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Quantum Mechanics

Rutherford. Quantum Mechanics. Through the Looking Glass. This is how the model of the atom has developed so far:. Bohr-Planetary Model. Correcting Bohr’s Planetary Model. …using the Photoelectric Effect. then why can’t particles have a wavelike nature?. Louis DeBroglie’s insight:.

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Quantum Mechanics

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  1. Rutherford Quantum Mechanics Through the Looking Glass This is how the model of the atom has developed so far: Bohr-Planetary Model

  2. Correcting Bohr’s Planetary Model …using the Photoelectric Effect

  3. then why can’t particles have a wavelike nature? Louis DeBroglie’s insight: If electrons are particles Electrons must have a wavelike nature If light radiation can have a particle nature  = h mv

  4. Heisenberg’s Uncertainty Principle Werner Heisenberg (1901-1976) There is an uncertainty in either the position or the momentum of an electron that cannot be reduced beyond a certain minimum level Is Shrodinger’s cat dead or alive?

  5. The Quantum Mechanical Model Describes the wave properties of electrons and regions of space surrounding the nucleus Called orbitals Where there is a high probability of finding electrons

  6. Bohr-Planetary Model Describing an electron’s address Bohr’s model places the electron in a quantum energy level (n)

  7. Describing an electron’s address using the Quantum Mechanical Model Electrons exist in orbitals A collection of orbitals with the same energy is called an electron shell designated (n) 1st quantum #-principle quantum number (n) n = (1,2,3,…, ) describes shell or energy level

  8. Describing an electron’s address using the Quantum Mechanical Model 2nd quantum # - azimuthal number(l), value 0 to n-1 describes sublevel 3rd quantum # - magnetic number (ml), value = l to 0 to-l The orientation of the orbital in space 4th Quatum # - Spin (ms), value is + or – ½, describes the spin

  9. The first energy level (n = 1) is constructed from a single orbital (l = 0), also designated ‘1s’, which is spherical ( ml = 0)

  10. The second energy level (n = 2) is constructed from a single orbital (l = 0) also designated ‘2s’ which is spherical ( ml = 0)

  11. The third energy level (n = 3) is constructed from a single orbital (l = 0) also designated ‘3s’ which is spherical ( ml = 0)

  12. Energy level ‘n = 2’ is more complex than energy level ‘n =1’ and is constructed from two kinds of orbitals The innermost part of ‘n =2’ consists of a single spherical orbital designated ‘2s’ The outermost part of ‘n = 2’ consists of three orbitals which are not spherical, (l = 1)

  13. Each dumbbell-shaped orbital (l = 1), also designated ‘2px, 2py,2pz’is oriented along the x, y, and z axes ( ml = -1, 0, 1) Like the ‘s’ orbital, the ‘p’ orbitals also repeat in subsequent energy levels

  14. Energy level ‘n = 3’ is more complex than energy level ‘n =1’ or ‘n = 2’ and consists of an innermost spherical orbital designated ‘3s’ The middle part of ‘n = 3’ consists of three dumbbell-shaped orbitals , (l = 1) The outermost part of ‘n = 3’ consists of five orbitals which are also not spherical, (l = 2)

  15. Each four-lobed orbital (l = 2), also designated ‘3 d orbital’is oriented along different planes ( ml = -2, -1, 0, 1, 2) Like the ‘s’ and ‘p’ orbitals, the ‘d’ orbitals also repeat in subsequent energy levels

  16. Energy level ‘n = 4’ is more complex than energy level ‘n =1, 2, or 3’ and consists of an innermost spherical orbital designated ‘4s’ The lower middle part of ‘n = 4’ consists of three dumbbell-shaped orbitals , (l = 1) The upper middle part of ‘n = 4’ consists of five orbitals which are also not spherical, (l = 2)

  17. The outermost part of ‘n = 4’ consists of seven orbitals, also designated ‘f ’ orbitals, which are also not spherical, (l = 3) In fact, they are a real nightmare ( ml = -3, -2, -1, 0, 1, 2, 3)

  18. Describing an electron’s address

  19. Quantum Mechanics: Where ever you go... there you are! Schwartzchild’s Radical • which of the following is not an allowable • quantum number • 4,4,3,1/2 • 3,2,2,1 • 5,2,-1,-1/2

  20. What are the maximum number of electrons allowed that have the quantum numbers designated? • 1. n=3 • 2. n=3, l=2 • 3. n= 3, l=2, ml = 1 • 4. n= 3, l=2, ml = 1, ms = 1/2

  21. Which of the following are in an excited state and what element do they represent? • 1. 1s22s22p63p64s23d104p65s24d105p6

  22. How many unpaired electrons are in each of the following. • Cr • Fe3+ • Cl1-

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