Question

Electrons with de Broglie wavelength $\lambda$ are bombarded on a metal target. It is found that photons are emitted from the metal target. The minimum wavelength of emitted photons is [m = mass of eletron]

Answer 1

Let $E_x$ be the K.E of the incident electron,

it's linear momentum ,$P=\sqrt{2mEx}$

Now,

de-Brogli wavelength related to electron is

$\lambda =\frac{h}{P}=\frac{h}{\sqrt{2mEx}}$

$or,Ex=\frac{h^2}{2m{\lambda }^2}$

The minimum wavelength ,${\lambda }_{\circ }$

$\frac{hc}{{\lambda }_{\circ }}=Ex=\frac{h^2}{2m{\lambda }^2}$

or, we get ${\lambda }_{\circ }=\frac{2mc{\lambda }^2}{h}$