Describe the hydrogen spectrum.

The Swedish spectroscopist,Johannes Rydberg,noted that all series of lines in the hydrogen spectrum could be described by the following expression: $\bar{v} = 109677 \left( \frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}} \right) \ cm^{-1}$.
Where,$n_{1} = 1, 2, 3 \ldots$ and $n_{2} = (n_{1} + 1), (n_{1} + 2), (n_{1} + 3) \ldots$.
The Rydberg constant for hydrogen is $R_{H} = 109677 \ cm^{-1}$.
The series of the hydrogen spectrum are classified based on the $n_{1}$ value:
$n_{1} = 1$: Lyman series,$n_{2} = 2, 3, 4 \ldots$ (Ultraviolet region).
$n_{1} = 2$: Balmer series,$n_{2} = 3, 4, 5 \ldots$ (Visible region).
$n_{1} = 3$: Paschen series,$n_{2} = 4, 5, 6 \ldots$ (Infrared region).
$n_{1} = 4$: Brackett series,$n_{2} = 5, 6, 7 \ldots$ (Infrared region).
$n_{1} = 5$: Pfund series,$n_{2} = 6, 7, 8 \ldots$ (Infrared region).
Among all elements,the hydrogen atom has the simplest line spectrum,which is a line emission spectrum.