In which of the following cases the heavier of the two particles has a smaller de-Broglie wavelength ? The two particles

Options

A. move with same speed
B. move with the same kinetic energy
C. move with the same linear momentum
D. have fallen through the same height.

Answer

a,b,d

Explanation

(i) `lambda=h/(mv) , lambda prop1/m` if `v` is same.
(ii) Also `lambda=h/(sqrt(2mE))` so `lambda prop1/(sqrt(m))` if `E` is same.
(iii) When two bodies fall from a some height, both acquire equl velocity (iv), so the `lambda` will be less for heavier particles for option (a), (b) and (d).