Question

An electron, a protons and an alpha particle have the same kinetic energy, which of these particles has the shortest de Broglie wave and which have longest wavelength.

Answer 1

Answer:

An alpha particle because they have the greatest mass.

The answer is the same at both relativistic and newtonian velocities. So we can use newtonian formula here

m is mass, v is velocity, K is kinetic energy, p is momentum and λ is wavelength.

K = 0.5 mv^2

K= 0.5p^2/m

p=sqrt (2mK)

λ = h/p

λ =h/sqrt (2mK)

So as m decreases, λ increases.

Electrons have the smallest m, so they have the greatest λ.

Alpha particles have the greatest m, so they have the smallest λ.

Hope it helps!♡