The Cosmic Ray Detector's Muon Energy Mystery · AI Generator #GEN-9623F883

Physics · modern-physics

Problem

A cosmic ray detector on a mountaintop uses the photoelectric effect to detect high-energy muons. When a muon passes through the detector's scintillator material, it produces photons with energy

E_{\text{photon}} = 3.2\;\text{eV}

. These photons then strike a photocathode made of cesium, which has a work function

\phi = 2.1\;\text{eV}

. The photoelectrons produced at the cathode are accelerated through a potential difference of

V = 850\;\text{V}

and then enter a magnetic field region where they follow circular paths. In this magnetic field of strength

B = 0.15\;\text{T}

, the photoelectrons have a measured orbital radius of

r = 1.8\;\text{mm}

. However, the detector also picks up background cosmic ray electrons that enter the magnetic field region directly (without going through the photoelectric process). These background electrons follow circular paths with radius

r_{\text{bg}} = 4.2\;\text{mm}

in the same magnetic field. (a) What is the kinetic energy of the photoelectrons when they enter the magnetic field region? (b) What is the kinetic energy of the background cosmic ray electrons? (c) By what factor do the background electrons have more kinetic energy than the photoelectrons?

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