IB Physics HL E 1 5 Photon Energy Questions

Calculate HL photon energy, frequency and wavelength from spectra and energy-level transitions, selecting the correct relationship and units.

Exam points

Calculate photon energy, wavelength and frequency for hydrogen and atomic transitions.
Analyse spectral transition diagrams and identify corresponding photon properties.
Apply quantized energy differences to emission and absorption of electromagnetic radiation.

[Maximum number: 2]

The diagram represents the three principal spectral lines in the visible region of the spectrum of atomic hydrogen.

Figure for Question IB Physics HL E 1 5 Photon Energy Questions question 1 — IB Physics HL

The electron in the hydrogen atom can only occupy certain allowed energy levels.

Determine the difference in energy between the two levels from which electron transitions give rise to the $\mathrm{H}_{\alpha}$ and $\mathrm{H}_{\gamma}$ spectral lines respectively.

difference in energy $=hc\left[\frac{1}{\lambda_{\gamma}}-\frac{1}{\lambda_{\alpha}}\right]$ ;
$=6.6 \times 10^{-34} \times 3 \times 10^{8} \times 10^{7} \times 0.0780=1.54 \times 10^{-19} \mathrm{~J}$ ;
or
$E_{\alpha}=\frac{hc}{\lambda_{\alpha}}=3.02 \times 10^{-19} \mathrm{~J}$ or $1.89 \mathrm{~eV}$ ;
$E_{\gamma}=\frac{hc}{\lambda_{\gamma}}=4.56 \times 10^{-19} \mathrm{~J}$ or $2.85 \mathrm{~eV}$ ;
difference in energy $=1.54 \times 10^{-19} \mathrm{~J}$ or $0.963 \mathrm{~eV}$ ;

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IB Physics HL E 1 5 Photon Energy Questions question 1