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Gateway to Spectroscopy > Physical Background > Nature of Light > Optical Transitions

### Optical Transitions

#### and light emission

If we could solve Schrödinger's equation for all the electrons in an atom, in its lowest energy state, we would have a detailed description of the electron structure of the atom and its electron energy.

But Schrödinger's equation tells us that other electron structures and energies are possible for that atom. The atom may change to one of these other configurations by the absorption or emission of an amount of energy equal to the difference in the energies of the two configurations.

A common mode for the change in atomic energy is the emission or absorption of a photon (a parcel of electromagnetic radiation, such as light). This process is called an 'optical transition'.

A photon is a disturbance of the electromagnetic field. The energy in a photon is

where h is Planck's constant, n is frequency, c is the speed of light in vacuum, and l is wavelength. A photon also has a momentum given by

#### Linewidth

When an atom absorbs a photon it is elevated to an excited state. This excited state will generally last for a limited time, typically 10-8 s. The atom can de-excite by emitting a photon. From Heisenberg's uncertainty principle, the finite lifetime Dt of the excited state means there will be an uncertainty in the energy of the emitted photon given by

Combining this with equation (1) above [don't forget to differentiate!] gives a minimum width of

So the finite lifetime of the excited state means that when we measure the wavelength of the emitted photon it will have a spread of wavelengths around the mean value l. For a line at 450 nm and a lifetime of 10-8 s, the minimum (or natural) linewidth is 0.01 pm.

#### Momentum

A spontaneous optical transition is a sudden and directional process. It therefore involves the exchange of momentum between the atom and the exciting photon. In absorption, the atom receives momentum in the direction of the incoming photon. This is a fundamental aspect of quantum mechanics, first derived by Einstein and quite different from classical theories. The direction of emission is random, and it is only in averaging a large number of such events that emission appears to be  non-directional with zero momentum as predicted by classical theories.

First published on the web: 15 February 2000.

Author: Richard Payling

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