Atoms

d = \frac{2Ze^2}{4\pi\varepsilon_0 K}

\frac{1}{4\pi\varepsilon_0} \frac{e^2}{r^2} = \frac{mv^2}{r}

r = \frac{e^2}{4\pi\epsilon_0mv^2}

K = \frac{1}{2}mv^2 = \frac{e^2}{8\pi\epsilon_0r}

U = -\frac{e^2}{4\pi\epsilon_0r}

E = K + U = \frac{e^2}{8\pi\epsilon_0r} - \frac{e^2}{4\pi\epsilon_0r} = -\frac{e^2}{8\pi\epsilon_0r}

L = nh/2\pi

r_n = \left(\frac{n^2}{m}\right)\left(\frac{h}{2\pi}\right)^2 \frac{4\pi\varepsilon_0}{e^2}

E_n = -\frac{me^4}{8n^2\varepsilon_0^2 h^2}

E_n = -\frac{13.6}{n^2} \text{ eV}

h\nu_{if} = E_{ni} - E_{nf}