Chapter 6, Problem 77QAP

In 1885, Johann Balmer, a mathematician, derived the following relation for the wavelength of lines in the visible spectrum of hydrogen

$\lambda =\frac{364.5{\text{n}}^2}{\left({\text{n}}^2-4\right)}$where $\lambda$

in nanometers and n is an integer that can be 3, 4, 5, . . . Show that this relation follows from the Bohr equation and the equation using the Rydberg constant. Note that in the Balmer series, the electron is returning to the $\text{n}=2$ level.