Quantum numbers

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Quantum numbers

  1. 1. Quantum Numbers
  2. 2. The Three Physicists Louie de Broglie Erwin Schrodinger Werner Karl Heisenberg Quantum Mechanical Model
  3. 3. Quantum mechanics • examines the wave motion of objects Atomic orbital • Specified by three quantum numbers
  4. 4. Quantum Numbers According to Heisenberg’s Uncertainty Principle, it is not possible to give the exact position of an electron and its energy at the same time. But the probability of finding an electron in an orbital of given energy can be determined.
  5. 5. The 3 Quantum Numbers Principal Quantum Number, n Azimuthal Quantum Number, l Magnetic Quantum Number, ml
  6. 6. Principal Quantum Number main energy level of an orbital. Indicates the relative size of the orbital an increase in n also means increase in the energy of the electron in the orbital. n= 1, 2, 3….
  7. 7. Azimuthal Quantum Number also called Angular Momentum Number defines the shape of the orbital. values range from 0 to n-1. l = n - 1
  8. 8. Azimuthal Quantum Number l Sublevel Orbital Shape 0 sharp - s spherical 1 principal - p dumbbell- shaped 2 diffused - d cloverleaf 3 fundamental - f too complex
  9. 9. S- orbital • Spherical shape with the nucleus at its center
  10. 10. P-orbital • “dumb-bell shape”
  11. 11. D-orbital • With 5 different orientations
  12. 12. Azimuthal Quantum Number A sublevel in a particular main energy level is defined by its n and its l values. n l Kind of Sublevel 1 0 1s 3 1 3p
  13. 13. Magnetic Quantum Number, ml describes the orientation of the orbital in space. values are –l to +l values per sublevel = 2l +1.
  14. 14. Magnetic Quantum Number, ml Sublevel l ml s 0 0 p 1 -1,0,+1 d 2 -2,-1,0,1,+2 f 3 -3,-2,-1,0,+1,+2,+3
  15. 15. Sublevel and Capacity of Each Main Energy Level Main Energy Level No. of Sublevel Identity of Sublevels No. of Orbitals (n2) Max. No. of Electrons (2n2) 1 1 1s 1 2 2 2 2s 2p 1 3 2 6 3 3 3s 3p 3d 1 3 5 2 6 10 4 4 4s 4p 4d 4f 1 3 5 7 2 6 10 14
  16. 16. Orbital Diagram
  17. 17. Exercise No. 1 Quantum Numbers Give all the possible quantum numbers for electrons in the 2nd energy level. Give all the possible quantum numbers for electrons in: a. 3s orbital b. 4d orbital Give the quantum numbers in: a. 4f3 b. 3p5
  18. 18. Exercise No. 2 Quantum Numbers Which of the following sets of QN is NOT possible? Write possible or impossible and justify your answer. a. n=2, l=1 c. n=1, ml=+1 d. l=4, ml=-3

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