The Rydberg formula suggests that the observed spectral lines can be grouped into series, the lines of each series being generated when a particular value of n2 is used in the Rydberg formula. Rydberg formula is the formula for expressing the wave number of a spectral line.

The general Rydberg Formula is,

Rydberg formula = $\frac{1}{\lambda}$ = $\nu$ = R $\left (\frac{1}{n^{2}} - \frac{1}{m^{2}} \right)$.
Where n and m are positive integers and R is the Rydberg constant. The value 109,677 cm-1 is called Rydberg constant for hydrogen.

Since Rydberg formula generates the frequencies of all the spectral lines of the hydrogen atom, it provides a concise analytical summary of the hydrogen spectral data.

Some of the solved problems based on Rydberg formula is given below:

Question 1: Calculate the wavelength of emitted light for the transition of energy level n = 4 to energy level n = 1 for the hydrogen transition. In which region of electromagnetic spectrum does this radiation fall.
Solution:

According to Rydberg formula,

Here n2 = 4 and n1 = 1

$\nu$ = 109,677 $\left(\frac{1}{1^{2}} - \frac{1}{4^{2}}\right)$

= $\frac{1}{102822}$ cm

= 9.7 $\times$ 10-6cm = 9.7 $\times$ 10-6 $\times$ 107nm = 97 nm

Question 2: Calculate the wavelength of the first line in the Balmer series of hydrogen spectrum.
Solution:

For the first line in Balmer series n1 = 2 and n2 = 3

$\nu$ = 109677 $\left[\frac{1}{2^{2}} - \frac{1}{3^{2}}\right]$

= 109677 $\times$ $\frac{5}{36}$ = 15232.9 cm-1

= 6.565 $\times$ 10-5 cm = 656.5 nm