If the particles listed below all have the same kinetic energy, which one would possess the shortest de-Broglie wavelength?

Question

If the particles listed below all have the same kinetic energy, which one would possess the shortest de-Broglie wavelength? (A) Deuteron (B)  α -particle (C) Proton (D) Electron

Tardigrade Admin · Accepted Answer

As per the formula, λ=( h / p ) Since λ=( h / mv ) thus, λ propto (1/√ m ) Wavelength and mass has inverse dependence. Since, mass of electron is the least out of all the three particles . ., electron has the largest de-Broglie wavelength.

Q. If the particles listed below all have the same kinetic energy, which one would possess the shortest de-Broglie wavelength?

Deuteron

$α$ -particle

Proton

Electron

As per the formula,
$λ = \frac{h}{p}$
Since $λ = \frac{h}{m v}$
thus, $λ \propto \frac{1}{m}$
Wavelength and mass has inverse dependence.
Since, mass of electron is the least out of all the three particles . ., electron has the largest de-Broglie wavelength.