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
⇒I∝1r2
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, n∝I∝1r2
⇒n1∝1r21 and n2∝1r22
⇒n2n1=r21r22
∴n2=122n1
∴n2=14n1
Hence, if the distance of source increases twice the number of photoelectrons emitted will become one fourth.