Line Emission Spectrum of Hydrogen

When a substance absorbs energy — whether from incoming radiation or from heating — its atoms, molecules or ions are said to become 'excited'. When an excited species subsequently gives away that absorbed energy in the form of radiation, the process is called emission, and the recorded spectrum of the emitted radiation is called an emission spectrum. Hydrogen, being the simplest atom, produces the simplest atomic emission spectrum of any element, and when an electric discharge is passed through hydrogen gas the emitted light — when spread out and recorded — is not a continuous rainbow but a set of sharp, discrete lines at specific frequencies. Late in the 19th century, five different scientists independently recorded groups ('series') of these lines in different regions of the spectrum. In 1885, Balmer found an empirical formula fitting the lines that fall in the visible region: $\bar\nu = 109677\left(\frac{1}{2^2}-\frac{1}{n^2}\right)\ \text{cm}^{-1}$ for $n = 3,4,5,\ldots$ — these lines are now called the Balmer series. J. Rydberg then generalised Balmer's formula to cover all five known series at once: $\bar\nu = R_H\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)\ \text{cm}^{-1}$, where $n_1 = 1,2,3,\ldots$ and $n_2 = (n_1+1),(n_1+2),(n_1+3),\ldots$ The constant $R_H = 109677\ \text{cm}^{-1}$ is called the Rydberg constant for hydrogen. The five series — Lyman ($n_1=1$, ultraviolet), Bal …