Question

In which of the following situations does the heavier of the two particles has smaller de Broglie wavelength? The two particles

This question has multiple correct options
A

move with the same speed

B

move with the same linear momentum

C

move with the same kinetic energy

D

have fallen through the same height.

Medium

Solution

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Correct options are A) , C) and D)

The De Broglie wavelength of a particle is given by:
If the two particles have same velocity, we compare using the equation:
The one with larger mass has a smaller De Broglie wavelength.
Hence option A is correct.
If two particles have the same kinetic energy or fall from the same height (by which they get the same Kinetic energy) we use the second relation:
In which case the particle with higher mass has a smaller De Broglie wavelength. Hence options C and D are correct.
If the two particles have the same linear momentum, then they have the same wavelength hence option B is wrong.
Thus options A,C,D are correct.

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