If E and P are the energy and the momentum of a photon respectively,then on reducing the wavelength of photon

Options

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

Answer

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

### Step-by-Step Solution:

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

2. **Analyzing the Effect of Reducing Wavelength**:
- When the wavelength (λ) of the photon is reduced, we can observe the effects on energy and momentum.
- From the energy equation, if λ decreases, E will increase because E is inversely proportional to λ.
- From the momentum equation, if λ decreases, P will also increase for the same reason.

3. **Conclusion**:
- Therefore, when the wavelength of the photon is reduced, both the energy (E) and momentum (P) of the photon will increase.

### Final Answer:
When the wavelength of a photon is reduced, both the energy (E) and momentum (P) will increase.

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