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Wave Optics

Question
CBSEENPH12038537

The maximum velocity of electrons, emitted from a metal surface of negligible work function is v, when frequency of light falling on it is f. What will be the maximum velocity when the frequency of incident light made 4f?

Solution
Maximum velocity of electrons = v
Frequency of incident light = f

Max. velocity when incident light is 4f = ?

Using Einstein's photoelectric equation, we have

                    1 half mv subscript straight x squared space equals space hf space minus space straight ϕ
Since, work function is negligibe, straight ϕ space equals space 0 

                   straight v subscript straight x squared space equals fraction numerator 2 hf over denominator straight m end fraction comma space space straight v subscript straight x space equals space square root of fraction numerator 2 hf over denominator straight m end fraction end root 

Thus, for frequency, straight f apostrophe space equals space 4 straight f 

we have,               straight v subscript straight x apostrophe space equals space square root of fraction numerator 2 straight h 4 straight f over denominator straight m end fraction end root space equals space 2 straight v subscript straight x 

Thus, maximum velocity will be doubled when, frequency is made 4 times.

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