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# Rydberg Formula

The Rydberg constant was introduced into atomic physics near the end of the last century. When Balmer ans Rydberg independently derived empirical relations which accounted for the observed features of atomic spectra.

Rydberg Formula was much more general, applying to the spectra of many elements. Their results may be summarized by the formula.

where both n1 and n2 are integers but n2 is always greater than n1. R is a constant and called Rydberg constant and the formula is commonly written as

The modern value of the Rydberg constant is 109677.57 cm-1; it is one of the most accurately known physical constants.

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## Rydberg Problems

Solved problems based on Rydberg formula are given below.

### Solved Examples

Question 1: Calculate the wavelength of the second line in the Paschen series and show that this line lies in the near infrared, that is in the infrared region near the visible.
Solution:

In the Paschen series n1=3 and n2=4, 5, 6...
Thus the second line in the Paschen series is given by setting n1=3 and n2=5 and

Substituting the values in the above equation we get
$\bar \nu$ = 7.799 $\times$ 103cm-1
and
$\lambda$ = 1.282 $\times$ 10-4cm = 1282nm
Which  is in the near infrared region.

Question 2: Calculate the $\bar\nu$ for the transition involving n1=6 to n2=3 in an hydrogen atom.
Solution:

Since mass of nucleus is much larger than that of electron,

R = 109737.32cm-1

$\bar\nu$ = (109737.32cm-1)($\frac{1}{3^{2}}$ - $\frac{1}{6^{2}}$)

$\bar\nu$ = 9144.78cm-1

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