Consider an atomic nucleus to be equivalent to a onedimensio

Consider an atomic nucleus to be equivalent to a one-dimensional infinite potential well with L = 2.2 times 10^-24m, a typical nuclear diameter. What would be the ground-state energy (In GeV) of electron if it were trapped in such a potential well? Nuclei do not contain electrons, the tolerance is +/-5%

Solution

energy in one D wall = n^2h^2/(8mL^2)

=> E in n=1 = h^2/(8mL^2)

=> E = (6.62*10^-34)^2/(8*9.1*10^-31*(2.2*10^-14)^2) = 1.2437*10^-10 J = 0.776 GeV