Behavior of Waves

In-phase rays reinforce

Out-of phase rays annihilate each other

Rays out of phase by an exact number of wavelengths reinforce each other

Shapes of OrbitalsBohr atom assumed

spherical orbits

Wave mechanics make no such assumptions and result

in quantum theory.

Changes from a fixed orbit to a description based on

probability statistics

Energy Levels

Calculations produce a series of solutions to the equations giving a series of energy levels characterized by a series of number options

known as quantum numbers

Quantum numbers

Ist quantum number n=1,2,3………..n2nd quantum number l=0,1,2…………(n-1)3rd quantum number m= -l…….0…….+l4th quantum number s = ±½

Energy LevelsOriginal calculations were made for the hydrogen atom.

All theories of structure and bonding were based on that work

Electronic Structure

Electronic structure is determined by the atomic number

e.g. atomic number = 15 gives 1s2 2s2 2p6 3s2 3p3

Electronic StructureAll properties are determined, ultimately, by the electronic structure,

as it determines the bonding, which determines all properties

1s orbital

2s orbital

Electronic Structure

p orbitals

Electronic Structure

d orbitals

Removing an Electron

COSTS ENERGY

For electron to be removed to make

a compound energy must be obtained from

elsewhere

Adding an electron

Energy is released, but is lower than the energy needed to remove an electron from the other atom

Ionic Bonding

For ions to form and produce a stable structure extra energy must be released.

Energy comes from electrostatic attractions between the ions created.

Electrostatic interaction can be attractive or repulsive

Electronic interaction is always repulsive in nature.

Ionic bonding in terms of forces

Attractive force between anion and cation

Repulsive force between electron clouds of the two ions

Balance occurs when the forces are equal, and determines the bond length

Ionic bonding in terms of energy

Electrostatic attraction produces a lower energy

Electronic repulsion produces a higher energy

Minimum in energy corresponds to stable state and determines the bond length

Equations for ionic bonding

The equation for the electrostatic interaction is simply Coulomb’s equation from electrostatics

Where A is given by

Energy and force approaches are linked by this well-known equation

The repulsive energy equation comes from quantum mechanics

Covalent bondingHybridization of orbitals to new symmetrical states of equal energy

sp3 found in saturated carbon compounds

Sp3 Bonding

Ammonia Methane

Covalent bonding

Hybridization of orbitals to new symmetrical states of equal energysp2 found in unsaturated carbon compounds with double bonds

Sp2 Bonding in Ethylene

Sp2 hybridization produces three sp2 bonds in a triangle for each C-atom

2 C-atoms bond

C-H bonds follow

Each C-atom has one p-orbital unhybridized

They hybridize to produce two molecular orbitals: one filled (shown) and one unfilled

The unfilled orbital is known as an anti-bonding orbital

Covalent bonding

Hybridization of orbitals to new symmetrical states of equal energysp found in unsaturated carbon compounds with triple bonds

Sp bonding in acetyleneTwo sp hybrids are formed leaving 2p orbitals on each C-atom

The sp hybrids result in a C-C bond and two C-H bonds

The four p-orbitals hybridize to four new molecular orbitals, two of which are filled. The two unfilled MOs are known as anti-bonding orbitals

Bonding in benzene

Sp2 hybrids, as in ethylene

Bonding gives a planar ring

Each C-atom has one p-orbital left

The six p-orbitals hybridize to produce six molecular orbital (one shown)

The first three are filled; the other three are unfilled

What really happens in many atom systems?As atoms approach they affect each other’s electronic states.

There are as many states for each type of orbital as there are atoms.

Each orbital type becomes a band

Closer-in states require closer approach for band to form

What determines the band structure of an element?The bond length is determined the atomic size

The atomic size determines the band structure

Only the outermost energy levels become bands

Determines the electronic behavior.

Will a material be

a conductor, or

an insulator, or

a semiconductor?

Band structures

(a) (a) and (b) are conductors

(c) is an insulator

(d) is a intrinsic semiconductor

Conductors

Electrons acquire thermal energy and jump into unpaired states

When raise temperature, atomic or lattice vibrations interfere with motion of electrons. Conductivity decreases with increasing temperature.

Insulators and Intrinsic Semiconductors

Electron cannot acquire enough energy to jump in insulator

Electron can occasionally find enough energy to jump in semiconductor

Increasing temperature allows more electrons to jump; conductivity increases with increasing temperature

Mechanism of Conductivity in a Semiconductor

Concept of electrons and holes as independent species

Extrinsic Semiconductors

N-type

e.g. P atom has extra electron

Without an impurity atom, silicon is an insulator at normal

temperatures

Extrinsic Semiconductors

(2) P-typee.g. B atom has one fewer electron