Question

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

• 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.

Answer 1

Answer: (A), (C), (D)

The De Broglie wavelength of a particle is given by:

$\lambda =\frac{h}{mv}=\frac{h}{\sqrt{2Em}}$

If the two particles have same velocity, we compare using the equation:

$\lambda =\frac{h}{mv}$ 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:

$\lambda =\frac{h}{\sqrt{2Em}}$ 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.