Question

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

• A. Both have a free 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 1

Answer: (A), (B), (D)

Both have a free through the same height.
Both move with the same kinetic energy.
Both move with the same speed.

When both particles fall through same height, they would both have the same speed. The de-Borglie wavelength is

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

Thus for same speed, $\lambda \propto \frac{1}{m}$

Hence options A and D are correct.

The momentum of a particle can be expressed in terms of kinetic energy as

$mv=p=\sqrt{2mK}$

Hence for same kinetic energy,

$\lambda \propto \frac{1}{\sqrt{m}}$

Hence option B is correct.

However when the particles have same linear momentum, $\lambda =\frac{h}{p}$ for both of them.

Hence option C is incorrect.