| Date | May 2012 | Marks available | 5 | Reference code | 12M.2.HL.TZ2.14 |
| Level | Higher level | Paper | Paper 2 | Time zone | Time zone 2 |
| Command term | Determine and Outline | Question number | 14 | Adapted from | N/A |
Question
Part 2 Energy levels of the hydrogen atom
The diagram represents the three principal spectral lines in the visible region of the spectrum of atomic hydrogen.
The electron in the hydrogen atom can only occupy certain allowed energy levels.
(i) Outline how the spectral lines provide evidence for the existence of these energy levels.
(ii) Determine the difference in energy between the two levels from which electron transitions give rise to the Hα and Hγ spectral lines respectively.
Markscheme
(i) spectral lines are discrete;
therefore energy of photon is discrete/quantized;
photon energy is equivalent to difference in energy that electron has in each (discrete) level / ΔE = hf / OWTTE;
(so electron levels are themselves discrete)
(ii) difference in energy = \(hc\left[ {\frac{1}{{{\lambda _\gamma }}} - \frac{1}{{{\lambda _\alpha }}}} \right]\);
=6.6×10-34×3×108×107×0.0780=1.54×10-19J;
or
\({E_\alpha } = \left[ {\frac{{hc}}{{{\lambda _\alpha }}}} \right] = \frac{{6.6 \times {{10}^{ - 34}} \times 3 \times {{10}^8}}}{{6.56 \times {{10}^{ - 7}}}} = 3.02 \times {10^{ - 19}}{\rm{J}}\) or 1.89eV
\({E_\gamma } = \left[ {\frac{{hc}}{{{\lambda _\gamma }}}} \right] = \frac{{6.6 \times {{10}^{ - 34}} \times 3 \times {{10}^8}}}{{4.34 \times {{10}^{ - 7}}}} = 4.56 \times {10^{ - 19}}{\rm{J}}\) or 2.85eV {(both needed for the mark)
difference in energy=1.54×10-19J or 0.963 eV;
Examiners report
(i) Although a good chain of argument was seen from many, some candidates struggled to relate the diagram to the existence of energy levels. Sometimes this resulted in a description of photon release that was accurate but irrelevant.
(ii) Simple algebraic misconceptions prevented many from obtaining a correct solution. It was common to see a subtraction of the values of the two wavelengths rather than a subtraction of the reciprocals. Candidates who carried both energies through separately scored more highly than those who attempted early subtractions.
