IB Physics HL E 1 4 Atomic Transitions Questions

Analyse HL atomic-transition questions by mapping electron energy levels to absorption or emission lines and counting the possible photon frequencies.

Exam points

Analyse multi-level atomic transitions and the resulting photon spectra.
Calculate photon wavelength, frequency and energy for atomic transitions.
Explain absorption and emission processes in hydrogen and discrete energy-level models.

[Maximum number: 3]

This question is in two parts.

The energies of the principal energy levels in atomic hydrogen measured in eV are given by the expression

E_{n}=-\frac{13.6}{n^{2}} \text { where } n=1,2,3

The visible lines in the spectrum correspond to electron transitions that end at n=2.

Show that the spectral line of wavelength $\lambda=485 \mathrm{~nm}$ is the result of an electron transition from n=4.

energy difference between levels $=\frac{h c}{\lambda e}=\frac{6.63 \times 10^{-34} \times 3 \times 10^{8}}{4.85 \times 10^{-7} \times 1.6 \times 10^{-19}}$ ;
=2.55 eV;
$[3.40-2.55]=0.85=\frac{13.6}{n^{2}}$ to give $n^{2}=16$ ;
n=4;

Marking guidance:

Award [3] for reversed argument.

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IB Physics HL E 1 4 Atomic Transitions Questions question 1