4.3.3.2 So­lu­tion hydc-b

Ques­tion:

What is the value of en­ergy level $E_2$? And $E_3$?

An­swer:

No need to put all the num­bers into

$$E_n = - \frac{\hbar^2}{2 m_{\rm e}a_0^2} \frac 1{n^2}$$

be­cause the only dif­fer­ence be­tween $E_2$ and $E_1$ is just a fi­nal fac­tor $\frac 14$. So $E_2$ $\vphantom0\raisebox{1.5pt}{$=$}$ $\frac 14E_1$ $\vphantom0\raisebox{1.5pt}{$=$}$ $\vphantom{0}\raisebox{1.5pt}{$-$}$3.4 eV. Sim­i­larly, $E_3$ $\vphantom0\raisebox{1.5pt}{$=$}$ $\frac 19E_1$ $\vphantom0\raisebox{1.5pt}{$=$}$ $\vphantom{0}\raisebox{1.5pt}{$-$}$1.51 eV.