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 Orbitals Bohr 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………..n 2nd quantum number l=0,1,2…………(n-1) 3rd quantum number m= -l…….0…….+l 4th quantum number s = ±½

Energy Levels Original 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 1s 2 2s 2 2p 6 3s 2 3p 3

Electronic Structure All 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 bonding Hybridization of orbitals to new symmetrical states of equal energy sp 3 found in saturated carbon compounds

Sp 3 Bonding Ammonia Methane

Covalent bonding Hybridization of orbitals to new symmetrical states of equal energy sp 2 found in unsaturated carbon compounds with double bonds

Sp 2 Bonding in Ethylene Sp 2 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 energy sp found in unsaturated carbon compounds with triple bonds

Sp bonding in acetylene Two 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 Sp 2 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-type e.g. B atom has one fewer electron