All Problems

Thermal Radiation. Quantum Nature of Light.

Problem 5.272

Find the wavelength of the short-wave limit of an X-ray continuous spectrum if electrons approach the anticathode of the tube with velocity \(v=0.85 c,\) where \(c\) is the velocity of light.

Reveal Answer
λmin=2π/mc(γ1)=2.8pm, where γ=1/1(v/c)2\lambda_{\min }=2 \pi \hbar / m c(\gamma-1)=2.8 \mathrm{pm}, \text { where } \gamma=1 / \sqrt{1-(v / c)^{2}}