Structure of the Atom — Formula Sheet

r_n = \frac{n^2 h^2 \varepsilon_0}{\pi m Z e^2}

v_n = \frac{Z e^2}{2 \varepsilon_0 n h}

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

\nu = R c Z^2 \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right)

\frac{1}{\lambda} = R Z^2 \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right)

Energy of electron in nth orbit is $E_n = -13.6/n^2$ eV.

Bohr postulated that the angular momentum of an electron in orbit is quantized and given by mvr = nh/2π, where n is a positive integer.