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.
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.
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1 Answer
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This is a Short Answer Type Questions as classified in NCERT Exemplar
Explanation- 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;
From the formula we can say that v=cRZ2 { }
Where p =1,2,3, … R os rydberg constant
When p<
V=cRZ2 { }
V=cRZ2 {
By binomial theorem
V=cRZ2 {
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 >> 1 .
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