Lyman series

The Lyman series is the series of transitions and resulting emission lines of the hydrogen atom as an electron goes from n ≥ 2 to n = 1 (where n refers to the energy level of the electron). The transitions are named sequentially by Greek letter: from n = 2 to n = 1 is called Lyman-alpha, 3 to 1 is Lyman-beta, 4 to 1 is Lyman-gamma, etc.

It has been known for some time that the radiation emmited from Hydrogen is non-continuous. Here is an illustration of the first series of Hydrogen emmision lines:

Many tried to find some mathematical formula to predict those lines. One that succeded was Rydberg. Then a schoolteacher, he managed to find a formula to math the known emmision lines and predict those which were not yet discovered. The formula was:

Where n is a natural number greater or equal than 2 (i.e. n=2,3,4,...).

Therefore, the lines seen in the image are the wavelengths corresponding to n=2 on the left, to n= on the right(There are infinite spectrum lines, but they become very dense as they approach to n=, so only several of the first lines and the last one appear).

Later, when Bohr laid his assumptions, the spectral lines were explained.
Bohr found that the electron bound to the Hydrogen atom must have quantitized energy levels described by the following formula:

Accordind to Bohr's 3rd assumption, whenever an electron falls from an initial energy level() to a final energy level(), the atom must emit radiation with a wavelength of:

There is also a more comfortable notation when dealing with energy in units of Electronvolt and wavelengths in units of Angstrom:

Replacing the Energy in the above formula with the expression for the energy in the Hydrogen atom where the initial energy corresponds to energy level-n and the final energy corresponds to energy level-m:
Where R is the same constant Lyman found. It is easy then to see the connection between what bohr found and what lyman found - When replacing m with 1 we get:
Which is exactly Rydberg's formula. Therefore, each wavelength of the emmision lines corresponds to an electron dropping from a certain energy level (greater than 1) to the first energy level.