Assertion : The kinetic energy of a photoelectron decrease with increases with increase in the wavelength of incident light.
Reason : All photoelectrons are not emitted with the same speed because of the range of wavelength in the white light.

Options

A. If both assertion and reason are correct and reason is a correct explanation of the assertion.
B. If both assertion and reason are correct but reason is not the correct explanation of assertion.
C. If assertion is correct but reason is incorrect
D. If assertion is incorrect but reason is correct.

Answer

To solve the question regarding the assertion and reason related to the photoelectric effect, we can break it down step by step.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that "The kinetic energy of a photoelectron decreases with an increase in the wavelength of incident light."
- According to the photoelectric effect, the kinetic energy (K.E.) of the emitted photoelectrons is given by the equation:
\[ K.E. = h\nu - \phi \]
where \(h\) is Planck's constant, \(\nu\) is the frequency of the incident light, and \(\phi\) is the work function of the material.

2. **Relating Wavelength and Frequency**:
- The frequency \(\nu\) is related to the wavelength \(\lambda\) by the equation:
\[ \nu = \frac{c}{\lambda} \]
where \(c\) is the speed of light.
- Thus, as the wavelength \(\lambda\) increases, the frequency \(\nu\) decreases.

3. **Effect on Kinetic Energy**:
- From the equation \(K.E. = h\nu - \phi\), if \(\nu\) decreases (due to an increase in \(\lambda\)), the kinetic energy \(K.E.\) will also decrease, assuming the work function \(\phi\) remains constant.
- Therefore, the assertion is correct: the kinetic energy of a photoelectron decreases with an increase in the wavelength of incident light.

4. **Understanding the Reason**:
- The reason states that "All photoelectrons are not emitted with the same speed because of the range of wavelengths in white light."
- White light consists of multiple wavelengths (and thus multiple frequencies), which means that photoelectrons emitted due to different wavelengths will have different kinetic energies and speeds.

5. **Evaluating the Relationship**:
- While both the assertion and reason are correct, the reason does not explain the assertion directly. The assertion is based on the relationship between wavelength and kinetic energy, while the reason discusses the variability in speeds of photoelectrons due to the spectrum of white light.
- Hence, the reason is correct but does not serve as a correct explanation for the assertion.

### Conclusion:
- Both the assertion and reason are correct, but the reason is not the correct explanation of the assertion.

### Final Answer:
- The correct option is: **Both assertion and reason are correct, but reason is not the correct explanation of assertion.**

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