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

The frequency of any line in a series in the spectrum of hydrogen like atoms corresponding to the transition of electrons from (n + p) level to nth level can be expressed as a difference of two terms.

where, m = n + p,(p = 1, 2,3, …) and R is Rydberg’s constant.

p«n

Thus, the first few frequencies of light that is emitted when electrons fall to the nth level from levels higher than n, are approximate harmonic (i.e. in the ratio 1:2:3 …) when n»l.