If the intensity of radiation incident on a photocell be increased four times, then the number of photoelectrons and the energy of photoelectrons emitted respectively become.

Options

A. four times, doubled
B. doubled, remains unchanged
C. remains unchanged, double
D. four times, remains unchanged

Explanation

To solve the problem, we need to analyze how the intensity of radiation affects the number of photoelectrons emitted and their energy.

### Step-by-Step Solution:

1. **Understanding Intensity and Number of Photons:**
- The intensity of radiation is directly proportional to the number of photons incident on the surface of the photocell.
- Mathematically, we can express this as:
\[ I \propto N \]
where \( I \) is the intensity and \( N \) is the number of photons.

2. **Increasing Intensity:**
- If the intensity of radiation is increased four times, we can denote the new intensity as:
\[ I' = 4I \]
- Since the number of photons is directly proportional to the intensity, the new number of photons \( N' \) will also be four times the original number of photons \( N \):
\[ N' = 4N \]

3. **Photoelectrons Emitted:**
- The number of photoelectrons emitted is directly proportional to the number of incident photons. Therefore, if the number of photons increases four times, the number of emitted photoelectrons will also increase four times:
\[ N_{\text{photoelectrons}}' = 4N_{\text{photoelectrons}} \]

4. **Energy of Photoelectrons:**
- The energy of the emitted photoelectrons depends on the energy of the incident photons, which is given by:
\[ E = \frac{hc}{\lambda} \]
where \( h \) is Planck's constant, \( c \) is the speed of light, and \( \lambda \) is the wavelength of the incident light.
- This energy is independent of the intensity of the radiation. Therefore, even after increasing the intensity, the energy of the emitted photoelectrons remains unchanged:
\[ E' = E \]

5. **Final Conclusion:**
- Thus, if the intensity of radiation incident on a photocell is increased four times, the number of photoelectrons emitted becomes four times, while the energy of the photoelectrons remains unchanged.

### Summary of Results:
- Number of photoelectrons: **Four times the original**
- Energy of photoelectrons: **Unchanged**