Assertion (A) : The energy (E ) and momentum (p) of a photon are related as `p= E//c`
Reason (R ): The photon behaves like a particle.

Options

A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true and R is NOT the correct explanation of A
C. A is true but R is false
D. A is false and R is true

Explanation

To solve the assertion and reason question regarding the relationship between the energy and momentum of a photon, we will analyze both the assertion (A) and the reason (R) step by step.

### Step 1: Understanding the Assertion
The assertion states that the energy (E) and momentum (p) of a photon are related as:
\[ p = \frac{E}{c} \]
where \( c \) is the speed of light.

### Step 2: Deriving the Relationship
To derive this relationship, we start with the known equations for energy and momentum of a photon:
1. The energy of a photon is given by:
\[ E = h \nu \]
where \( h \) is Planck's constant and \( \nu \) is the frequency of the photon.

2. The momentum of a photon can be expressed as:
\[ p = \frac{E}{c} \]
This is derived from the relationship between energy and momentum in the context of special relativity.

### Step 3: Verifying the Assertion
From the above equations, we can see that:
\[ p = \frac{E}{c} \]
This confirms that the assertion is true.

### Step 4: Understanding the Reason
The reason states that "the photon behaves like a particle."

### Step 5: Justifying the Reason
Photons, although massless, exhibit particle-like properties. The momentum of a photon can be expressed using the formula:
\[ p = mv \]
However, since photons do not have mass (m = 0), we use the relationship derived from energy:
\[ p = \frac{E}{c} \]
This indicates that photons can be treated as particles in certain contexts, particularly when considering their momentum and energy.

### Step 6: Conclusion
Both the assertion (A) and the reason (R) are true, and the reason correctly explains the assertion. Therefore, the correct answer is that both A and R are true, and R is the correct explanation of A.

### Final Answer
Both the assertion and reason are true, and the reason is the correct explanation of the assertion.

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