The Quantum Lighthouse · AI Generator #GEN-430B36B8
Physics · modern-physics
Problem
A deep-space communication station uses a novel quantum beacon consisting of a rotating cylindrical crystal doped with radioactive atoms. The cylinder has radius R=2.0cm and rotates at angular velocity ω=1200rad/s. The radioactive atoms emit gamma rays with energy Eγ=150keV in their rest frame.
Due to the relativistic Doppler effect, the emitted gamma rays are frequency-shifted depending on the instantaneous velocity of the emitting atoms. A distant detector positioned in the equatorial plane of the cylinder measures the energy spectrum of the received gamma rays.
(a) Find the range of photon energies ΔE observed by the detector due to the Doppler shift.
(b) If the detector has an energy resolution of δE=0.50keV, determine how many distinct energy peaks can be resolved in the spectrum.
(c) Now consider that some gamma rays undergo Compton scattering off free electrons in the interstellar medium before reaching the detector. For gamma rays that scatter through an angle θ=90°, what is the energy of the scattered photons when they originated from atoms moving directly toward the detector?
Use c=3.0×108m/s and electron rest mass energy mec2=511keV.