What is the frequency of the light emitted by atomic hydrogen with m = 8 and n = 12? (The Rydberg constant is R =1.097 x 107 m-1, c = 3.00 x 108...

The Rydberg equation is

1/λ = RZ2(1/n12 - 1/n22)

where λ is the wavelength of the photon emitted

R is the Rydberg constant

Z is the atomic number which in this case is 1 since we are dealing with the hydrogen atom

n1 is the same as m which is 8

n2 is  12

So we work out the wavelength of the emitted photon as follows:

 1/λ  = 1.097 x 10^7 (1/8^2 - 1/12^2)

1/λ  = 1.097 x 10^7 x 0.00868

1/λ  =9.522 x 10^4 m^-1

λ= 1.050 x 10^-5m

We then use  f= c/λ to calculate the frequency

              f  = 3.00 x 10^8/1.050 x 10^-5

              f =  2.86 x 10^13 Hz

The wavelength and frequency that we just found tell us that the transition emits energy in the infra-red region of the electromagnetic spectrum. So one would not expect to see a spectral line for a transition from m =8 to m = 12