# 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?

Problem:

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

Solution: Given,

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

$$Z=1$$,

$${{n}_{1}}=1\,\,\,\And \,\,\,{{n}_{2}}=3$$,

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

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

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

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