Question

The maximum wavelength an electromagnetic wave can have and still eject an electron from a copper surface is 264 nm .What is the work function of a copper surface?

Answer 1

4.71 eV

Step-by-step explanation:

For an electromagnetic wave with wavelength

`\lambda=264 nm = 2.64\cdot 10^(-7) m`

the energy of the photons in the wave is given by

`E=(hc)/(\lambda)=((6.63\cdot 10^(-34)Js)(3\cdot 10^8 m/s))/(2.64\cdot 10^(-7)m)=7.53\cdot 10^(-19) J`

where h is the Planck constant and c the speed of light. Therefore, this is the minimum energy that a photon should have in order to extract a photoelectron from the copper surface.

The work function of a metal is the minimum energy required by the incident light in order to extract photoelectrons from the metal's surface. Therefore, the work function corresponds to the energy we found previously. By converting it into electronvolts, we find:

`E=(7.53\cdot 10^(-19) J)/(1.6\cdot 10^(-19) J/eV)=4.71 eV`