What is the frequency of a Hydrogen photon resulting from the transition of n = 7 → n = 1 ?
I would do this
1/wavelength = R(1/1^2 - 1/7^2)
Then convert wavelength to frequency from
c = frequency x wavelength.
R = Rydberg constant. I can look that up if you don't have it.
Thanks so much.
To determine the frequency of a hydrogen photon resulting from the transition of n = 7 to n = 1, we can use the Rydberg formula. The Rydberg formula describes the wavelengths (or frequencies) of photons emitted or absorbed during electronic transitions in hydrogen.
The formula is given as:
1/λ = R * (1/n1^2 - 1/n2^2)
where λ is the wavelength, R is the Rydberg constant, and n1 and n2 are the principal quantum numbers corresponding to the initial and final energy levels, respectively.
Since we are interested in the frequency, we can rearrange the formula using the relation c = λ * ν, where c is the speed of light and ν is the frequency:
ν = c / λ
Now, substituting the Rydberg formula for λ:
ν = c / (R * (1/n1^2 - 1/n2^2))
For the hydrogen atom, the Rydberg constant is approximately R = 1.097 x 10^7 m^-1.
For n1 = 7 and n2 = 1:
ν = (3 x 10^8 m/s) / (1.097 x 10^7 m^-1 * (1/7^2 - 1/1^2))
Simplifying this expression gives us the frequency of the hydrogen photon resulting from the transition of n = 7 to n = 1.