A photoelectric experiment indicates that violet light of wavelength 420 nm is the longest wavelength radiation that can cause photoemission of electrons from a particular multi alkali photocathode surface.
(a) What is the work function of the photocathode surface, in eV?
(b) If a UV radiation of wavelength 300 nm is incident upon the photocathode surface, what will be the maximum kinetic energy of the photo emitted electrons, in eV?

(a). The formula for the photoelectric effect is

Ef = W + Ek

where

Ef = photon energy.

W = work function.

Ek = kinetic energy of an electron ripped of a metal

In this case the electron does not have kinetic energy, Ek = 0. Hence

Ef = W

But  Ef = hv (h: Planck constant, v: frequency of the photon)

We can calculate the photon energy by taking into account the wave length and spped of the ligth

Ef = hv = hc/λ = 6.62*10^(-34)*3*10^(8)/(420*10^(-9)) = 4.72*10^(-19) J

But in eV

Ef =  4.72*10^(-19)*6.24*10^(18) = 2.94 eV

(b). Ek = Ef - W = hc/λ - W

    Ek = 6.62*10^(-34)*3*10^(8)/(300*10^(-9)) J - 2.94 eV

    Ek = 6.62*10^(-19)*6.24*10^(18) eV - 2.94 eV

    Ek = 1.19 eV

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