Hard Practice — Advanced Set

Quick Recap — Multi-step Atomic-Structure Calculations (Hard)

• $E_n=-\dfrac{13.6\,Z^2}{n^2}$ eV; $r_n=0.529\dfrac{n^2}{Z}$ Å; transition $\Delta E=E_{high}-E_{low}$.
• Photon: $E(\text{eV})=\dfrac{1240}{\lambda(\text{nm})}$; de Broglie: $\lambda=\dfrac{12.27}{\sqrt{V}}$ Å for an electron through $V$ volts.
• Spectral lines from level $n$: $\dfrac{n(n-1)}{2}$; magnetic moment $\mu=\sqrt{n(n+2)}$ BM.
• Capacities: shell $2n^2$; nodes: radial $n-l-1$, total $n-1$.