The linear momentum of a 3 MeV photon is

Options

A. `0.01eVsm^(-1)`
B. `0.02eVsm^(-1)`
C. `0.03eVsm^(-1)`
D. `0.04eVsm^(-1)`

Explanation

To find the linear momentum of a 3 MeV photon, we can use the relationship between energy and momentum for photons. The formula for the momentum \( P \) of a photon is given by:

\[ P = \frac{E}{c} \]

where:
- \( P \) is the momentum,
- \( E \) is the energy of the photon,
- \( c \) is the speed of light in a vacuum (approximately \( 3 \times 10^8 \) m/s).

### Step 1: Convert the energy from MeV to Joules
The energy of the photon is given as 3 MeV. We need to convert this energy into Joules. The conversion factor is:

\[ 1 \text{ MeV} = 1.6 \times 10^{-13} \text{ Joules} \]

So, we calculate:

\[ E = 3 \text{ MeV} = 3 \times 1.6 \times 10^{-13} \text{ Joules} = 4.8 \times 10^{-13} \text{ Joules} \]

### Step 2: Use the momentum formula
Now that we have the energy in Joules, we can substitute it into the momentum formula. We also need to use the speed of light \( c = 3 \times 10^8 \text{ m/s} \):

\[ P = \frac{E}{c} = \frac{4.8 \times 10^{-13} \text{ Joules}}{3 \times 10^8 \text{ m/s}} \]

### Step 3: Calculate the momentum
Now we perform the division:

\[ P = \frac{4.8 \times 10^{-13}}{3 \times 10^8} = 1.6 \times 10^{-21} \text{ kg m/s} \]

### Step 4: Convert the momentum to electron volt meter per second
To convert the momentum from kg m/s to electron volt meter per second, we use the conversion factor:

\[ 1 \text{ Joule} = 6.242 \times 10^{12} \text{ eV} \]

Thus, we convert:

\[ P = 1.6 \times 10^{-21} \text{ kg m/s} \times \frac{6.242 \times 10^{12} \text{ eV}}{1 \text{ Joule}} = 1.0 \times 10^{-8} \text{ eV s/m} \]

### Final Result
The linear momentum of a 3 MeV photon is approximately:

\[ P \approx 1.0 \times 10^{-8} \text{ eV s/m} \]