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Photoelectric cell is illuminated by a small intense source distant 1 m from it. When the same source is placed at a distance 2 m then the number of photoelectrons emitted from the cathode will be

A
Half
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B
One fourth
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C
Each carries one fourth of its previous energy
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D
Each carries one fourth of its previous momentum
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Solution

The correct option is A One fourth
Let, the distance of source are r1=1m and r2=2m
The intensity o incident light is given by is given by

I=P4πr2

I1r2

The photocurrent is directly proportional to the intensity of incident light.
Also, number of photoelectrons emitted (say)n are directly proportional to the photocurrent.
Hence,
nI1r2

n11r21 and n21r22

n2n1=r21r22

n2=122n1

n2=14n1

Hence, if the distance of source increases twice the number of photoelectrons emitted will become one fourth.
So, the answer is option (B).

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