A photocell is illuminated by a small bright source placed 1m away. When the same source of light is placed (1/2)m away, the number of electrons emitted by photocathode would

Options

A. decrease by a factor of 2
B. increase by a factor of 2
C. decrease by a factor of4
D. icrease by a factor of 4

Answer

D

Explanation

`I = (P)/( 4pi d ^(2))`
Here, we assume light to spread uniformly in all directions. The number of photo-electrons emitted from a surface depends on the intensity of light I falling on it. Thus, the number of electrons emitted n depends directly on I. Premains constant as the source is the same.
`therefore ( I _(2))/( I _(1)) = ( n _(2))/( n _(1)) implies ( P _(2))/( P _(1)) ((d _(1))/( d _(2))) ^(2) = (n _(2))/( n _(1))`
`therefore ( n _(2))/( n _(1)) = ((P)/(P)) ((1)/(1//2))^(2) = (4)/(1)`
`(because P _(1) = P _(2) = P)`