There are times when a physicist must settle for inaccurate measurements,
but these spectral frequencies are among the most accurate quantities
that can be measured. Atomic spectra had been observed, measured,
and cataloged in detail prior to the development of quantum mechanics,
but the reasons for them were not understood at all.
Bohr proposed that an atom can absorb radiation only at a frequency,
that corresponds to the difference in energy, E,
between two allowed quantum states:
This is illustrated on the right. An electron cannot jump from a
lower to a higher energy state unless this exact amount of energy
is supplied to it. Conversely, when an atom in a higher state falls
to a lower state, the frequency of radiation given off is dictated
by the relationship just given.