All Problems

Optics of Moving Sources

Problem 5.226

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

Reveal Answer
Δλ=λ2T/mc2cosθ=26nm\Delta \lambda=-\lambda \sqrt{2 T / m c^{2}} \cos \theta=-26 \mathrm{nm}