# An electron, an a-particle, and a proton have the same kinetic energy. Which of these particles has the shortest de Broglie wavelength?

Apoorva Arora IIT Roorkee
askIITians Faculty 181 Points
8 years ago
We know that,
$\lambda =\frac{h}{P}$
where h is the planck’s constant
in terms of KE,
$\lambda =\frac{h}{\sqrt{2mKE}}$
if the kinetic energy is same,
wavelength is inversely proportional to the root of mass of the particle.
So, out of the three, the heaviest is alpha particle and hence has the shortest de-broglie wavelength.
Thanks and Regards
Apoorva Arora
IIT Roorkee