When photons of energy h ν fall on a metal plate of work function W 0 , photoelectrons of maximum kinetic energy K are ejected. If the frequency of radiation is doubled, the maximum kinetic energy o

Question

When photons of energy h ν fall on a metal plate of work function W 0 ​ , photoelectrons of maximum kinetic energy K are ejected. If the frequency of radiation is doubled, the maximum kinetic energy of ejected photoelectrons will be

TestHub · Accepted Answer

Using Einstein's photoelectric equation for the initial state:

$K = h ν - W_{0}$

When the frequency of radiation is doubled, the new energy of the incident photons becomes $2 h ν$ . Let the new maximum kinetic energy be $K^{'}$ .

$K^{'} = 2 h ν - W_{0}$

This can be rewritten as:

$K^{'} = h ν + (h ν - W_{0})$

Substituting $h ν - W_{0} = K$ into the equation:

$K^{'} = h ν + K$

Answer: $K + h ν$

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