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CHEMISTRY 161 Chapter 7 Quantum Theory and Electronic Structure of the Atom www.chem.hawaii.edu/Bil301/welcome.html. REVISION. H = E . atomic orbital wave function of an electron in an atom. 2. probability of finding an electron at a given location. Schroedinger. - PowerPoint PPT Presentation
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CHEMISTRY 161
Chapter 7
Quantum Theory and Electronic Structure of the Atom
www.chem.hawaii.edu/Bil301/welcome.html
Schroedinger
H = E REVISION
atomic orbital
wave function of an electron in an atom
2
probability of finding an electron at a given location
ORBITALS AND QUANTUM NUMBERS
1.principle quantum number
2. angular momentum quantum number
3. magnetic quantum number
4. spin quantum number
n = 1, 2, 3, 4, 5…
l = 0, 1, … (n-1)
ml = -l, (-l +1), … 0…… (+l-1) +l
ms = -1/2; + 1/2
(n, l, ml, ms) ATOMIC ORBITALS
n l ml orbitals designation
1 0 0 1 1s
2 0 0 1 2s
1 -1,0,+1 3 2px,2py,2pz
3 0 0 1 3s
1 -1,0,+1 3 3px,3py,3pz
2 -2,-1,0,+1,+2 5 3dxy,3dyz,3dxz,
3dx2-y2,3dz2
4 … … … …
Ψ(n, l, ml, ms) = Rn,l(r) Yml(Θ,Φ)
4πr2[Rn,l(r)]2
Yml(Θ,Φ)
x
z
y
(x,y,z)
r
Θ
Φ
1s, 2s, 3s
2pz
Yml(Θ,Φ)
Ψ1,0 = 1s
probability of finding
the electron within
a sphere of a radius r
r
90 %
‘boundary surfaces’
1s, 2s, 3s
3s2s1s
s orbitals do not depend on Φ or Θ
p orbitals
+ and – refers to Ψ, but the figure shows Ψ2
2px, 3px, 4px
4px3px2px
d orbitals
Orbital Energies
energy level diagram H atom
3s 3p 3d
2s 2p
1s
E
energy depends only on principal quantum number
orbitals with same n but different l are degenerate
1s
E
2s2p
3s3p
3d4s
4p5s
4d
MULTI-ELECTRON ATOM
orbitals with same n and different l are not degenerate
energy depends on n and ml
Orbital Energies
Homework
Chapter 7, pages 267-271 problems