Sommerfeld atomic model

source : b.biglobe.ne.jp

## Sommerfeld atomic model –

This model explains the fine spectrum of Hydrogen atom.The important postulates of Sommerfeld atomic model are-

*1) The orbits may be both circular or elliptical.*

source : Fossil Hunters

*2) When path is elliptical , then there are two axis – major axis & minor axis. When length of major & minor axis become equal then orbit is circular.*

*3) The angular momentum of electron moving in an elliptical orbit is kh/ 2π.*

*k is an integer except zero.*

*Value of k = 1,2,3,4…..*

*n/k = length of major axis / length of minor axis*

*With increase in value of k , ellipticity of the orbit decreases. When n= k,then orbit is circular.*

source : nptel

*4) Sommerfeld suggested that orbits are made up of sub energy levels . These are s,p,d,f. These sub shells possess slightly different energies.*

*Bohr gave a quantum number ‘n’ , which determines the energy of electron.*

*Sommerfeld introduced a new quantum number called Orbital or Azimuthal Quantum number ( l ) which determines the orbital angular momentum of electron.*

*Values of l =0 to (n-1)*

*For, n=1 ; l=0 ; 1s su*

*n=2 ; l=0,1 ; 2s , 2p sub shell*

*n=3 ; l=0,1 ,2 ; 3s , 3p , 3d sub shell*

*n=4 ; l=0, 1, 2 , 3 ; 4s , 4p , 4d , 4f sub shell*

source : Readorrefer.in

*5) When an electron jumps from one orbit to another orbit, the difference of energy (ΔE ) depends upon sub energy levels.*

*6) It explains the splitting of individual spectral lines of hydrogen & thus fine spectrum . It could not predict the exact number of lines which are actually present in the fine spectrum.*

## Defects of Sommerfeld atomic model-

*1) This model does not explain the behavior of system having more than one electron.*

*2) This model does not explain the Zeeman & Stark effect.*