Answer to Question #86678 in Atomic and Nuclear Physics for Rabindra Kumar

Question

The energy of the lowest allowed level for an electron in a 1-D box is 10.0 eV. Can the electron ever have an energy of 200 eV? Justify.

Answer 1

The allowed energies for an electron in a 1-D box

$$E_n=\frac{n^2\pi^2\hbar^2}{2mL^2}, \quad n=1,2,3,...$$

So

$$\frac{E_n}{E_k}=\frac{n^2}{k^2}$$

$$\frac{200\:\rm{eV}}{10.0\:\rm{eV}}=\frac{n^2}{1^2}$$

$$n=\sqrt{20.0}=4.47$$

Since n is non-integer, so the electron would not have an energy of 200 eV.