Download Chapter 7 Lect. 2

I.
Indeterminacy and Probability Distribution Maps
A.
Newton’s classical mechanics laws for particle behavior are deterministic
1. We can predict exactly where a macroscopic particle is going to go if we know where it’s been
2. This behavior correlates with what we see in everyday behavior of objects
B.
Quantum Mechanics is based on Uncertainty and Probability: Indeterminate
1. We can’t predict exactly where an electron is going, or even where it is right now
2. This behavior does not correlate to everyday objects, but correctly predicts small particle behavior
C. Solutions to the Schrodinger Equation Hˆ   E
1. There are many, quantized solutions
2. These solutions are related through Quantum Numbers that are the results
of how the solutions are arrived at.
3. These Quantum Numbers will eventually help us explain the shapes of
orbitals, as well as the format of the Periodic Table
4. Preview:
II. Quantum Numbers (QN)
A. Principal QN (n = 1, 2, 3, . . .)
1. Related to size of the atomic orbital (distance from the nucleus).
2. Larger n value indicates higher energy
3. Larger n value means electrons are less strongly bound to nucleus
B. Angular Momentum QN (l = 0 to n  1)
1. Relates to shape of the atomic orbital.
2. Each l number is assigned a letter
3. n = 3, l = 0, 1, 2 (s, p, and d orbitals in the third shell)
C. Magnetic QN (ml = l to  l)
1. Relates to orientation of the orbital in space relative to other orbitals.
2. For l = 2, ml = -2, -1, 0, 1, 2 (Five d-orbitals)
D. Electron Spin QN (ms = +1/2, 1/2)
1. Relates to the spin states of the electrons.
2. Electrons are –1 charged and are spinning
3. Spinning charge creates a magnetic field
4. You can tell the direction of the spin by which way the magnetic
moment lines up in an external magnetic field
5. The two possible spin directions are called +½ and –½
E. Pauli Exclusion Principle
1. In a given atom, no two electrons can have the same set of four quantum
numbers (n, l, ml, ms).
2. Therefore, an orbital can hold only two electrons, and they must have
opposite spins.
3.
Electrons can have the same n, l, and ml values
a) n = 3, l = 2 (d-orbital), ml = -2 (a single d-orbital)
b) That single d-orbital can only hold 2 e-, one with
ms = +1/2, and one with ms = 1/2
III. Orbital Shapes and Energies
A. Atomic orbital shapes are surfaces that surround 90% of the total
probability of where its electrons are
1. Look at l = 0, the s-orbitals
2. Basic shape of an s-orbital is spherical
centered on the nucleus
3. Basic shape is same for same l values
4. Nodes = areas of zero probability
5. Number of nodes changes for larger n
6. We will usually just use outer surface
to describe the shape of an orbital
B. p-orbitals
1. There are no 1p orbitals (n = 1, l = 0 only)
2. 2p orbitals (n = 2, l = 1) have 2 lobes with a node at the nucleus
3. There are three different p-orbitals (l = 1, ml = -1, 0, 1)
a. 2px lies along the x-axis
b. 2py lies along the y-axis
c. 2pz lies along the z-axis
4. All three 2p orbitals have the same energy = degenerate
5. 3p, 4p, 5p, etc… have the same shape and number, just larger, internal lobes
C. d-orbitals
1. There are no 1d or 2d orbitals (d needs l = 2, so n = 3)
2. 5 degenerate d-orbitals (ml = -2, -1, 0, 1, 2)
3. 4 of the d-orbitals have 4 lobes which lie in planes on or between the xyz axes:
3dxy, 3dxz, 3dyz, 3dx2-y2
4. 1 is composed of 2 lobes and a torus-shaped area:
3dz2
5. The 4d orbitals etc…are the same shape, only larger
D. f-orbitals
1. n = 4, l = 3, ml = -3, -2, -1, 0, 1, 2, 3
2. 7 f-orbitals in the fourth shell are degenerate
3. The f-orbital are only used for the lanthanides and actinides and are
complex shapes. We won’t use them.
E. Orbital Energies
1. Orbital energies are largely determined by
the n value: 3 > 2 > 1 for H atom (s = p)
2. But, for polyelectron atoms, the different
l values are not all degenerate (s ≠ p)
a. 2s is larger than 2p orbital
b. 2s “penetrates” the 2p, so is lower energy
c. Penetration effects help explain energy ordering
F. The Phase of Orbitals
1. Waves can have + and – areas above and below the origin
2. The area above zero is called Positive Amplitude
3. The area below zero is call Negative Amplitude
4. The +/- have nothing to do with the electrical charge, it is just a way to
mathematically differentiate between parts of orbitals
G. Spherical Nature of Atoms:
All the orbitals taken together = sphere