First slide

Photo Electric Effect

Question

A photo cell is illuminated by a small bright source placed at 1m away. When the same source of light is placed 2m away, which of the following is true about the electrons emitted by the photo cathode?

Moderate

A

Each carry one quarter of their previous energy
B

Each carry one quarter of their previous momenta
C

Are half as numerous
D

Are one quarter as numerous

Solution

Number of photo electrons is directly proportional to solid angle $ϕ$ . Since distance d is large compared to the size of the metal surface we can write $ϕ = \frac{A}{d^{2}}$ where A is the area of target metal. Hence $n \propto \frac{1}{d^{2}}$ where n is the number of free electrons.
$∴ \frac{n^{1}}{n} = {(\frac{d}{d^{1}})}^{2} = {(\frac{d}{2 d})}^{2} = \frac{1}{4}$

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