2003 AIPMT Dual Nature of Radiation and MatterEffect of Intensity on Photoelectric Effect Easy Question 73 of 82 in Dual Nature of Radiation and Matter

A photoelectric cell is illuminated by a point source of light 1 m away. When the source is shifted to 2m then -

A each emitted electron carries one quarter of the initial energy
B number of electrons emitted is half the initial number
C each emitted electron carries half the initial energy
D number of electrons emitted is a quarter of the initial number

The answer is D.

Solution

For a point source, intensity at distance r: $I \propto \dfrac{1}{r^2}$.
When the distance is doubled from 1 m to 2 m, the intensity becomes $\dfrac{1}{4}$ of the initial value.
The number of photoelectrons emitted per second is proportional to the intensity (number of photons falling per second). So the number of electrons emitted becomes a quarter of the initial number.
The energy of each photoelectron depends only on the frequency of light ($KE_{max} = h\nu - \phi$), not on intensity, so it does not change.
So the number of electrons emitted is a quarter of the initial number.

Concept Intensity and number of photoelectrons

Dual Nature of Radiation and Matter in past papers

82 questions from this chapter have appeared across 27 exam years.