Lyman Series - Explanation and Derivation

Explanation and Derivation

In 1913, when Niels Bohr produced his Bohr model theory, the reason why hydrogen spectral lines fit Rydberg's formula was explained. Bohr found that the electron bound to the hydrogen atom must have quantized energy levels described by the following formula:

According to Bohr's third 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 electronvolts and wavelengths in units of angstroms:

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 is the same Rydberg constant for hydrogen from Rydberg's long known formula.

For the connection between Bohr, Rydberg, and Lyman, one must replace m by 1 to obtain:

which is Rydberg's formula for the Lyman series. Therefore, each wavelength of the emission lines corresponds to an electron dropping from a certain energy level (greater than 1) to the first energy level.