How do you calculate the frequency and wave length of hydrogen atom spectrum when electron transfer from 5 = 5 to n = 2?
1 Answer
The frequency is
The calculations used to find these values are shown below...
Explanation:
To answer this question, we start with Bohr's result for the energies of the stationary states of hydrogen. These are the quantized, allowable energies the electrons may possess.
The equation is
Depending on the units you use, the first bracket is a collection of constants, and can be replaced with a single value.
In Chemistry-friendly terms, I will set this value to be
Thus,
Now, we evaluate the energy for
Subtract and you get
This change in the energy of the atom equals the energy carried off by the photon that is released.
To convert to frequency, we apply Planck's relation:
as the frequency.
The wavelength comes from the relation
Finally
which is in the violet portion of the visible spectrum.