Question

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?

Answer 1

(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