Question

Assertion: Mass of moving photon varies inversely as the wavelength.
Reason: Energy of the particle = Mass $\times \text{speed of light}^2$
A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true but R is not correct explanation of A
C. A is true but R is false
D. A and R are false

Answer 1

Hint: In order to solve this question, we have to consider relativistic mechanics as a photon is a relativistic particle since it has zero rest mass and also wavelength of the moving particle is given by de-broglie relation so, using these two concepts we will determine the correctness of assertion and reason.

Complete step by step solution:
In 1923, Louis De Broglie proposed that light behaves simultaneously as a particle and a wave. This theory is known as the wave-particle duality of light. The wave-particle duality of light is one of the most fundamental concepts in quantum mechanics. In the early 1800s, scientists believed that light was a wave. However, in the late 1800s, scientists discovered that light could also behave as a particle. This raised the question of how light could be both a wave and a particle.

The wave-particle duality of light is due to the fact that light is a quantum object. A quantum object can have both wave-like and particle-like properties. In the case of light, the wave-like properties are due to the fact that light consists of energy packets (photons). The particle-like properties are due to the fact that photons can be individually detected.

The wave-particle duality of light has been experimentally verified many times. One of the most famous experiments was the double-slit experiment. In this experiment, light is passed through two slits. The pattern of the light that is observed on the other side of the slits is a result of the wave-like properties of light. The interference pattern is caused by the fact that the photons from the light beam are interfering with each other. For example, light can be diffracted like a wave, as seen in the famous double-slit experiment. However, light can also be detected as a particle, as shown by the photoelectric effect.

We all know the famous De Broglie wavelength equation that is $p = \dfrac{h}{\lambda }$ . Here, $p = {\text{momentum}},{\text{ h = planck constant, }}\lambda {\text{ = wavelength}}$. So we can say ${\text{m }}\infty \dfrac{\text{1}}{{\lambda }}$ . So the assertion is true. We all know the famous formula of Einstein that Energy of the particle = Mass $\times \text{speed of light}^2$, so the reason is also correct. But it is not reason of the assertion.

Hence option B is the correct option.

Note: In order to solve this problem, we must have to know the concept of the theory of relativity and De-Broglie wavelength equation and these two theories are very important in Physics. Also we should know about the basic concepts of photons such as they are massless, always move at the speed of light in vacuum, the rest mass of photons is zero in space etc.