Question

If c is the velocity of light in free space, the correct statements about photon among the following are:
A. The energy of a photon is E = hν.
B. The velocity of a photon is c.
C. The momentum of a photon, \(p=\frac{hv}{c}\).
D. In a photon-electron collision, both total energy and total momentum are conserved.
E. Photon possesses positive charge.
Choose the correct answer from the options given below:

• A. A and B only
• B. A, B, C and D only
• C. A, C and D only
• D. A, B, D and E only

Answer 1

The Correct Option is B

The correct answer is Option 2: A, B, C, and D only. Let’s evaluate each statement step by step:

Statement Analysis

• A: The energy of a photon is E = hν.

  This is true. The energy of a photon is given by E = hν, where h is Planck’s constant and ν is the frequency.

• B: The velocity of a photon is c.

  This is true. Photons travel at the speed of light, c ≈ 3 x 10^8 m/s, in free space.

• C: The momentum of a photon, p = hν/c.

  This is true. Momentum is derived as p = hν/c, consistent with E = pc.

• D: In a photon-electron collision, both total energy and total momentum are conserved.

  This is true. Conservation laws hold in processes like Compton scattering.

• E: Photon possesses positive charge.

  This is false. Photons are electrically neutral.

Evaluating Options

• Option 1: A and B only – Incorrect, excludes true statements C and D.
• Option 2: A, B, C, and D only – Correct, includes all true statements and excludes false E.
• Option 3: A, C, and D only – Incorrect, excludes true statement B.
• Option 4: A, B, D, and E only – Incorrect, includes false statement E.

Final Answer

Option 2: A, B, C, and D only

Answer 2

Step 1: Verify Statement A - Photon Energy 

From Planck’s equation, the energy of a photon is given by:

$$ E = h \nu $$

• h = Planck’s constant
• \(\nu\) = Frequency of the photon

Since this is a fundamental relation, Statement A is correct.

Step 2: Verify Statement B - Velocity of a Photon

In free space, all photons travel at the speed of light:

$$ c = 3.0 \times 10^8 \text{ m/s} $$

Thus, Statement B is correct.

Step 3: Verify Statement C - Photon Momentum

A photon's momentum is given by:

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

Since this equation is derived from special relativity, Statement C is correct.

Step 4: Verify Statement D - Conservation of Energy and Momentum

During a photon-electron collision (e.g., Compton effect), both total energy and total momentum are conserved. This is a fundamental principle of quantum mechanics.

Thus, Statement D is correct.

Step 5: Verify Statement E - Charge of a Photon

A photon is a neutral elementary particle; it has no charge. The statement that a photon possesses a positive charge is incorrect.

Thus, Statement E is incorrect.

Step 6: Conclude

The correct statements are A, B, C, and D. Hence, the correct answer is option (2).