The momentum of a photon of energy `1 MeV` "in"` kg m//s` will be

Options

A. `0.33 xx 10^(6)`
B. `7 xx 10^(-24)`
C. `10^(-22)`
D. `5 xx 10^(-22)`

Answer

To find the momentum of a photon with an energy of 1 MeV, we can use the relationship between energy (E), momentum (p), and the speed of light (c). The formula we will use is:

\[ E = pc \]

Where:
- \( E \) is the energy of the photon,
- \( p \) is the momentum of the photon,
- \( c \) is the speed of light, approximately \( 3 \times 10^8 \, \text{m/s} \).

### Step-by-Step Solution:

1. **Convert Energy from MeV to Joules**:
The energy of the photon is given as \( 1 \, \text{MeV} \). We need to convert this to joules. The conversion factor is:
\[ 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \]
Therefore,
\[ 1 \, \text{MeV} = 1 \times 10^6 \, \text{eV} = 1 \times 10^6 \times 1.6 \times 10^{-19} \, \text{J} \]
\[ E = 1.6 \times 10^{-13} \, \text{J} \]

2. **Use the Energy-Momentum Relation**:
From the equation \( E = pc \), we can rearrange it to find momentum:
\[ p = \frac{E}{c} \]

3. **Substitute the Values**:
Now, substituting the values of \( E \) and \( c \):
\[ p = \frac{1.6 \times 10^{-13} \, \text{J}}{3 \times 10^8 \, \text{m/s}} \]

4. **Calculate the Momentum**:
Performing the division:
\[ p = \frac{1.6}{3} \times 10^{-13} \times 10^{-8} \]
\[ p = \frac{1.6}{3} \times 10^{-21} \]
\[ p \approx 0.533 \times 10^{-21} \, \text{kg m/s} \]
\[ p \approx 5.33 \times 10^{-22} \, \text{kg m/s} \]

5. **Final Answer**:
The momentum of the photon is approximately:
\[ p \approx 5.33 \times 10^{-22} \, \text{kg m/s} \]