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A parallel beam of light of intensity $I$ and cross-section area $S$ is incident on a plate at normal incidence. The photoelectric emission efficiency is 100%. The frequency of beam is $ν$ and the work function of the plate is $ϕ (h ν > ϕ)$ . Assuming all the electrons ejected normal to the plane and with the same maximum possible speed. Calculate the net force exerted on the plate only due to striking of photons and subsequent emission of electrons

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$\frac{I S}{h ν} (\frac{h}{λ} + \sqrt{m (h ν - ϕ)})$

$\frac{I S}{h ν} (\frac{h}{λ} + \sqrt{2 m (h ν - ϕ)})$

$\frac{h ν S}{I} (\frac{h}{λ} + \sqrt{2 m (h ν - ϕ)})$

None of these

answer is B.

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Detailed Solution

The net force on the plate is due to incidence of photons + due to emission of electrons.

The number of photons incidents per second on the plate = n = number of electrons emitted per second

For the beam of light,

$n (h ν) = I S$

$\Rightarrow n = \frac{I S}{h ν}$

The momentum of photon is $\frac{h}{λ}$ and that of electron is $\sqrt{2 m K_{max}} = \sqrt{2 m (h ν - ϕ)}$ where $m$ is the mass of the electron.

Hence the net force exerted on the metal plate is

$F = \frac{I S}{h ν} (\frac{h}{λ} + \sqrt{2 m (h ν - ϕ)})$

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