Lecture 10: Wave Function/Equation, Orbitals, and Quantum Numbers

Ψ:\Psi :  Wave function/equation atomic orbital

Ψ2:\Psi^{2} :  A measure of the intensity of electron density distribution

Ψ2dv:\int \Psi ^{2}dv: Probability

Ψ\Psi must by finite, single valued and continuous

\int (Over all space) Ψ2dv=1\Psi ^{2}dv=1 (normalization)

1 - Finite probability of finding the electron (but don't know where)

Ψ=R(r)Θ(Θ)Φ(Φ)\Psi = R(r)\Theta (\Theta )\Phi (\Phi ) Cartesian coordinates to Polar coordinate


S Orbital

  • Vertical
  • Doesn't have an angle

P Orbital

  • Has an angle
  • X, Y Z axis


Plug in Equation - Ψ=nlm\Psi = nlm

  • n - Defines Orbital size = 1,2,3 (Principle Quantum number)
  • l - Defines Orbital shape = 0, 1, 2, 3 (Azimuthal Q, N) -n-1
  • m - Defines Orbital orientation = -l.....0.....+l (Magnetic Q.N)
  • s - Defines direction of ee^{-}spin = +12or12.+\frac{1}{2} or -\frac{1}{2}. (Spin Q, N)

+12+\frac{1}{2} - Clockwise

12-\frac{1}{2} - Counter clockwise


Quantum Numbers

l = 0 - S orbital (vertical shape)

l = 1 - P orbital (dumbshell shape) Px,Py,PzP_{x}, P_{y}, P_{z}

l = 2 - d orbital (double dumbshell shape)

l = 3 - f orbital

l = 1 m = -1, 0, +1

l = 2 m = -2, -1, 0. +1, +2

Px,Py,PzP_{x}, P_{y}, P_{z} have the same size and energy - "Degenerate Orbital"




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