1. Quantum Theory and Electronic Structure of the Atom
CHEMISTRY 161
Chapter 7
Quantum Theory and Electronic Structure of the Atom

2. H = E  2 REVISION atomic orbital
wave function of an electron in an atom 2
probability of finding an electron
at a given location
Schroedinger

3. ORBITALS AND QUANTUM NUMBERS
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

4. (n, l, ml, ms) ATOMIC ORBITALS n l ml orbitals designation 1 1s 2 2s1s 2 2s
-1,0,+1 3
2px,2py,2pz 3s
3px,3py,3pz
-2,-1,0,+1,+2 5
3dxy,3dyz,3dxz,
3dx2-y2,3dz2 4 …

5. Ψ(n, l, ml, ms) = Rn,l(r) Yml(Θ,Φ)

6. 4πr2[Rn,l(r)]2

7. Yml(Θ,Φ) z
(x,y,z) r Θ Φ y x

8. 1s, 2s, 3s

9. 2pz

10. Yml(Θ,Φ)

11. probability of finding
Ψ1,0 = 1s
probability of finding
the electron within
a sphere of a radius r r
90 %
‘boundary surfaces’

12. s orbitals do not depend on Φ or Θ
1s, 2s, 3s 1s 2s 3s
s orbitals do not depend on Φ or Θ

13. + and – refers to Ψ, but the figure shows Ψ2
p orbitals
+ and – refers to Ψ, but the figure shows Ψ2

14. 2px, 3px, 4px
2px
3px
4px

15. d orbitals

16. Orbital Energies E energy level diagram H atom
3s 3p 3d
2s 2p 1s E
energy level diagram H atom
energy depends only on principal quantum number
orbitals with same n but different l are degenerate

17. energy depends on n and ml
MULTI-ELECTRON ATOM 1s E 2s 2p 3s 3p 3d 4s 4p 5s 4d
energy depends on n and ml
orbitals with same n and different l are not degenerate

18. Orbital Energies

19. Homework
Chapter 7, pages
problems