Balmer Series - Balmer's Formula

Balmer's Formula

Balmer noticed that a single number had a relation to every line in the hydrogen spectrum that was in the visible light region. That number was 364.50682 nm. When any integer higher than 2 was squared and then divided by itself squared minus 4, then that number multiplied by 364.50682 (see equation below) gave a wavelength of another line in the hydrogen spectrum. By this formula, he was able to show that certain measurements of lines made in his time by spectroscopy were slightly inaccurate and his formula predicted lines that were later found although had not yet been observed. His number also proved to be the limit of the series.

The Balmer equation could be used to find the wavelength of the absorption/emission lines and was originally presented as follows (save for a notation change to give Balmer's constant as B):

Where

is the wavelength.

B is a constant with the value of 3.6450682×10-7 m or 364.50682 nm.

n is equal to 2

m is an integer such that m > n.

In 1888 the physicist Johannes Rydberg generalized the Balmer equation for all transitions of hydrogen. The equation commonly used to calculate the Balmer series is a specific example of the Rydberg formula and follows as a simple reciprocal mathematical rearrangement of the formula above (conventionally using a notation of n for m as the single integral constant needed):

where λ is the wavelength of the absorbed/emitted light and R_H is the Rydberg constant for hydrogen. The Rydberg constant is seen to be equal to in Balmer's formula, and this value, for an infinitely heavy nucleus, is meter = 10,973,731.57 meter−1.