Calculate the frequency of the n=2 line in the lyman series of hydrogen

Approximately .

Explanation:

The Lyman Series of a hydrogen atom are due to electron transitions from energy levels to the ground state where . In this case, the electron responsible for the line started at and transitioned to

A hydrogen atom contains only one electron. As a result, Bohr Model provides a good estimate of that electron's energy at different levels.

In Bohr's Model, the equation for an electron at energy level (

(note the negative sign in front of the fraction,)

where

The electron that produced the line was initially at the

.

The electron would then transit to energy level . Its energy would become:

.

The energy change would be equal to

.

That would be the energy of a photon in that spectrum line. Planck constant relates the frequency of a photon to its energy:

, where

In this case, . Hence,

.

Note that .