Question

The wavelength of matter waves does not depend on
A. Momentum
B. velocity
C. Mass
D. Charge

Answer 1

Hint: We can solve this problem with the concept of matter wave which is the important topic in quantum mechanics. In the earlier time it was considered that light has only wave like property and small particles have only matter property but after the time of De Broglie, it is crystal clear that the light and matter both can have wave like and the particle like nature. Any moving particle either is heavy or light will be associated with the wave property, hence this type of wave called matter wave.

Complete step-by-step answer:
 According to Louis de Broglie, all matter exhibits wave-like properties and behaviour for example electrons have the diffraction phenomena such as light. His hypothesis is called the De Broglie hypothesis. The wavelength associated with matter wave is related to its momentum and the plank constant such as: $\lambda = \dfrac{h}{p} = \dfrac{h}{{mv}}$ ,
Where $m$ is the mass of a particle ,$v$ is the velocity of a particle, $p$ is the momentum and $h$ is planck constant. From this equation it is clear that the wavelength of the matter wave is dependent upon the momentum, mass and velocity of particles and it does not depend on the charge. So for the given question,
The correct answer is option D.

Note: From the above discussions, it is clear that the particles have dual nature. Hence the wavelength of the matter wave does not depend on charge because the wave is always dependent on momentum, velocity and mass. It is clear from the De Broglie hypothesis that particles have dual nature.