Question

The wavelength of the matter wave is independent of
(A) Mass
(B) Velocity
(C) Momentum
(D) Charge

Answer 1

To find the dependency of one quantity on another quantity, don’t use theoretical analysis directly.
Formula used:
For the dependency of the matter wave with other quantities,
${{\lambda = }}\dfrac{{{h}}}{{{{mv}}}}$
where m = mass of the matter waves,
v = velocity of the matter
h = Planck’s constant.
Then relate the formula with other quantities and find out the required relation.

Complete step by step answer:
The wavelength of the matter waves depends upon the mass of the matter waves and the velocity of the waves.
WKT, the formula for wavelength of the matter wave is given by
${{\lambda = }}\dfrac{{{h}}}{{{{mv}}}}$

We also know that the product of mass and velocity is momentum. Momentum is represented by ${{p}}$. Formula for momentum is given by
${{p = m \times v}}$

Since the product of mass (m) and the velocity (v) of the matter wave is momentum (p). Therefore, the wavelength of the matter waves also depends upon momentum.
Thus, the wavelength of the matter wave is dependent on the mass (m), velocity (v) and momentum (p) but not on charge (q) or wavelength of the matter wave is independent of charge.

Hence, the correct answer is option (D).

Note: Since Planck’s constant is a constant, so wavelength of the matter wave does not depend upon a constant quantity but depends upon variable quantity. As mass (m) and velocity (v) are the variable quantities. Therefore, the wavelength of the matter waves will depend upon the mass, velocity and the product of the mass and velocity i.e. momentum.