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 from frequency or wavelength using E=hf and E=hc/λ, with consistent units and significant figures
compare photon energy, frequency and wavelength for different spectral lines or electron transitions
use an energy-level difference to identify the emitted photon and determine its wavelength, frequency or energy

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Study E.1.5—Photon energy conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

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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