Question

A photocell is receiving light from a source placed at a distance of 1m. If the same source is to be placed at a distance of 2m, then the ejected electrons:
A) Moves with one-fourth energy as that of the initial energy.
B) Moves with one-fourth of momentum as that of the initial momentum
C) Will be half in number
D) Will be one-fourth in number

Answer 1

Hint: Photocell is an optoelectronic device that works on the principle of photoelectric effect. In photocell the intensity of ejected electrons varies inversely proportional with the distance as:
\[I \propto \dfrac{1}{{{d^2}}}\], where I is intensity of the source and d is the separation of photocell from the source

Complete answer:
Since, the number of electrons ejected from the photocell is inversely proportional to the square of the distance between source and the photocell.
i.e. \[I \propto \dfrac{1}{d^2}\]……………… (i)
\[\Rightarrow I \propto n\]………………………….. (ii)
(where n is the number of electrons ejected)
From equation (i) and equation (ii), we have
\[\Rightarrow n \propto \dfrac{1}{{{d^2}}}\]
\[\Rightarrow n = k\dfrac{1}{{{d^2}}}\]…………………… (iii)
Calculate the ratio of number of electrons emitted in case 1 to case 2.
\[ \Rightarrow \dfrac{{{n_1}}}{{{n_2}}} = {\left( {\dfrac{{{d_2}}}{{{d_1}}}} \right)^2}\]…………………………….(iv)
Substitute the values: \[{d_1} = 1m\] and \[{{\text{d}}_2} = 2m\] in equation (iv), we get
\[\Rightarrow \dfrac{{{n_1}}}{{{n_2}}} = {\left( {\dfrac{2}{1}} \right)^2}\]
\[\Rightarrow {n_2} = \dfrac{{{n_1}}}{4}\]
Therefore, one-fourth electrons will eject.

Hence, option (D) is the correct answer.

Note: Photocells produce energy by the process of photoelectric effect. The photoelectric effect is when particles of light called photons strike the surface of a metal and an electron from the metal is ejected. The energy of incident photons is transferred to the kinetic energy of the escaping electron and some of it goes into removing the electron which is called the work function of a metal used in photocell.
Applications of Photoelectric cells are:-
1. It can be used for automatic operation of switching on and off the street light.
2. It can be used in obtaining electrical energy from sunlight energy.
3. They are used for producing sound in cinematography.
4. It can be used to study the temperature and spectra of stars.