Answer :

We know that the wavenumber of the emitted wavelength during transition from and of the electron is given as,

--------(1)


(where R is Rydberg’s constant)


Now putting



Putting this in equation (1), we get,



c= speed of light


and = the final and initial orbital level respectively


Now let us consider , where p in any integer 1,2,3….


Putting this in equation 1 we get,



By binomial expansion the above equation becomes we get,



For p=1


For p=2


For p=3


the ratios of frequencies,



Hence, we can say that the first few frequencies of light that is emitted when electrons fall to the nth level from levels higher than n, are approximate harmonics (i.e. in the ratio 1: 2: 3...) when n >>1.


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