Question

ASSERTION: The de Broglie equation is having significance for any microscopic or submicroscopic particles.
REASON: The de Broglie wavelength is inversely proportional to the mass of the object when the velocity is a constant.
A. both the assertion and reason are correct and reason is the correct explanation for this question.
B. both the assertion and reason are correct but the reason is not the correct explanation for this question
C. assertion is correct but reason is incorrect
D. both the assertion and the reason is incorrect.

Answer 1

Hint: Mass of microscopic and submicroscopic particles is negligibly small. Therefore according to De Broglie’s equation, these particles are trying to behave like a wave with a particular finite wavelength. The equation for De Broglie wavelength is given as,
$\lambda =\dfrac{h}{mv}$
These all will help us to solve this question.

Complete step-by-step answer:
De Broglie’s equation of particle is given by the formula,
$\lambda =\dfrac{h}{mv}$
Where $\lambda $be the wavelength, $m$ be the mass of the particle and $v$ is the velocity of a particle.
Therefore from this equation we can derive a relationship between the wavelength of the object and the mass of the particle.
As Planck’s constant and velocity of object are constants, the wavelength of light will be inversely proportional to the mass of the particle. That is,
$\lambda \propto \dfrac{1}{m}$
In the case of microscopic particles, as their mass is negligible, the wavelength will be in significant amount so that the De Broglie’s equation will be having significance. Therefore we can conclude that both the assertion and reason are correct and the reason is the correct explanation for the assertion.

So, the correct answer is “Option A”.

Note: In the case of macroscopic particles like table and chair, as their mass is very high the wavelength of the object is very small. So the de Broglie equation is not having any significance here. De Broglie’s equation implies the dual nature of particles.