Download Quantum Mechanical Model

Orbitals
 Orbitals are NOT circular orbits for
electrons
Orbitals are “areas of probability” for
locating electrons
 A function of the coordinates (x, y, and z)
of the electron’s position in 3-D space
Heisenberg Uncertainty Principle
 “ There is a fundamental limitation on how
precisely we can know both the position
and momentum of a particle at a given
time.”
 The more accurately we know the position
of any particle, the less accurately we can
know its momentum and vice versa
Physical Meaning of a Wave
Function
 Square of the absolute value of the wave function
gives a probability distribution
 Electron density map indicates the most probable
distance from the nucleus
 Wave functions and probability maps do not
describe
 How an electron arrived at its location
 Where an electron will go next
 When the electron will be in a particular location
Quantum Numbers
 Principal Quantum
Number (n)
 Integral values: 1,2,3,
etc
 Indicates probable
distance from the
nucleus
 Higher number –
greater distance
 Greater distance –
less tightly bound
 Higher energy
 Angular Momentum
Quantum (l)
 Integral values from 0
to n-1 for each
principal quantum
number n
 Indicates the shape of
the atomic orbital
Angular Momentum & Orbital
Angular Momentum Quantum Numbers and
Corresponding Atomic Orbital Number
Value of l
(angular)
0
1
2
3
Letter Used
s
p
d
f
Quantum Numbers
 Magnetic Quantum Number (ml)
 Integral values from l to -l (including 0)
 Related to the orientation of the orbital in space
relative to the other orbitals
 Electron Spin Quantum Number
 An orbital can hold only two electrons
 They must have opposite spins
 + ½ or - ½
Pauli Exclusion Principle
 No two electrons can have the same
set of four quantum numbers
Quantum Numbers for the First Four
Levels of Orbitals in the H Atom
n
l
Orbital
ml
# of orbitals
1
0
1s
0
1
2
0
2s
0
1
1
2p
-1, 0, 1
3
0
3s
0
1
1
3p
-1, 0, 1
3
2
3d
-2, -1, 0, 1, 2
5
0
4s
0
1
1
4p
-1, 0, 1
3
2
4d
-2, -1, 0, 1, 2
5
3
4f
-3, -2, -1, 0, 1, 2, 3
7
3
4
Orbital Shapes & Energies
 Size of Orbitals
 Defined as the surface that contains 90% of the total
electron probability
 Orbitals of the same shape (eg: s) grow larger as n
increases
S Orbitals
 Spherical
 Nodes (s orbitals of
n≥2)
 Internal regions of
zero probability
 See p. 309
p Orbitals
 Two lobes each
 Occur in levels n≥2
 Each orbital lies
along an axis
 2px 2py 2pz
d Orbitals
 Occur in levels n≥3
 Two fundamental shapes
 Four orbitals with four lobes each
 Centered on each indicated plane
 dxz, dyz, dxy, dx2y2
 Fifth orbital is uniquely shaped
 Two lobes along the z axis and a belt centered
in the xy plane – dz2
d Orbitals
f Orbital
 Occur in levels n≥4
 Highly complex shapes
 Not involved in bonding in most
compounds
Orbital Energies
 All orbitals with the same value of n
have the same energy
 The lowest E state is the ground state
 When atoms absorb energy – electrons
may move to higher energy levels
 Excited state