AIIMS 2005 Physics Photon Properties Assertion Reason Question

To understand the assertion and reason given in the question, let's analyze each part carefully.

Assertion:

The energy (E) and momentum (p) of a photon are related by $p = \frac{E}{c}$.

Explanation of the Assertion:

This statement is true. In quantum physics, a photon, which is a quantum of light, has both energy and momentum. The energy $E$ of a photon is given by the equation:

$$E = hf$$

where $h$ is Planck's constant and $f$ is the frequency of the photon. The momentum $p$ of a photon can be expressed as:

$$p = \frac{E}{c}$$

where $c$ is the speed of light in a vacuum. This relationship arises from the fact that photons are massless particles, and their momentum is directly proportional to their energy divided by the speed of light.

Reason:

The photon behaves like a particle.

Explanation of the Reason:

This statement is also true. Photons exhibit both wave-like and particle-like properties, a phenomenon known as wave-particle duality. As particles, photons can be thought of as discrete packets of energy, which allows them to interact with matter and carry momentum.

Conclusion:

Since both the assertion and the reason are true, and the reason correctly explains the assertion (the behavior of photons as particles is foundational to the relationship between energy and momentum), the correct answer is:

A) Both assertion and reason are true and reason is the correct explanation of assertion.

Clarification of Other Options:

• Option B: Both assertion and reason are true but reason is not the correct explanation of assertion.

  • This option is incorrect because the reason does indeed explain why the relationship $p = \frac{E}{c}$ holds, relating to the particle-like behavior of photons.

• Option C: Assertion is true but reason is false.

  • This option is incorrect because both the assertion and reason are true.

• Option D: Both assertion and reason are false.

  • This option is incorrect because we have established that both statements are true.

Summary of Relevant Concepts:

1. Photon Energy: $E = hf$
2. Photon Momentum: $p = \frac{E}{c}$
3. Wave-Particle Duality: Photons exhibit both wave-like and particle-like characteristics.

By understanding these concepts, it becomes clear why the answer is A. The relationship between energy and momentum for photons is a fundamental aspect of quantum mechanics, underlining their dual nature.