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Optics of Moving Sources

Problem 5.235

One of the spectral lines of atomic hydrogen has the wavelength λ=656.3nm.\lambda=656.3 \mathrm{nm} . Find the Doppler shift Δλ\Delta \lambda of that line when observed at right angles to the beam of hydrogen atoms with kinetic energy T=1.0MeVT=1.0 \mathrm{MeV} (the transverse Doppler effect).

Reveal Answer
Δλ=λT/m0c2=0.70nm, where m0 is the mass of the atom\Delta \lambda=\lambda T / m_{0} c^{2}=0.70 \mathrm{nm}, \text { where } m_{0} \text { is the mass of the atom}
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