Question

What wavelength must electromagnetic radiation have if a photon in the beam is to have the same momentum as an electron moving at a speed of $7 \cdot 28 \times 10^{4} ms ^{-1}$?

Answer 1

SOLUTION — Momentum of an electron $=m v$.

According to de Broglie relation

$\lambda=\frac{h}{p} \text { where } p=\text { momentum of photon. } \quad \therefore p=\frac{h}{\lambda}$

Given, $m v$ for electron $=\frac{h}{\lambda}$ for photon

$ 9 \cdot 1 \times 10^{-31} \times 7 \cdot 28 \times 10^{4}=\frac{6 \cdot 626 \times 10^{-34}}{\lambda}$

$\therefore \quad  \lambda=\frac{6 \cdot 626 \times 10^{-34}}{9 \cdot 1 \times 7 \cdot 28 \times 10^{-27}} m =10^{-8} m =10 nm .$