A metal surface is illuminated by a light of given intensity and frequency to cause photoemission. If the intensity of illumination is reduced to one-fourth of its original value, then the maximum KE of emitted photoelectrons will become.

Options

A. `((1)/(16))`th of original value
B. unchanged
C. twice the original value
D. four times the original value

Explanation

To solve the problem, we need to analyze the relationship between the intensity of light, the frequency of light, and the kinetic energy of emitted photoelectrons in the context of the photoelectric effect.

### Step-by-Step Solution:

1. **Understanding the Photoelectric Effect**:
- The photoelectric effect describes the emission of electrons from a metal surface when it is illuminated by light of sufficient frequency. The energy of the incoming photons is given by the equation:
\[ E = hf \]
where \(E\) is the energy of the photon, \(h\) is Planck's constant, and \(f\) is the frequency of the light.

2. **Energy Relation**:
- The maximum kinetic energy (KE) of the emitted photoelectrons can be expressed as:
\[ KE_{\text{max}} = hf - W \]
where \(W\) is the work function of the metal. The work function is the minimum energy required to remove an electron from the metal surface.

3. **Effect of Intensity**:
- The intensity of light is related to the number of photons hitting the surface per unit time. If the intensity is reduced to one-fourth, it means that the number of photons hitting the surface per unit time is also reduced to one-fourth, assuming the frequency remains constant.
- However, the energy of each individual photon is determined by its frequency, not the intensity. Therefore, reducing the intensity does not affect the energy of each photon.

4. **Kinetic Energy Independence**:
- Since the maximum kinetic energy of the emitted photoelectrons depends only on the frequency of the light and the work function of the metal, and not on the intensity, we can conclude that:
\[ KE_{\text{max}} \text{ remains unchanged.} \]

5. **Final Conclusion**:
- Thus, when the intensity of illumination is reduced to one-fourth of its original value, the maximum kinetic energy of the emitted photoelectrons will remain the same.

### Final Answer:
The maximum kinetic energy of emitted photoelectrons will remain unchanged.

---