Materials will have different energies associated with the electrons inside them
ID: 1731024 • Letter: M
Question
Materials will have different energies associated with the electrons inside them. This is related to how strongly bound they are by their work function. If we sandwich a material with a very low energy between two materials with a high energy, we create a trap for an electron. If this trap is very narrow in one direction in comparison to the others, this is approximately a 1-dimensional box that confines the electron. What is the lowest energy of an electron in the box if the thinnest direction across the materials is 4.81 nm?
Explanation / Answer
given, length of the gap, l= 4.81 nm
then longest wavelength possible is 2l
alambda = 2l
p = h/lambda ( momentum)
mass of electron = m
hence energy
E= p^2/2m = h^2/8l^2*m
h = 6.67*10^-34
m =9.1*10^-31 kg
hence
E = 2.504*10^-21 J = 0.14065 eV