Question

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

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

Answer 1

The Correct Option is D

The problem involves understanding the effect of distance on the intensity of light and the resulting photoelectric effect. Here, we are analyzing the change in the number of electrons emitted when a point source of light illuminating a photoelectric cell is moved from 1 meter to 2 meters away.

1. The intensity of light I from a point source is inversely proportional to the square of the distance r from the source. This is described by the formula:
   I \propto \frac{1}{r^2}
2. Initially, when the light is at a 1-meter distance:
   I_1 \propto \frac{1}{1^2} = 1
3. When the source is moved to a distance of 2 meters:
   I_2 \propto \frac{1}{2^2} = \frac{1}{4}
   This means the intensity of light at 2 meters is one-fourth of that at 1 meter.
4. According to the photoelectric effect, the number of electrons emitted n is directly proportional to the intensity of the incoming light. Therefore, if the intensity becomes one-fourth, the number of emitted electrons also becomes one-fourth.
5. Based on this reasoning, when the distance is doubled from 1 meter to 2 meters, the number of electrons emitted becomes one-fourth of the initial number.

Conclusion: The correct answer is that the number of electrons emitted is a quarter of the initial number. This corresponds to option: "number of electrons emitted is a quarter of the initial number".