Atomic energy levels and emission line spectra

An electron in an atom can have only certain energies. These allowed energies are called discrete energy levels: the electron cannot occupy an energy between them.

When an electron moves from a higher energy level to a lower one, the atom emits the energy difference as a photon. If the higher level is $$$E_1$$$ and the lower level is $$$E_2$$$ , the photon energy is:

hf = E_1 - E_2

Here, $$$h$$$ is the Planck constant and $$$f$$$ is the frequency of the emitted photon. A larger energy difference produces a photon with a higher frequency.

Atomic emission line spectra

Because an atom has only particular allowed energy levels, transitions between them can produce only particular energy differences. The atom therefore emits photons at particular frequencies, rather than at every possible frequency.

These frequencies appear as separate lines in an emission line spectrum. The lines provide evidence that atomic energy levels are quantised: restricted to discrete values. Atomic hydrogen produces a line spectrum because its electrons can make transitions between its allowed energy levels.

Energy levels in electronvolts

Energy levels may be given in joules or electronvolts. The electronvolt is a unit of energy, with $1,\text{eV} = 1.60 \times 10^{-19},\text{J}$ .

When calculating frequency using $$$h$$$ in joule seconds, first express the energy difference in joules. For example, an energy difference of $2.00,\text{eV}$ is $3.20 \times 10^{-19},\text{J}$ . Using $h = 6.63 \times 10^{-34},\text{J s}$ gives:

f = \frac{3.20 \times 10^{-19}\,\text{J}}{6.63 \times 10^{-34}\,\text{J s}} = 4.83 \times 10^{14}\,\text{Hz}