An electron, an `alpha-`particle, and a proton have the same kinetic energy. Which of these particles has the shortest 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 associated with the particle is inversely proportional to the square root of their masses. A proton `(""_(1)^(1)H)` is 1836 times massive than an electron and an `alpha`-particle `(""_(2)^(4)He)` four times that of a proton.
Hence, `alpha-` particle has the shortest de Broglie wavelength