Question

Photocell cell is enlightended by small bright source \(1 \mathrm{~m}\) away. If the same light source is placed \((1 / 2) \mathrm{m}\) away, number of electrons emitted by cathode will be........ (A) increases twice (B) decreases twice (C) increases 4 times (D) decreases 4 times

Short answer

The number of electrons emitted by the cathode will increase 4 times when the same light source is placed at half the distance from the photocell. This is because the new intensity of light becomes 4 times stronger due to the inverse square law, which directly impacts the number of emitted electrons. The correct answer is (C) increases 4 times.

Step-by-step solution

Understand the inverse square law for light intensity

The inverse square law states that the intensity (I) of light is proportional to the inverse square of the distance (d) from the light source. Mathematically, it is given by: \(I ∝ \frac{1}{d^2}\) When the distance changes, the intensity of light also changes. We can use this principle to find the new intensity of light (I') when the light source is placed at half the distance.

Determine the change in the intensity of light

Initially, the light source is placed at a distance of 1 m. The new distance d' is given as: \(d'= \frac{1}{2} m \) To determine the change in intensity, first find the ratio between the initial and new distance squares: \(\frac{d'^2}{d^2} = \frac{\left(\frac{1}{2}\right)^2}{1^2}\) Now, simplify the expression: \(\frac{d'^2}{d^2} = \frac{1}{4}\) According to the inverse square law, the intensity of light is inversely proportional to the square of the distance. Therefore, the new intensity (I') will be 4 times stronger than the initial intensity (I).

Calculate the change in the number of emitted electrons

The number of emitted electrons is directly proportional to the intensity of light. As the new intensity is 4 times stronger than the initial intensity, the number of emitted electrons will also increase by 4 times. So, the correct answer is (C) increases 4 times.