An excited hydrogen atom emits light with a wavelength of 397.2 nm to reach the energy level for which n = 2. In which principal quantum level did the electron begin? It would be very helpful if the last step could be over explained, thats where my answer is going wrong.
wavelength = 397.2 nm
= 3.972*10^-7 m
Here photon will be emitted
1/lambda = R* (1/nf^2 - 1/ni^2)
R is Rydberg constant. R = 1.097*10^7
1/lambda = R* (1/nf^2 - 1/ni^2)
1/3.972*10^-7 = 1.097*10^7* (1/2^2 - 1/ni^2)
(1/2^2 - 1/ni^2) = 0.2295
1/ni^2 = 2.05*10^-2
ni^2 = 49
ni = 7
Answer: 7
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