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Question

# 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 fourthLet, the distance of source are r1=1m and r2=2mThe intensity o incident light is given by is given byI=P4πr2⇒I∝1r2The photocurrent is directly proportional to the intensity of incident light.Also, number of photoelectrons emitted (say)n are directly proportional to the photocurrent.Hence,n∝I∝1r2⇒n1∝1r21 and n2∝1r22⇒n2n1=r21r22∴n2=122n1∴n2=14n1Hence, 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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