The work function (W0) of a metal is the minimum energy required to just remove an electron from the surface of the metal without giving it any kinetic energy. The threshold frequency (f0) is the minimum frequency of the incident light below which no photoelectric emission takes place, however intense the light may be. They are related by W0 = h f0, where h is Planck's constant.

W0 = h f0

(1) For a given metal, photoelectric emission occurs only if the frequency of the incident light is greater than a certain minimum value (threshold frequency), whatever the intensity. (2) The maximum kinetic energy of the emitted photoelectrons depends on the frequency of the incident light and the nature of the metal, but is independent of the intensity of the light. (3) The number of photoelectrons emitted per second (photoelectric current) is directly proportional to the intensity of the incident light. (4) The emission is instantaneous, with no measurable time lag.

The de Broglie hypothesis states that every moving particle has a wave associated with it, called a matter wave. The de Broglie wavelength is lambda = h/p = h/(m v), where h is Planck's constant, p is the momentum, m is the mass and v the velocity of the particle. In terms of kinetic energy, lambda = h/sqrt(2 m KE). This shows the dual (wave-particle) nature of matter; the wavelength is significant only for very small particles like electrons.

lambda = h/(m v)

From the scattering of alpha particles by a thin gold foil, Rutherford concluded that: (1) most of the atom is empty space, since most alpha particles passed straight through; (2) the entire positive charge and almost all the mass of the atom are concentrated in a very small central region called the nucleus, since a few alpha particles were deflected through large angles; and (3) the electrons revolve around the nucleus, and the size of the nucleus is very small compared with the size of the atom.

The energy of the electron in the nth orbit of hydrogen is En = -13.6/n^2 eV. For n = 2, E2 = -13.6/2^2 = -13.6/4 = -3.4 eV. The negative sign shows that the electron is bound to the nucleus, and the energy increases (becomes less negative) as n increases.

En = -13.6/n^2 eV

(1) Bohr's model applies successfully only to hydrogen and hydrogen-like single-electron atoms; it fails to explain the spectra of atoms having more than one electron. (2) It could not explain the fine structure of spectral lines or the relative intensities of the lines, and it does not account for the splitting of spectral lines in electric and magnetic fields (the Stark and Zeeman effects). Also, it arbitrarily assumes quantisation without explaining it (later explained by de Broglie).

Einstein's mass-energy relation is E = m c^2, which states that mass and energy are interconvertible, where c is the speed of light. Using this relation, the energy equivalent of 1 atomic mass unit (1 u = 1.66 x 10^-27 kg) is about 931 MeV (mega electron volt). This relation explains the large amount of energy released in nuclear reactions such as fission and fusion.

E = m c^2; 1 u = 931 MeV

The mass defect is the difference between the sum of the masses of the individual protons and neutrons (nucleons) and the actual mass of the nucleus; the actual nuclear mass is always less than the sum. This missing mass (delta m) is converted into energy that binds the nucleons together. The binding energy is the energy equivalent of the mass defect, BE = (delta m) c^2; it is the energy required to break the nucleus into its constituent nucleons.

BE = (delta m) c^2

The three types of radioactive radiations are: (1) alpha rays, which are helium nuclei (2 protons + 2 neutrons), positively charged and with low penetrating power; (2) beta rays, which are fast-moving electrons, negatively charged and with greater penetrating power than alpha rays; and (3) gamma rays, which are high-energy electromagnetic waves (photons), electrically neutral and with very high penetrating power. In a magnetic field, alpha and beta rays are deflected in opposite directions while gamma rays are undeflected.

Nuclear fission is the process in which a heavy nucleus (such as uranium-235) splits into two lighter nuclei of comparable masses, with the release of a few neutrons and a large amount of energy. For example, when a uranium-235 nucleus captures a slow neutron, it splits into barium and krypton nuclei plus three neutrons and energy. The released neutrons can cause further fissions, leading to a chain reaction, which is used in nuclear reactors and atom bombs.

Nuclear fusion is the process in which two light nuclei (such as isotopes of hydrogen) combine to form a heavier nucleus, with the release of an enormous amount of energy. It is the source of energy of the sun and stars, where hydrogen nuclei fuse to form helium. It requires very high temperature (millions of degrees) because the positively charged nuclei must overcome their strong electrostatic repulsion to come close enough to fuse.

An intrinsic semiconductor is a pure semiconductor (such as pure silicon or germanium) with no added impurity; its conductivity is low and is due to the equal number of electrons and holes generated thermally. An extrinsic semiconductor is one to which a small amount of a suitable impurity has been added (doping); this greatly increases its conductivity. Extrinsic semiconductors are of two types, n-type and p-type.

An n-type semiconductor is formed by doping a pure semiconductor (silicon) with a pentavalent impurity (such as phosphorus or arsenic), which donates free electrons; the majority carriers are electrons and the minority carriers are holes. A p-type semiconductor is formed by doping with a trivalent impurity (such as boron or aluminium), which creates holes; the majority carriers are holes and the minority carriers are electrons. Both types are electrically neutral overall.

When a p-n junction is formed, electrons from the n-side diffuse into the p-side and holes from the p-side diffuse into the n-side, and they recombine near the junction. This leaves a region near the junction that has no free charge carriers but has immobile charged ions; this region is called the depletion region (or depletion layer). The immobile ions set up an internal electric field that opposes further diffusion; the potential difference developed across the depletion region is called the potential barrier.

In forward biasing, the p-side is connected to the positive terminal and the n-side to the negative terminal of the battery; this reduces the width of the depletion region and the potential barrier, so a large current flows and the diode conducts. In reverse biasing, the p-side is connected to the negative terminal and the n-side to the positive terminal; this increases the width of the depletion region and the potential barrier, so only a very small (negligible) current flows and the diode does not conduct.

A Zener diode is a special heavily doped p-n junction diode designed to operate in the reverse breakdown region without being damaged. In this region, the voltage across it remains almost constant (equal to its Zener voltage) even when the current through it changes over a wide range. Because of this property, its main use is as a voltage regulator, that is, to provide a constant output voltage to a load in spite of changes in the input voltage or load current.

Crystalline solids have a regular, long-range ordered arrangement of particles, sharp melting points, definite geometrical shapes and are anisotropic (properties differ with direction); e.g. sodium chloride and diamond. Amorphous solids have only a short-range order (irregular arrangement), no sharp melting point (they soften over a range), no definite shape and are isotropic (same properties in all directions); e.g. glass and rubber.

A unit cell is the smallest repeating three-dimensional portion of a crystal lattice which, when repeated in different directions, generates the entire crystal. In a primitive (simple) unit cell, the constituent particles are present only at the corners of the unit cell. In a centred unit cell, particles are present at positions other than the corners as well, such as body-centred (one at the centre of the body), face-centred (one at the centre of each face) or end-centred.

Schottky defect is a vacancy defect in which an equal number of cations and anions are missing from their lattice sites, so the density of the solid decreases; it occurs in ionic solids with high coordination number and similar cation and anion sizes (e.g. NaCl, KCl). Frenkel defect is a dislocation defect in which an ion (usually the smaller cation) leaves its lattice site and occupies an interstitial site, so the density remains unchanged; it occurs in solids with a large difference in the sizes of the ions (e.g. AgCl, ZnS).

Packing efficiency is the percentage of the total space occupied by the particles. Simple cubic: packing efficiency 52.4 percent, coordination number 6. Body-centred cubic (bcc): packing efficiency 68 percent, coordination number 8. Face-centred cubic (fcc, also ccp/hcp): packing efficiency 74 percent (the highest), coordination number 12.