Question

The electron with The electron with de Broglie wavelength $\lambda$ is bombarded on a metal target. Found that photons are emitted through de Broglie wavelength.

Answer 1

Let $E_k$ be the K.E of incident electrons, its linear momentum $P=\sqrt{2m{E}_k}$

De-Broglie wavelength relates to electron is

$\lambda =\frac{h}{p}=\frac{h}{\sqrt{2m{E}_k}}$

$E_k=\frac{n^2}{2m\lambda }$

The cut-off wavelength of the emitted x-ray is related to K.E of incident electron.

$\frac{hc}{{\lambda }_o}=E_k=\frac{h^2}{2m\lambda }$

$\Rightarrow \lambda =\frac{2mc{\lambda }^2}{h}$.