Question

An electron is contained in the rectangular corral of figure, with widths $L_x=800pm$ and $L_x=1600pm$. What is the electron's ground state energy?

Answer 1

We can the $m{c}^2$ value for an electron from Table and $hc=1350eV.nm$ by writing as

$E_{nx,ny}=\frac{2h^2}{8m}(\frac{n_x^2}{L_x^2}+\frac{n_y^2}{L_y^2})=\frac{(hc{)}^2}{8(mc{)}^2}(\frac{n_x^2}{L_x^2}+\frac{n_y^2}{L_y^2})$

For $n_x=n_y=1$, we obtain

$E_{1,1}=\frac{(1240ev.nm)}{8(611\times {10}^{3}eV)}(\frac{1}{(0.800nm{)}^2}+\frac{1}{(1.600nm{)}^2})=0.731eV$.