Physics 9702 · AS & A Level · Energy levels in atoms and line spectra

Energy levels in atoms and line spectra — practice question

Fig. 8.1 displays the three lines with the lowest frequencies in the section of the hydrogen emission spectrum that corresponds to electron transitions down to the ground state (level $n = 1$). The figures give the frequencies, in $10^{15}\,\text{Hz}$, for the spectral lines.
(a)[3]

Use the photon model of electromagnetic radiation to explain how the appearance of spectral lines in the emission spectrum shows that electron energy levels in the hydrogen atom are discrete.

(b(i))[1]

The ground-state energy (level $n = 1$) of a hydrogen atom is $-13.6\,\text{eV}$. Calculate the energy, in J, of the ground state.

(b(ii))[2]

Show that the energy difference between levels $n = 1$ and $n = 2$ is $10.2\,\text{eV}$.

(b(iii))[4]

Complete Table 8.1 to show the energy differences from the ground state, together with the energies of the levels up to $n = 4$, in the hydrogen atom. Use the space for any working.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: an electron moving between energy levels emits one photon

  • Full mark scheme, point by point
  • Step-by-step worked solution
  • Write your answer & get it marked instantly by AI