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

Explanation

For a particle , de Broglie wavelength , `lambda`=h/p
Kinetic energy, `K=p^2//2m`
Then, `lambda=h//sqrt(2mK)`
For the same kinetic energy K, the de Broglie wavelength associatedwith the particle is inversely proportional to the square root of their masses. A proton`(._1^1H)` is 1836 times massive than an electron and an `alpha`-particle ` (._2^4He)` four times that of a proton.Hence, `alpha` – particle has the shortest de Broglie wavelength.