All Problems

Optics of Moving Sources

Problem 5.226

One of the spectral lines emitted by excited He +^{+} ions has a wavelength λ=410nm\lambda=410 \mathrm{nm}. Find the Doppler shift Δλ\Delta \lambda of that line when observed at an angle θ=30∘\theta=30^{\circ} to the beam of moving ions possessing kinetic energy T=10MeVT=10 \mathrm{MeV}.

Reveal Answer
Δλ=−λ2T/mc2cos⁡θ=−26nm\Delta \lambda=-\lambda \sqrt{2 T / m c^{2}} \cos \theta=-26 \mathrm{nm}
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