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

identify electron transitions between energy levels as absorption or emission and match their energy differences to spectral lines
determine the number and relative wavelengths or frequencies of possible emitted photons from a set of energy levels
use energy-level diagrams to select allowed transitions and explain which photons are absorbed or emitted for a stated energy difference

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Study E.1.4—Atomic transitions conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

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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