(a) Electrons in atoms are only permitted to have certain energy values, these values being called the energy levels for the atoms concerned. All other values of energy are not allowed.

If an electron in an atom receives sufficient energy it can be raised to a higher energy level. When the electron falls back down to its original energy level the 'surplus' energy E is emitted as a photon, a packet of electromagnetic radiation of a specific frequency f:

E=hf

where h is the Planck constant. Within the atoms there is a range of permitted energy levels that an electron can move to and hence a range of different energy photons that can be emitted when the electron falls back down the levels. Hence a range of discrete frequencies can be emitted by an element, i.e. it has an emission line spectrum.

(c) The energy gained by accelerating an electron, charge e, through a potential difference V is eV If all this energy is given to a single photon then eV = hf = hc/l

      hence minimum wavelength = hc / (eV)

      l = 6.6 x 10^-34  x  3 x 10⁸

            1.6 x 10^-19  x  12  x  10³

        = 1.03 x 10 ^–10 m