Question

A proton and an alpha particle have the same de broglie wavelength. Determine the ratio of
1. Their accelerating potentials
2.their speeds

Answer 1

De Broglie wavelength for alpha and proton particles=λ
valpha=h/4mλ
and vproton=h/mλ
ii⎞⎠ therefore ratio of velocity of proton to velocity of alpha particle
= vproton/valpha=h/mλ/h/4mλ=4/1
i⎞⎠ The accelerating potential of an alpha particle
=Valpha=4mvalpha^2/2×2 e
=2mvalpha^2/2e
​​Simmilarly The accelerating potential of a proton particle
=Vproton=mvproton^2/2×e
Therefore ratio of ACCELERATING POTENTIAL of proton to ACCELERATING POTENTIAL of alpha particle
= Vproton/Valpha
=mvproton^2/2×e2mvalpha^2/2e
=vproton^2/valpha^2
=(vproton/2valpha)^2
=16/4
=4/1