Answer to Question #220413 in Physics for Ethan

Question

Electrons in an x-ray tube are accelerated by a p.d. of 10 kV. If an electron produces one photon on impact with the target, what is the minimum wavelength of resulting x-rays? What is the velocity with which the electron hit the target? Mass of the electron= 9.1 x 10^-31 kg.

Answer 1

(a)

$$\lambda_{\rm min}=\frac{12400\mathring{A}}{V}\\ =\frac{12400\mathring{A}}{10000V}=1.24\mathring{A}=12.4\:\rm nm$$

(b)

$$\frac{mv^2}{2}=eV$$

$$v=\sqrt{\frac{2eV}{m}}=\sqrt{\frac{2*1.6*10^{-19}*10000}{9.1*10^{-31}}}=5.9*10^7\:\rm m/s$$