Consider two particles of different masses. In which of the following situations the heavier of the two particles will have smaller de Broglie wavelength?

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

de Broglie wavelength,
`lamda = (h)/(p) = (h)/(mv) = (h)/(sqrt(2mE))` [h = Planck's constant, m = mass, v = velocity, p = momentum, E = kinetic energy]
If the linear momentums of the two particles are equal, their wavelengths will also be equal. Velocities of the particles are same in both cases (A) and (D), hence `lamda` will be relatively smaller for the heavier particle. Similarly, E of the two particles is the same for case (B), hence `lamda` will be smaller again for the heavier particle.