A nickel crystal produces a certain diffraction pattern for X-rays. The same pattern is obtained using electrons. If each X-ray photon has energy 20.0 keV, find the electron kinetic energy in eV.
Physics · Photoelectric effect and dual nature of matter
JEE Mains Advanced

Question

A nickel crystal produces a certain diffraction pattern for X-rays. The same pattern is obtained using electrons. If each X-ray photon has energy 20.0 keV, find the electron kinetic energy in eV.

G1 Physics · Accepted Answer

Identical diffraction patterns mean equal wavelengths. X-ray wavelength λ=hc/Eγ. Electron de Broglie λ=h/√(2mK). Equating gives K=Eγ²/(2mc²), which for Eγ=20 keV gives approximately 391 eV.