In which of the following situations, the heavier of the two particles has smaller de broglie wavelength ? The two particle

Options

A. Both have a free fall through the same height
B. Both move with the same kinetic energy
C. Both move with the same linear momentum
D. Both move with the same speed

Answer

A, B, D

Explanation

(a,b,d) : de-Broglie wavelength of a particle is given by ,
`lambda = (h)/(p) = (h)/(mv) = (h)/(sqrt(2mK))`, K = Kinetic energy .
(a) If both the particles are allowed to fall through same height their speed will be same.
`v = sqrt(2gh)`
`therefore prop (1)/(m)`
So heavier block will have smallar de-Broglie wavelenght , i,e option (a) is correct.
(b) For same kinetic energy (K).
`lambda prop (1)/(sqrt(m))`
Again heavier block will have smaller de-Broglie wavelength i.e , option (b) is correct.