Sommerfeld atomic model

Sommerfeld atomic model

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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

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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.