 Sep 2004 (UTC)

 * Be nice to have people editing this book. You may notice I've made some changes to some of the chapters, and added some extra material, both to reflect the previous changes in chapter order from the base text and to enhance the presentation of pysics as a subject with a underlying unity, not just a random collection of formulas.

 * This does mean that half the chapter you just uploaded has already been incorporated into other chapters, and the the rest will need some revision, with 'Event horizons' being folded into it, that being rather a short chapter to stand alone and material that will work best closer to its diagram. :)

 * Since we're both working on this book, perhaps it'll be best if we both keep an eye on what the other is doing, to make sure the book retains its unity. Carandol 06:17, 24 Sep 2004 (UTC)

 * Ok, I agree with that, especially the re-orientation away from a formula based text, I had a bit of a struggle understanding most of them myself. For now I'm going to read over whats been written already, and then I'll start adding/editing stuff again, mostly on weekends. I like the changes you made as well, though I might redraw a few of those diagrams in inkscape, at the moment they look a bit straggly. --flonejek 00:11, 26 Sep 2004 (UTC)

 * Hey, I'd be quite keen to help out on some physics books here. I started by deriving the time-independent Shrôdinger equation and correcting a couple of mistakes in the Operators page. Is that cool or am I being a bit too formula-y? Spitvalve 22:27, 12 October 2005 (UTC)

Another source
Another source available is http://www.physicsforfree.com, which has three "copyright free" textbooks. --Laura Scudder | Talk 02:27, 15 July 2005 (UTC)

Navigation Template
I'm going to be doing alot of work and contributing to the electromagnetics section of this book, and I've created a handy template that (i think) we should employ throughout this book: ModernPhysicsNav. This template creates a backlink to the main page if no arguments are provided, and it will provide a link to a section page if an argument is provided. More information about this template, and the way to use it can be found On the template page itself, HERE. --Whiteknight (talk) (projects) 14:11, 30 June 2006 (UTC)

 * It would take the same amount of time to rename a page to create automatic backlinks as it would using this template, so I personally don't see it as being needed. What I find to be a lot more useful are links to the next chapter of a book, rather than back to the contents page. See Chess/Navigation for an example. The format would be  on the bottom of each page. --hagindaz 07:00, 1 July 2006 (UTC)

 * I see it's already been added. Nevermind then! No need to redo everything. :) --hagindaz 07:05, 1 July 2006 (UTC)

 * Sorry, I was a little hasty, perhaps. I got very frustrated very quickly by the lack of page navigation in this book. If you go to The Waves Chapter, you can see that people have already provided individual navigation templates for pages in an individual section. I propose that we extend that idea to cover each individual section in this book. --Whiteknight (talk) (projects) 13:36, 3 July 2006 (UTC)

 * As per your suggestion, Hagindaz, I'll edit the navigation template to optionally take 2 more parameters: A link to the previous page, and a link to the next page. In this way, we can add this kind of navigation on a per-page basis, if we want to, or let other navigation templates do the job, such as on the Waves section. --Whiteknight (talk) (projects) 14:23, 3 July 2006 (UTC)

 * I am in favour of each section of this book being written as a book in its own right. Published modern physics textbooks are usually 2 or more volumes with at least 1000 pages. Perhaps the template could be used in each subsidiary book ie: Quantum physics : Heisenberg uncertainty principle. rather than Modern physics: Quantum Physics: Heisenberg etc. Each template would have a link to the Modern Physics introductory page. RobinH 14:42, 17 July 2006 (UTC)

Stub Template
I created a specific template for use in marking stubs for this book: ModernPhysicsStub. This template automatically puts all stub pages of this book into /Stubs, which is a sub-category of :. We can use this template and these categories to quickly find all stub pages in this book that require attention. --Whiteknight (talk) (projects) 17:42, 30 June 2006 (UTC)

 * Combined, here is a list of available templates and category designations that are specifically designed for use with this book:

 * Template:ModernPhysicsTOC
 * Template:ModernPhysicsNav
 * Template:ModernPhysicsStub
 * :
 * /Stubs

 * All of these tools are explained on their respective module and talk pages. --Whiteknight (talk) (projects) 19:04, 30 June 2006 (UTC)

Contributors
These people were listed as "Contributors" on the front page, but none of them have been active on wikibooks for at least 1 year (and in some cases much more). I have removed the names from the front page, therefore, and put them here. I don't think that we need to list contributors (especially not on the front page), but we could create a separate page for it (or a separate section on this talk page) if we really wanted to --Whiteknight (talk) (projects) 19:24, 7 July 2006 (UTC)

 * Carandol Has done the majority of the usability formatting, current main contributor
 * Flonejek Improved navigation and copied over a few chapters
 * I'm still in highschool, and as such this wikibook is a bit of a struggle for me to keep working on, mainly because its too complex for me and I'm too lazy to currently try and comprehend the next few chapters that need work... --flonejek 06:20, 28 Nov 2004 (UTC)

 * Frontier Has written chapters for a number of sections
 * Hfs ???

completion of printable book
This Wikibook is marked as "complete" but it appears to really just be a collection of several smaller books, several of which are not complete. I would suggest downgrading the Modern Physics Wikibook to "books nearing completion" until all of the chapters have been written. I have gone through the tables of contents and collected the completed pages at " ," but there are so many missing sections and inconsistencies between sections that I would describe the book to be barely printable as a single complete work. Nicole Sharp (discuss • contribs) 00:53, 31 May 2017 (UTC)

title: Talk:Modern Physics


text:
Linear Algebra

This book discusses proof-based linear algebra. The book was designed specifically for students who have not previously been exposed to mathematics as mathematicians view it: that is, as a subject whose goal is to rigorously prove theorems starting from clear consistent definitions. This book attempts to build students up from a background where mathematics is simply a tool that provides useful calculations to the point where the students have a grasp of the clear and precise nature of mathematics. A more detailed discussion of the prerequisites and goal of this book is given in the introduction.

Because of the proof-based nature of this book, readers are recommended to be familiar with mathematical proof before reading this book (although this is not a prerequisite, strictly speaking), so that their reading experiences can be smoother. To gain familiarity with mathematical proof and also some basic mathematical concepts, readers may read the wikibook Mathematical Proof. For a milder introduction to linear algebra that is not too proof-based, see the wikibook Introductory Linear Algebra.

Table of Contents

 * Cover
 * Notation
 * Introduction

Linear Systems
 Solving Linear Systems Linear Geometry of n-Space Reduced Echelon Form Topic: Computer Algebra Systems Topic: Input-Output Analysis Input-Output Analysis M File Topic: Accuracy of Computations Topic: Analyzing Networks Topic: Speed of Gauss' Method
 * 1) Gauss' Method
 * 2) Describing the Solution Set
 * 3) General = Particular + Homogeneous
 * 4) Comparing Set Descriptions
 * 5) Automation
 * 1) Vectors in Space
 * 2) Length and Angle Measures
 * 1) Gauss-Jordan Reduction
 * 2) Row Equivalence

Vector Spaces
 Definition of Vector Space Linear Independence Basis and Dimension Topic: Fields
Topic: Crystals
Topic: Voting Paradoxes
Topic: Dimensional Analysis

 * 1) Definition and Examples
 * 2) Subspaces and Spanning sets
 * 1) Definition and Examples
 * 1) Basis
 * 2) Dimension
 * 3) Vector Spaces and Linear Systems
 * 4) Combining Subspaces

Maps Between Spaces

Isomorphisms
Homomorphisms
Computing Linear Maps
Matrix Operations
Change of Basis
Projection
Topic: Line of Best Fit
Topic: Geometry of Linear Maps
Topic: Markov Chains
Topic: Orthonormal Matrices

 * 1) Definition and Examples
 * 2) Dimension Characterizes Isomorphism
 * 1) Definition of Homomorphism
 * 2) Rangespace and Nullspace
 * 1) Representing Linear Maps with Matrices
 * 2) Any Matrix Represents a Linear Map
 * 1) Sums and Scalar Products
 * 2) Matrix Multiplication
 * 3) Mechanics of Matrix Multiplication
 * 4) Inverses
 * 1) Changing Representations of Vectors
 * 2) Changing Map Representations
 * 1) Orthogonal Projection Onto a Line
 * 2) Gram-Schmidt Orthogonalization
 * 3) Projection Onto a Subspace

Determinants

Definition
Geometry of Determinants
Other Formulas for Determinants
Topic: Cramer's Rule
Topic: Speed of Calculating Determinants
Topic: Projective Geometry

 * 1) Exploration
 * 2) Properties of Determinants
 * 3) The Permutation Expansion
 * 4) Determinants Exist
 * 1) Determinants as Size Functions
 * 1) Laplace's Expansion

Similarity

Complex Vector Spaces
Similarity
Nilpotence
Jordan Form
Topic: Geometry of Eigenvalues
Topic: The Method of Powers
Topic: Stable Populations
Topic: Linear Recurrences

 * 1) Factoring and Complex Numbers: A Review
 * 2) Complex Representations
 * 1) Definition and Examples
 * 2) Diagonalizability
 * 3) Eigenvalues and Eigenvectors
 * 1) Self-Composition
 * 2) Strings
 * 1) Polynomials of Maps and Matrices
 * 2) Jordan Canonical Form

Unitary Transformations

Inner product spaces
Unitary and Hermitian matrices
Singular Value Decomposition
Spectral Theorem

Appendix
The following is a brief overview of some basic concepts in mathematics. For more details, reader can read the wikibook Mathematical Proof.
 * Propositions
 * Quantifiers
 * Techniques of Proof
 * Sets, Functions, Relations

Resources and Licensing

 * Licensing And History
 * Resources
 * Bibliography (see individual pages for references)
 * Index

جبر خطي de:Mathematik: Lineare Algebra Álgebra Lineal Algèbre linéaire אלגברה לינארית Lineáris algebra 線型代数学 Álgebra linear 線性代數

title: Linear Algebra


text:
User:Jimregan

See en:User:Jimregan

User:Jimregan/Introductory Physics: Preface User:Jimregan/Introductory Physics: Waves in one Dimension

User:Jimregan/C Primer chapter 1 User:Jimregan/C Primer chapter 2 User:Jimregan/C Primer chapter 3 User:Jimregan/C Primer chapter 4 User:Jimregan/C Primer chapter 5 User:Jimregan/C Primer chapter 6 User:Jimregan/C Primer chapter 7

title: User:Jimregan


text:
Talk:Programming:c

There's a nice public domain C/C++ primer available here; there are also two FDL licensed books on http://savannah.gnu.org which I'll dig up if there's interest, and a C++ wiki, linked from the Wikipedia C++ article.

Would it be a good idea to integrate these as a basis? I'd go with the first link for the general basis, as it covers both languages. I'll do the conversion if people agree that it's a good idea. -- Jimregan 17:53 17 Jul 2003 (UTC)

 * I don't like the general idea of C/C++ being taught as one - printf and scanf are not useful/recommended in C++ and cout< > are invalid in C. Vectorsite (your first link) covers C with a footnote on C++ at the end. File methods are different, memory allocation is different, string manipulation is different (I'd love to be using std::string if I knew it better than the char* methods)...if not separate C and C++ books, there should be C- and C++-specific variants of some sections/chapters. Even Bjarne Stroustrop mentions somewhere on his website he doesn't like the phrase "C/C++" - the languages are too different. Geoffrey 00:11 18 Jul 2003 (UTC)

I agree with the C/C++ problem. I've decided that it might be good to just do a version of each chapter. And then a third chapter that will compare the differences between each language. What do you guys think? Josh

Well, when I said use them as a basis, that's what I meant. The languages have many differences, yes, but they also have a lot in common. I've put a wikified version of the vectorsite stuff in my user namespace; I would use them as a basis, and split them out - it's a primer, not a textbook proper.

We could easily have textbooks for different angles; C++ for beginners, C++ for C programmers, or C for C++ programmers. There's a lot of overlap here, articles could be shared, others adapted for a different approach. For example, the introduction to classes in C++ would be the same for absolute beginners as it would be for C programmers interested in C++. I think it's better to start with something than to start from scratch, and the vectorsite stuff gives that. And if nothing else, the quick reference would make a good appendix.

-- Jimregan 17:37 18 Jul 2003 (UTC)

I think that the vectorsite stuff could make a good reference, but I don't like its methods. I remember that when I was originally learning how to program that I read some of those books, but they never really helped me a lot. I never really got good at programming until I actually tried to write some semi-big programs. So I was thinking of trying to teach it, and introduce all of the concepts through the use in programming something. For example, I've written a really small game, Pitfall (you an ASCII character falling down a pit of ascii characters), that can be programmed to introduce most of the beginning concepts of programming. I don't just plan to give it to them, and then explain it line by line, I was thinking I'd walk them through the process of programming (introduce them to the mind set of programming) it.

-- Josh /time

The languages are only really common at core syntax. C++ includes C functionality, but it is expected that most of it is not used. Completely different approaches are taken to the same tasks. For example, #define versus const. A "dual" approach will have to explain that in C, const variables can't be used in constant expressions. Beyond the most basic things, C++ does things differently than C: printf versus cout, malloc versus new, pointer versus reference, array versus vector, char* versus string, and so on. The basic syntax is similar but that is hardly grounds for the whole languages being similar. (Occasionally, the lower-level C things like #define's are proper and necessary, but they'll still not the usual C++ way.)

Also, those who only want to learn one or the other will be annoyed with all the extraneous information.

I think we should have separate textbooks for each language, which do not closely parallel each other. (Many C++ things don't have any C parallels, anyway.)

Eric119 22:19 20 Jul 2003 (UTC)

Can the title "Programming:c" be changed to "Programming:C" ? Lfwlfw 02:53 24 Jul 2003 (UTC)

Begat?
Why say that (for example) A begat B; B begat C etc... Rather than using a less archaic word?

title: Talk:Programming:c


text:
User:Geoffrey~enwikibooks

 * en:User:Geoffrey | en:User talk:Geoffrey

Something I may not have mentioned at en: and is relevant here: I am a high school student. And I don't like the textbooks there.

I am open to relicensing my own contributions here and on en:.

title: User:Geoffrey~enwikibooks