Chapter 2, Problem 2.71SP

One series of lines of the hydrogen spectrum is caused by emission of energy accompanying the fall of an electron from outer shells to the fourth shell. The lines can be calculated using the Balmer–Rydberg equation:

$\frac{1}{\lambda }=R_{\infty }\left[\frac{1}{m^2}-\frac{1}{n^2}\right]$

where m = 4, R_∞ = 1.097 × 10⁻² nm⁻¹, and n is an integer greater than 4. Calculate the wavelengths in nanometers and energies in kilojoules per mole of the first two lines in the series. In what region of the electromagnetic spectrum do they fall?