Answer:
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
is a constant.
is the atomic number of that atom.
for hydrogen.
is the energy level of that electron.
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
is the energy of the photon.
is the Planck constant.
is the frequency of that photon.
In this case, . Hence,
.
Note that .