A photoelectric cell is illuminated by a point soures of light 1 m away. When the soures is shifted to 2 m then

Options

A. each emitted electron carries one quarter of the initial energy
B. number of electrons emitted is half the initial number
C. each emitted electrons carries half the initial energy
D. number of electrons emitted is quarter of the initial number

Explanation

To solve the problem regarding the effect of distance on the number of electrons emitted from a photoelectric cell when illuminated by a point source of light, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship Between Intensity and Distance**:
The intensity (I) of light from a point source is inversely proportional to the square of the distance (d) from the source. This can be expressed mathematically as:
\[ I \propto \frac{1}{d^2} \]

2. **Identify the Initial and Final Distances**:
Initially, the distance from the light source to the photoelectric cell is 1 meter (d₁ = 1 m). When the source is moved to 2 meters, the new distance is d₂ = 2 m.

3. **Calculate the Change in Intensity**:
Using the relationship from step 1, we can find the initial intensity (I₁) and the final intensity (I₂):
\[ I_1 \propto \frac{1}{(1)^2} = 1 \]
\[ I_2 \propto \frac{1}{(2)^2} = \frac{1}{4} \]
Therefore, when the distance is doubled, the intensity becomes one-fourth of the initial intensity:
\[ I_2 = \frac{1}{4} I_1 \]

4. **Relate Intensity to the Number of Electrons Emitted**:
The number of photoelectrons emitted per second (n) is directly proportional to the intensity of the incident radiation:
\[ n \propto I \]
Thus, if the intensity decreases to one-fourth, the number of emitted photoelectrons will also decrease to one-fourth of the initial number:
\[ n_2 = \frac{1}{4} n_1 \]

5. **Conclusion**:
Therefore, when the light source is moved from 1 meter to 2 meters away, the number of electrons emitted from the photoelectric cell becomes one-fourth of the initial number.

### Final Answer:
The number of electrons emitted is a quarter of the initial number.

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