Spontaneous emission is the process by which a molecule in an excited state drops to the ground state, resulting in the creation of a photon. In science, a molecule is the smallest particle of a pure chemical substance that still retains its chemical composition and properties. ... In quantum mechanics, an excited state of a system (such as an atom, molecule or nucleus) is any configuration of the system that has a higher energy than the ground state (that is, more energy than the absolute minimum). ... In physics, the ground state of a quantum mechanical system is its lowest-energy state. ... In physics, the photon (from Greek φοτος, meaning light) is a quantum of excitation of the quantised electromagnetic field and is one of the elementary particles studied by quantum electrodynamics (QED) which is the oldest part of the Standard Model of particle physics. ...

If the atom is in the excited state with energy E₂, it may spontaneously decay into the ground state, with energy E₁, releasing the difference in energies between the two states as a photon. The photon will have frequency ν and energy hν, given by: Sine waves of various frequencies; the lower waves have higher frequencies than those above. ...

E₂ − E₁ = hν,

where h is Planck's constant. The phase of the photon in spontaneous emission is random as is the direction the photon propagates in. This is not true for stimulated emission. In science, a physical constant is a physical quantity whose numerical value does not change. ... Phase, from the Greek phasis, meaning appearance, has a number of related meanings in English. ... In optics, stimulated emission is the process by which, when perturbed by a photon, matter may lose energy resulting in the creation of another photon. ...

An energy level diagram illustrating the process is shown below:

 Before emission After emission --------O--------- ------------------ E2 | Atom in | excited state | ~~~> | Photon hν | V ------------------ ---------O-------- E1 Atom in ground state 

In a group of such atoms, if the number of atoms in the excited state is given by N, the rate at which spontaneous emission occurs is given by:

,

where A₂₁ is a proportionality constant for this particular transition in this particular atom. (The constant is referred to as an Einstein A co-efficient.) The rate of emission is thus proportional to the number of atoms in the excited state, N. Portrait of Albert Einstein taken by Yousuf Karsh on February 11, 1948 Albert Einstein (March 14, 1879 – April 18, 1955) was a theoretical physicist who is widely regarded as the greatest scientist of the 20th century. ...

The above equation can be solved to give:

,

where N(0) is the initial number of atoms in the excited state, and τ₂₁ is the lifetime of the transition, τ₂₁ = (A₂₁)^-1.

It can be seen that spontaneous emission occurs in a way rather similar to the decay of radioactive particles, in particular that the lifetime is analogous to a half-life. Particle radiation is the radiation of energy by means of small fast-moving particles that have energy and mass. ... Half-Life For a quantity subject to exponential decay, the half-life is the time required for the quantity to fall to half of its initial value. ...

There are two different ways in which decay or relaxation can occur: radiative and nonradiative. In nonradiative relaxation, the energy is absorbed as phonons, more commonly known as heat. Nonradiative relaxation is nearly impossible to measure and cannot be inferred except in very small particles because the difference in the temperature before and after a relaxation is so small that it is in the noise of any measurement for practical systems. A phonon is a quantized mode of vibration occurring in a rigid crystal lattice, such as the atomic lattice of a solid. ... Heat (abbreviated Q, also called heat change) is the transfer of thermal energy between two bodies which are at different temperatures. ...

Nonradiative relaxations occur when the energy difference between the levels is very small, and these typically occur on a much faster time scale than radiative transitions. For many materials (for instance, semiconductors), electrons move quickly from a high energy level to a meta-stable level via small nonradiative transitions and then make the final move down to the bottom level via an optical or radiative transition (This final transition is the transition over the bandgap in semiconductors.). Large nonradiative transitions do not occur frequently because the crystal structure generally can not support large vibrations without destroying bonds (which generally doesn't happen for relaxation). Meta-stable states form a very important feature that is exploited in the construction of lasers. Specifically, since electrons decay slowly from them, they can be piled up in this state without too much loss and then stimulated emission can be used to boost an optical signal. A semiconductor is a material that is an insulator at very low temperature, but which has a sizable electrical conductivity at room temperature. ... In solid state physics and related applied fields, the band gap is the energy difference between the top of the valence band and the bottom of the conduction band in insulators and semiconductors. ... Rose des Sables (Sand Rose), a formation of gypse crystal In mineralogy and crystallography, a crystal structure is a unique arrangement of atoms in a crystal. ... Laser (US Air Force) A laser (Light Amplification by Stimulated Emission of Radiation) is a device which uses a quantum mechanical effect, stimulated emission, to generate a coherent beam of light from a lasing medium of controlled purity, size, and shape. ... In optics, stimulated emission is the process by which, when perturbed by a photon, matter may lose energy resulting in the creation of another photon. ...

See also absorption, stimulated emission, laser science. Absorption has a number of meanings: In physics absorption is a process in which particles of some sort encounter another material and are taken up by or even disappear in it. ... In optics, stimulated emission is the process by which, when perturbed by a photon, matter may lose energy resulting in the creation of another photon. ... Laser science is a branch of optics that describes the theory and practice of lasers. ...