$\frac{mv^{2}}{r_{n}}=\frac{ke^{2}}{r_{n}}$

$\frac{mv^{2}}{r_{n}}=\frac{ke^{2}}{r^{2}_{n}}$

$\frac{mv^{2}}{r^{2}_{n}}=\frac{ke^{2}}{r_{n}}$

$\frac{mv^{2}}{r_{n}}=\frac{k^{2}e}{r^{2}_{n}}$