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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

Rydberg_formula

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

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

Rydberg_formula

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

Rydberg formula

 

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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