Question

what is rydberg formula how does it help to calculate the wavenumber of different series of line of the hydrogen spectra​

Answer 1

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Explanation:

In an amazing demonstration of mathematical insight, in 1885 Balmer came up with a simple formula for predicting the wavelength of any of the lines in atomic hydrogen in what we now know as the Balmer series. Three years later, Rydberg generalized this so that it was possible to determine the wavelengths of any of the lines in the hydrogen emission spectrum. Rydberg suggested that all atomic spectra formed families with this pattern (he was unaware of Balmer's work). It turns out that there are families of spectra following Rydberg's pattern, notably in the alkali metals, sodium, potassium, etc., but not with the precision the hydrogen atom lines fit the Balmer formula, and low values of n2 predicted wavelengths that deviate considerably.

Rydberg's phenomenological equation is as follows:

ν˜=1λ=RH(1n21−1n22)(1.5.1)(1.5.2)

where RH is the Rydberg constant and is equal to 109,737 cm-1 and n1 and n2 are integers (whole numbers) with n2>n1 .

For the Balmer lines, n1=2 and n2 can be any whole number between 3 and infinity. The various combinations of numbers that can be substituted into this formula allow the calculation the wavelength of any of the lines in the hydrogen emission spectrum; there is close agreement between the wavelengths generated by this formula and those observed in a real spectrum.