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  2. 2. CONTENTS Thomson’s Atomic Model Drawbacks of Thomson’s Atomic Model Bohr atom model Drawbacks of Bohr atom model Sommerfeld’s atom model Sommerfeld’s relativistic atomic model Drawbacks of Sommerfeld’s atom model The vector atom model Conclusion References
  3. 3. Thomson’s Atomic ModelJ. J. Thomson 1. Electron enter into the constitution of all atoms 2. Since the atom as a whole is electrically neutral the quantity of positive and negative charge in it must be the same.
  4. 4. DrawbacksHe explained that hydrogen can give rise onlyto a single spectral lines.He couldnt explain the fine spectra
  5. 5. BOHR ATOM MODEL He proposed the following postulates- (1)An electron cannot revolve round the nucleus in all possible orbit. It can revolve round the nucleus in those allowed orbits for which the angular momentum of the electron is an integral multiple of h . 2Niels Bohr Bohr’s atomic model
  6. 6. (2)An atom radiates energy onlywhen electron jumps from astationary orbit of higher energy toone of lower energy. If electronjumps from an initial orbit ofenergy E i to the final orbit ofenergy E f ( E i E f ) ,a photon of Ei E ffrequency is emitted. h
  7. 7. The Bohr formulae -e +Ze rRadius of the nth permissible orbit forhydrogen 2 2 n h 0 rn 2 e m The total energy of the electron in the nth orbit 4 2 me Z En 2 2 2 8 0n h
  8. 8. Lyman n=1 Balmer n=2 n=3 Paschen Pfund n=4 n=5 n=7 n=6 BrackettDifferent spectral series of hydrogen atom according to Bohr.
  9. 9. The energy level diagram 4 2The equation me Z Can be diagrammatically En 2 2 2 8 0n hrepresented. Then it is called The energy leveldiagram. n ---------------------------------------------------- En (eV ) n=6 n=5 Pfund n=4 -085 Brackett n=3 -1.5 Paschen Balmer n=2 -3.4 H H H n=1 Lyman -13-6
  10. 10. DrawbacksSpectrograph of high resolving showed that linesare not single. Each spectral lines actuallyconsisted of several very close line packedtogether. This is called fine structure of spectrallines. Bohr theory could not explain this finestructure. Sommerfeld’s atom model Sommerfeld introduced two main modification in Bohr’s model: (1)The path of an electron around the nucleus, in general ,is an ellipse with the nucleus at one of the foci.
  11. 11. (2)The velocity of the electron moving in anelliptical orbit varies considerably at different partsof the orbit. electron r N Elliptical orbit for hydrogen atom
  12. 12. The condition that determines the allowed elliptical orbit is b n a n Whenn n, b a , 0 and the orbit become circular  n 0  n n n has n different values
  13. 13. n 2, n 1n 1, n 1 n 3, n 1 n 2, n 2 n 3, n 2 n 3, n 3TOTAL ENERGY 4 2 me Z En 2 2 2 8 0n h
  14. 14. Sommerfeld’s relativistic atomic model 1The velocity of electron in the elliptic orbits is C 137So Sommerfeld taking into account the variation of masswith velocity.He showed that the relativistic equation describing thepath of the electron is 1 1 cos (1) r a(1 2 ) 2 z 2e 4 1 16 2 0 p 2c 2 2
  15. 15. The path of the electron given by equation(1) is anellipse whose major axis precesses slowly in the planeof the ellipse about an axis through the nucleus.The total energy in the relativistic theory 4 2 4 4 2 me Z me Z n 3 1 En 2 2 2 2 2 ( ) 4 8 0n h 8 0h n 4 n e2 1 2 0 ch 137 is called the fine structure constant
  16. 16. Fine structure of the H linesH Line is due to the transition from n=3state to n=2 state of hydrogen atom. 33 32 31 22 21
  17. 17. DrawbacksSommerfeld’s theory was able to give anexplanation of the fine structure of the spectralline of hydrogen atom. But he could not predictthe correct of spectral lines.
  18. 18. The vector atom model The two distinct features of vector atom model are: The conception of spatial quantization The spinning electron hypothesis
  19. 19. Quantum no. associated with the Vector Atom Model• A total quantum number n, it can take only integral values 1,2,3..etc• An orbital quantum number l, which may take any integral value between 0 and (n-1) inclusively.• A spin quantum number s, the magnitude of which is always ½.• A total angular quantum number j, the resultant angular momentum of the electron due to both orbital and spin motions i.e vector sum of l and s.
  20. 20. Vector atom Model for Orbital Angular MomentumThe orbital angular momentum The diagram shows that the possiblefor an atomic electron can be values for the "magnetic quantumvisualized in terms of a vector number" ml for l=2 can take the valuesmodel where the angular ml =-2,-1,0,1,2momentum vector is seen as or, in general,precessing about a direction in ml=-l,-l+1,……..,l-1,lspace.
  21. 21. Vector atom Model for Total Angular Momentum When orbital angular momentum L and electron spin angular momentum S are combined to produce the total angular momentum of an atomic electron, the combination process can be visualized in terms of a vector model.
  22. 22. Conclusio nVector atom model can explain Zeeman effect, Stark effect.It can also explain the complex spectra of alkali metal like sodium. And also can explain how the orbital electrons in an atom are distributed around the nucleus.
  23. 23. References• ATOMIC PHYSICS - J.B. RAJAM• INTRODUCTION TO ATOMIC SPECTRA -HARVEY ELLIOTT WHITE• http://www.tutornext.com/lesson/vector-atom- model/1243900• http://www.chembio.uoguelph.ca/preuss/1_5_V ectorModel.pdf
  24. 24. THANK YOU