Question

An electron, an alpha $\left(\alpha \right)$ particle and a proton have same kinetic energies. Which one of these particles has largest de Broglie wavelength?

Answer 1

Debroglie wavelength is defined as:

$\lambda =\frac{h}{p}$

Also, kinetic energy of a particle is:

$KE=\frac{p^2}{2m}$

$⟹\lambda =\frac{h}{\sqrt{2mKE}}$

Since kinetic energy is same,

$\lambda \propto \frac{1}{\sqrt{m}}$

Since an electron has very low mass, it will have largest debroglie wavelength.