Question

The de-Broglie wavelength associated with a material particle is:
A. Inversely proportional to momentum
B. Inversely proportional to its energy
C. Directly proportional to momentum
D. Directly proportional to the energy

Answer 1

Before going through the question let us first have an idea about wavelength. The distance between two consecutive crests or troughs is the wavelength of a wave. It is calculated in the wave's direction.

Complete answer:
Let's start by learning about the de-Broglie wavelength. The de-Broglie wavelength is described as the ability of all particles to exhibit wave-like properties. The de Broglie wavelength of a particle specifies the length scale at which its wave-like properties are important. The symbol $\lambda$ or${\lambda _{dB}}$ is commonly used to describe the De Broglie wavelength. The de Broglie wavelength for a particle with momentum $p$ is defined as:
${\lambda _{dB}} = \dfrac{h}{p}$
where $p$ is the Planck constant.
Now, it’s clear above from his equation that the magnitude of a particle's angular momentum is inversely proportional to the wavelength of a matter wave associated with that particle. The particle's speed is equal to the speed of the matter wave.

So, the correct answer is option A.

Note: Now the question is, what is the most significant implementation of the de Broglie concept? Its most common use is in the creation of electron microscopes, which are used to measure very small artefacts.de Broglie wavelength is an important concept while studying quantum mechanics. The wavelength (λ) that is associated with an object in relation to its momentum and mass is known as de Broglie wavelength. A particle’s de Broglie wavelength is usually inversely proportional to its force.