Question

The momentum of a photon of energy 1 MeV in kg m/s, will be :

• A. 0.33 x 10⁶
• B. 8 x 10^-24
• C. 5 x 10^-23
• D. 5 x 10^-22

Answer 1

The Correct Option is D

To determine the momentum of a photon with energy 1 MeV, we can use the relation between the energy (E) and momentum (p) of a photon, given by:

E = pc

Where:

• E is the energy of the photon.
• p is the momentum of the photon.
• c is the speed of light in a vacuum, approximately 3 \times 10^8 \, \text{m/s}.

Step 1: Convert energy from MeV to joules.

1 MeV = 1.602 \times 10^{-13} \, \text{J}

Hence, E = 1 \, \text{MeV} = 1.602 \times 10^{-13} \, \text{J}.

Step 2: Use the energy-momentum relation.

Rearrange the formula E = pc to solve for p:

p = \frac{E}{c}

Substituting the values:

p = \frac{1.602 \times 10^{-13}}{3 \times 10^8}

Step 3: Calculate the momentum.

Simplifying the expression:

p \approx \frac{1.602}{3} \times 10^{-21} = 0.534 \times 10^{-21} \, \text{kg m/s}

Rounding to appropriate significant figures gives:

p \approx 5.3 \times 10^{-22} \, \text{kg m/s}, which is approximately equal to 5 \times 10^{-22} \, \text{kg m/s}.

Conclusion:

The momentum of a photon with energy 1 MeV is approximately 5 \times 10^{-22} \, \text{kg m/s}, which matches the given correct answer option.