Question

a photocell is illuminated by small bright source placed 1m away.when the source of light placed 1/2m away,the number of electrons emitted by photocathode would 1) increase by a factor of 2. 2) decrease by a factor of 2. 3) increase by 4. 4) decrease by 4​

Answer 1

Explanation:

When source is placed 2m away, then I′=I/4. The number of electrons emitted is directly proportional to intensity. Hence, number of emitted electrons is reduced to one-fourth.

Answer 2

Solution :-

Small bright source of light can be considered as a spherical light source.

We know that :-

1. Intensity of light emitted by a spherical source at a distance 'r' is inversely proportional to r².
2. Also, number of photons incident on the photo tube will vary directly to the intensity of light at a distance 'r'.
3. And, number of emitted electrons will also depend directly on number of emitted photons.

Concluding all three statements, we came to the fact that number of emitted electrons from the influence of a point source at a distance 'r' is inversely proportional to r².

Hence,

$\frac{(Number\ of\ incident\ electrons\ initially)}{(Number\ of\ incident\ electrons\ finally)} =({\frac{Initially\ separation}{Final\ separation}})^2$

$\frac{(Number\ of\ incident\ electrons\ initially)}{(Number\ of\ incident\ electrons\ finally)} =({\frac{1}{(1/2)}})^2$

$Number\ of\ incident\ electrons\ initially=Number\ of\ incident\ electrons\ finally\times4$

Hence, the number of electrons emitted by photocathode would increase by a factor of 4.

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