The photoelectric effect consists of the emission of electrons (electric current) that occurs when light falls on a metal surface under certain conditions.
If the light is a stream of photons and each of them has energy, this energy is able to pull an electron out of the crystalline lattice of the metal and communicate, in addition, a kinetic energy.
This is what Einstein proposed:
Light behaves like a stream of particles called photons with an energy
[tex]E=h.f[/tex] (1)
So, the energy [tex]E[/tex] of the incident photon must be equal to the sum of the Work function [tex]\Phi[/tex] of the metal and the kinetic energy [tex]K[/tex] of the photoelectron:
[tex]E=\Phi+K[/tex] (2)
Where [tex]\Phi[/tex] is the minimum amount of energy required to induce the photoemission of electrons from the surface of a metal, and its value depends on the metal.
In the case of Copper [tex]\Phi=4.7eV[/tex]
Now, applying equation (2) in this problem:
[tex]E=4.7eV+1.10eV[/tex] (3)
[tex]E=5.8eV[/tex] (4)
Now, substituting (1) in (4):
[tex]h.f=5.8eV[/tex] (5)
Where:
[tex]h=4.136(10)^{-15}eV.s[/tex] is the Planck constant
[tex]f[/tex] is the frequency
Now, the frequency has an inverse relation with the wavelength [tex]\lambda[/tex]:
[tex]f=\frac{c}{\lambda}[/tex] (6)
Where [tex]c=3(10)^{8}m/s[/tex] is the speed of light in vacuum
Substituting (6) in (5):
[tex]\frac{hc}{\lambda}=5.8eV[/tex] (7)
Then finding [tex]\lambda[/tex]:
[tex]\lambda=\frac{hc}{5.8eV } [/tex] (8)
[tex]\lambda=\frac{(4.136(10)^{-15} eV.s)(3(10)^{8}m/s)}{5.8eV }[/tex]
We finally obtain the wavelength:
[tex]\lambda=213^{-9}m=213nm[/tex]
