# Rydberg Formula

The Rydberg formula is the mathematical formula to determine the wavelength of light emitted by an electron moving between the energy levels of an atom. When an electron transfers from one atomic orbital to another, it’s energy changes. When an electron shift from an orbital with high energy to a lower energy state, a photon of light is generated. A photon of light gets absorbed by the atom when the electron moves from low energy to a higher energy state. The Rydberg Formula applicable to the spectra of the different elements and is it is expressed as

$\dpi{120}&space;\large&space;\bar{v}=\frac{1}{\lambda&space;}=R(\frac{1}{n^{2}_{1}}-\frac{1}{n^{2_{2}}}$

Where,

n1 and n2 are integers and n2 is always greater than n1.

R is constant, called Rydberg constant and formula is usually written as

$\dpi{120}&space;\large&space;\bar{v}=R_{H}(\frac{1}{n^{2}_{1}}-\frac{1}{n^{2}_{2}})$

The modern value of Rydberg constant is known as 109677.57 cm-1 and it is the most accurate physical constant.

$\dpi{120}&space;\large&space;\bar{v}=\frac{1}{\lambda}=109680(\frac{1}{n^{2}_{1}}-\frac{1}{n^{2}_{2}})cm^{-1}(n_{2}>n_{1}&space;)$

Solved Examples

Example 1

According to Paschen series, n1 = 3 and n2 = 4, 5…

Therefore, the second line in the Paschen series is set by putting n1 = 3 and n2 = 5

$\dpi{120}&space;\large&space;\bar{v}=\frac{1}{\lambda}=109680(\frac{1}{n^{2}_{1}}-\frac{1}{n^{2}_{2}})cm^{-1}(n_{2}>n_{1}&space;)$

Substitute the above values in the equation

ν¯ = 7.799 x 103 cm-1

λ = 1.282 x 10-4 cm = 1282 nm which is in near infrared region.

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