Question

The number of electrons emitted by cathods in a photo tube is 3.0 x 104 when it is illuminated
by a small bright source placed 50 cm away. If the source is carried to a distance of 100 cm,
the number of electrons emitted by photocathode would be

Answer 1

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{3\times10^{4}}{(Number\ of\ incident\ electrons\ finally)} =({\frac{50}{100}})^2$$12\times10^{4}=Number\ of\ incident\ electrons\ finally$

Hence, the number of electrons emitted by photocathode finally will be 12 × 10⁴.

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