# Rydberg Formula

## 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 shifts 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 applies to the spectra of various elements and is given by

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

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 109677.57 cm-1 and the most precise known physical constant.

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

Example 1

Determine the ν¯ for the transition wherein n1=6 to n2 = 3 in a hydrogen atom.

Solution:

Since, the mass of nucleus is much greater than mass of an electron,

Therefore, R = 109737.32 cm-1

ν¯ = 109737 x (1/132 – 1/162)

ν¯ = 9144.78 cm-1

Determine the wavelength of the second line in the Paschen series and prove that this line lies near to the visible, infrared region.

Example 2

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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#### Practise This Question

The chart shows the number of sunny days and the number of windy days in six months. Which months had more sunny days than windy days?
Here the horizontal axis is x axis which represents months and vertical axis is y axis which represents number of days. The scale is x-axis 1cm = 1 month and y axis 5cm = 10 days