question_answer 38)

  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.

Answer:

                  When on electron jumps from mth orbit to nth orbit, the frequency of electromagnetic radiation emitted, according to Bohr's formula, is Where R is Rydberg constant.  Let us take m=(n + p) , where p=1,2,3.....                              AS p =1, 2, 3?.., therefore, first few frequencies of light emitted are approximate harmonics (i.e., in the ratio 1:2:3?..), when n>>p.