Question

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.

Answer 1

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