If the energy of a photon is E, then its momentum is (c is velocity of light )

Options

A. E/c
B. E/2c
C. 2E/c
D. It has no momentum

Answer

To find the momentum of a photon given its energy \( E \), we can follow these steps:

### Step-by-Step Solution

1. **Understand the relationship between energy and wavelength**:
The energy \( E \) of a photon can be expressed in terms of its wavelength \( \lambda \) using the equation:
\[ E = \frac{hc}{\lambda} \]
where \( h \) is Planck's constant and \( c \) is the speed of light.

2. **Use de Broglie's hypothesis**:
According to de Broglie's hypothesis, the wavelength \( \lambda \) of a particle (or photon) is related to its momentum \( p \) by the equation:
\[ \lambda = \frac{h}{p} \]
Rearranging this gives us:
\[ p = \frac{h}{\lambda} \]

3. **Substitute the expression for wavelength into the momentum equation**:
From the energy equation, we can express \( \lambda \) in terms of \( E \):
\[ \lambda = \frac{hc}{E} \]
Now substituting this expression for \( \lambda \) into the momentum equation:
\[ p = \frac{h}{\lambda} = \frac{h}{\frac{hc}{E}} = \frac{E}{c} \]

4. **Final result**:
Therefore, the momentum \( p \) of the photon can be expressed as:
\[ p = \frac{E}{c} \]

### Conclusion
The momentum of a photon with energy \( E \) is given by:
\[ p = \frac{E}{c} \]