Question

A 10 W line source emits monochromatic light of wavelength 4000 AA when placed 1.0 m away from a photosensitive surface it liberates photoelectrons from surface.When the same source is moved 2.0 m away from same surface number of photoelectrons liberated reduce by a factor of​

Answer 1

Given:

A 10 W line source emits monochromatic light of wavelength 4000 A° when placed 1.0 m away from a photosensitive surface it liberates photoelectrons from surface.

To find:

When the same source is moved 2.0 m away from same surface number of photoelectrons liberated reduce by a factor of ?

Calculation:

We can say that the number of electrons ejected per unit time is directly proportional to the intensity of the light source.

Now , for a point light source the intensity is inversely proportional to the square of the distance.

Let number of photoelectrons emitted per unit time be denoted as N :

$\boxed{ \bold {\therefore \: N \propto \dfrac{1}{ {d}^{2} } }}$

So, taking corresponding ratios :

$\rm \therefore \: \dfrac{N_{1} }{ N_{2}} = \dfrac{ {( d_{2}) }^{2} }{ {(d_{1})}^{2} }$

$\rm \implies\: \dfrac{N_{1} }{ N_{2}} = \dfrac{ {(2) }^{2} }{ {(1)}^{2} }$

$\rm \implies\: \dfrac{N_{1} }{ N_{2}} = 4$

$\rm \implies\: \dfrac{N_{2} }{ N_{1}} = \dfrac{1}{4}$

$\rm\implies\: N_{2}=\dfrac{1}{4}N_{1}$

So, the number of photoelectrons emitted(when source is kept at 2m) becomes ¼th the initial value.

Hence , the value reduces by a factor of 4.