Explain the balmer and rydberg equations

It was in 1885 when Balmer first of all came up with a simple formula for predicting the wavelength of any of the lines in what we now know as the Balmer series. Balmer proposed the formula for correlating the wavenumber of the spectral lines emitted and the energy shells involved. This formula is given as where =109,677 cm-1

and n=3, 4, 5…

Balmer Series is defined today as when the electron jumps from any higher stationary orbit to the second stationary orbit with n=2, the spectral lines emitted are said to fall in the Balmer Series and this series of the hydrogen emission spectrum is known as the Balmer series. The Balmer series is such a series of lines in the electromagnetic spectrum that lies in the visible region. Later in 1888 Rydberg presented a general formula for this so that it was possible to calculate the wavelengths of any of the lines in the hydrogen emission spectrum.

What Rydberg came up with was:

RH is the constant named after him as the Rydberg constant. The value of the Rydberg constant for hydrogen is, 109,677 cm-1. n1 and n2 are whole numbers and n2 > n1. That means, if n1 is, say, 2 then n2 can be 3,4,5,6,7,8……

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