Question

The momentum of electron is:
A. Directly proportional to wavelength
B. Inversely proportional to wavenumber
C. Inversely proportional to wavelength
D. Cannot be determined

Answer 1

Hint: We have to remember that if an object is moving, then the object has momentum. Momentum is defined as mass in motion, all objects have masses. It depends on the variables, mass and velocity. We have to remember that an electron is a negatively charged elementary particle and it has low mass.

Complete step by step answer:
As we know that Louis de Broglie was a scientist. He derived an equation for the relationship between the wavelength and momentum of matter. The Louis de Broglie equation is commonly used to define the wave properties of matter. And it basically describes the wave nature electron basically. According to de Broglie equation, the wavelength of any object is inversely proportional to its momentum.
$\lambda = \dfrac{h}{{mv}}$
The above equation expressed an electron of mass $m,$moving with velocity $\nu $, should be associated with wavelength having $\lambda $.
Where,
$h$ is a Planck’s constant and
$mv$ is momentum of moving particles.
So the de Broglie relationship can be written as,
$m\nu = \dfrac{h}{\lambda }$
or
$m\nu = \dfrac{1}{\lambda }$
The equations $\lambda = \dfrac{h}{m\nu} $ and $m\nu = \dfrac{1}{\lambda} $, the momentum of a moving particle is inversely proportional to the wavelength of the wave associated with it.
Also momentum ($P$) is \[P = \dfrac{h}{\lambda }\]
Therefore \[P \propto \dfrac{1}{\lambda }\].
So the momentum of an electron is inversely proportional to wavelength.

So, the correct answer is Option C.

Note: We have to remember that the Louis de Broglie equation helps to understand the idea of matter having a wavelength. Light exhibits both wave and particle like properties. The relationship between the wavelength and momentum of matter is derived by Louis de Broglie, called the de Broglie relationship.