The energy of a photon is `E = hv` and the momentum of photon `p = (h)/(lambda)` , then the velocity of photon will be

Options

A. `E//p`
B. `Ep`
C. `((E )/(P))^(2)`
D. `3 xx 10^(8) m//s`

Explanation

To find the velocity of a photon using the given relationships for energy and momentum, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Relationships**:
- The energy of a photon is given by the equation:
\[ E = h \nu \]
where \( E \) is the energy, \( h \) is Planck's constant, and \( \nu \) (nu) is the frequency of the photon.
- The momentum of a photon is given by the equation:
\[ p = \frac{h}{\lambda} \]
where \( p \) is the momentum and \( \lambda \) is the wavelength of the photon.

2. **Relate Velocity to Frequency and Wavelength**:
- The velocity \( v \) of a photon can be expressed as:
\[ v = \nu \lambda \]
- Here, \( v \) is the velocity, \( \nu \) is the frequency, and \( \lambda \) is the wavelength.

3. **Express Frequency in Terms of Energy**:
- From the energy equation, we can express frequency as:
\[ \nu = \frac{E}{h} \]

4. **Express Wavelength in Terms of Momentum**:
- From the momentum equation, we can express wavelength as:
\[ \lambda = \frac{h}{p} \]

5. **Substitute Frequency and Wavelength into the Velocity Equation**:
- Now, substitute the expressions for frequency and wavelength into the velocity equation:
\[ v = \nu \lambda = \left(\frac{E}{h}\right) \left(\frac{h}{p}\right) \]

6. **Simplify the Equation**:
- The \( h \) in the numerator and denominator cancels out:
\[ v = \frac{E}{p} \]

7. **Conclusion**:
- Therefore, the velocity of the photon is given by:
\[ v = \frac{E}{p} \]

### Final Answer:
The velocity of the photon is \( v = \frac{E}{p} \).

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