Balmer discovered that there was a curious relationship between the wavelengths, λ of the visible atomic spectrum of hydrogen. The relationship could be expressed as

where n = 3, 4, 5 ... and R_H was Rydberg's constant, with value 1.097x10⁷ m^-1. With this information, calculate the wavelength of the longest visible wavelength of the hydrogen atomic emission spectrum.

Solution:

The wavelength must be in the range 700-400 nm. If we put n = 3 in the above equation, we get 1/λ = 1.097x10⁷ m^-1(1/4 - 1/9) = 1.52x10⁶ m^-1, from which we get λ = 6.56x10^-7 m or 656 nm.