An electron, an `alpha`-particle, and a photon have the same kinetic energy. Which of these particles has the shortest, de -broglie wavelenght?

Explanation

For a particle ,
de Broglie wavelength , `lambda = h//p`
Kinetic energy , `K = p^(2)/2"m"`
Then , `lambda = h /sqrt(2"mK")`
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 `alpha` - particle ( `._(2)^(4)He` ) four times that of a proton
Hence , `alpha ` - particle has the shortest de Broglie wavelength.