Quantum Theory and Electronic Structure of the Atom CHEMISTRY 161 Chapter 7 Quantum Theory and Electronic Structure of the Atom www.chem.hawaii.edu/Bil301/welcome.html

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

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

(n, l, ml, ms) ATOMIC ORBITALS n l ml orbitals designation 1 1s 2 2s 1s 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 …

Ψ(n, l, ml, ms) = Rn,l(r) Yml(Θ,Φ)

4πr2[Rn,l(r)]2

Yml(Θ,Φ) z (x,y,z) r Θ Φ y x

1s, 2s, 3s

2pz

Yml(Θ,Φ)

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

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

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

2px, 3px, 4px 2px 3px 4px

d orbitals

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

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

Orbital Energies

Homework Chapter 7, pages 267-271 problems