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Structure Of Atom

Question
CBSEENCH11005287

What is Rydberg formula? What is the value of Rydberg constant ? What is its significance?

Solution
In order to calculate the wavelengths of spectral lines, Rydberg gave a very simple theoretical formula
straight v with bar on top space equals space straight R open square brackets 1 over straight n subscript 1 squared minus fraction numerator 1 over denominator straight n subscript 2 superscript 2 end fraction close square brackets
where straight v with bar on top space equals space wave space number space of space spectral space line semicolon
R = Rydberg constant  = 109677 cm-1
and n1 and n2 are whole numbers and for a particular series, n1 is constant and varies.
The significance of Rydberg formula: Rydberg formula is very useful for calculating the wave number of different spectral lines belonging to a particular series of the hydrogen spectra. For example
For Lyman series, n1 = 1, n2 = 2, 3, 4....
For Balmer series,n2 =2, n3 = 3, 4, 5....
For Paschen series, n3 =3, n4 = 4, 5, 6....
For Brackett series, n4 =4, n5 = 5,6,7...
For Pfund series, n5 = 5, n6 = 6, 7......
By knowing the wave number, the frequency and also the wavelengths of different spectral lines can be calculated.