Rydberg Formula

Rydberg Formula

Rydberg formula is a mathematical formula used to predict the wavelength of light resulting from an electron moving between energy levels of an atom. If the state of an electron in a hydrogen atom is slightly perturbed, then the electron can make a transition to another stationary. The transition will emit a photon with a certain wavelength.

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 is given by:

\(\frac{1}{\lambda }=R{{z}^{2}}\left( \frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}} \right)\)  ; Where,

\(\lambda \) = Wavelength of the photon,

\(R\) = Rydberg Constant =\(1.097\times {{10}^{7}}{{m}^{-1}}\),

\(Z\) = Atomic number of the atom,

\({{n}_{1}}\) And \({{n}_{2}}\) are integers, where\({{n}_{2}}>{{n}_{1}}\).

How to find the wavelength using Rydberg Formula?


Find the wavelength of the electromagnetic radiation that is emitted from an electron relaxes from n=3 to n=1?

Solution: Given,

\(Rydberg\,\,Cons\tan t(R)=1.097\times {{10}^{7}}{{m}^{-1}}\),


\({{n}_{1}}=1\,\,\,\And \,\,\,{{n}_{2}}=3\),

Rydberg formula: \(\frac{1}{\lambda }=R{{z}^{2}}\left( \frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}} \right)\),

\(\frac{1}{\lambda }=1.0974\times {{10}^{7}}\left( \frac{1}{{{1}^{1}}}-\frac{1}{{{3}^{2}}} \right)=1.0974\times {{10}^{7}}\left( \frac{1}{1}-\frac{1}{9} \right)\),

\(\frac{1}{\lambda }=1.0974\times {{10}^{7}}(0.889)=0.9755886\times {{10}^{7}}\),

\(\therefore \,\,Wavelength(\lambda )=1.025\times {{10}^{-7}}m.\).