If E and P are the energy and the momentum of a photon respectively then on increasing the wavelenght of photon

Options

A. p and E both will decrease
B. p and E both will increase
C. p will increase and E will decrese
D. p will decrease and E will increase

Answer

To solve the problem, we need to analyze the relationships between the energy (E) and momentum (P) of a photon and its wavelength (λ).

### Step-by-Step Solution:

1. **Understand the Relationships**:
- The energy of a photon is given by the formula:
\[ E = \frac{hc}{\lambda} \]
where:
- \(E\) is the energy,
- \(h\) is Planck's constant,
- \(c\) is the speed of light,
- \(\lambda\) is the wavelength of the photon.

- The momentum of a photon is given by the formula:
\[ P = \frac{h}{\lambda} \]
where:
- \(P\) is the momentum.

2. **Analyze the Effect of Increasing Wavelength**:
- When the wavelength \(\lambda\) increases, we can observe the following:
- For energy \(E\):
\[ E = \frac{hc}{\lambda} \]
As \(\lambda\) increases, the denominator increases, which means \(E\) will decrease.

- For momentum \(P\):
\[ P = \frac{h}{\lambda} \]
Similarly, as \(\lambda\) increases, the denominator increases, which means \(P\) will also decrease.

3. **Conclusion**:
- Therefore, if the wavelength of the photon increases, both the energy \(E\) and momentum \(P\) will decrease.

### Final Answer:
On increasing the wavelength of a photon, both the energy \(E\) and momentum \(P\) will decrease.

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