An electron is bound in an 1D potential well of width 2 A° but of infinite height. Find its energy values in the ground state and in first excited state. (Given: Planck constant is 6.634x10-34 J-Sec)

Given: \(L=2\) Å \(=2\times10^{-10}\) m, \(h=6.634\times10^{-34}\) J s, \(m=9.1\times10^{-31}\) kg.

Formula: \(E_n=\dfrac{n^2h^2}{8mL^2}\)

Ground state (n = 1):

\[ E_1=\frac{(6.634\times10^{-34})^2}{8\times9.1\times10^{-31}\times(2\times10^{-10})^2}=\frac{4.401\times10^{-67}}{2.912\times10^{-49}}=1.511\times10^{-18}\ \text{J} \]

\(E_1=\dfrac{1.511\times10^{-18}}{1.6\times10^{-19}}=9.45\) eV

First excited state (n = 2): \(E_2=4E_1=6.045\times10^{-18}\) J \(=37.8\) eV

\(E_1\approx1.51\times10^{-18}\) J (9.45 eV); \(E_2\approx6.05\times10^{-18}\) J (37.8 eV)