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