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