Show that the first few frequencies of light

Question:

Show that the first few frequencies of light that are 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.

Solution:

Frequency of any line in the series on the spectrum of hydrogen is expressed as the difference between the two atoms

fcm = cRZ2[1/(n+p)2 – 1/n2]

where m = n + p

Substituting for p we get,

fcm = (2cRZ2/n3)p

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