Find the lowest three energies in eV for an electron in a on
Find the lowest three energies, in eV, for an electron in a one-dimensional box of length a = 0.2 nm (about the size of an atom).
Solution
E = n^2h^2/(8mL^2)
=> for n= 1
E1 = (1^2*(6.62*10^-34)^2))/(8*9.1*10^-31*(0.2*10^-9)^2) = 1.5049*10^-18 J = 9.39 eV
E2 = (2^2*(6.62*10^-34)^2))/(8*9.1*10^-31*(0.2*10^-9)^2) = 6.01949*10^-18 J = 37.5707 eV
E3 = (3^2*(6.62*10^-34)^2))/(8*9.1*10^-31*(0.2*10^-9)^2) = 13.5*10^-18 J = 84.260 eV
