Molecules and solids

Сентябрь 2, 2022

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Molecules and solids

Содержание

2. Molecular Bonds A potential energy function that can be used to model a molecule should account
3. Molecular Bonds Potential energy versus internuclear separation distance for a two-atom system is graphed in Figure.
4. Molecular Bonds Ionic Bonding Total energy versus internuclear separation distance for Na+ and Cl- ions.
5. Molecular Bonds Covalent Bonding A covalent bond between two atoms is one in which electrons supplied
6. Molecular Bonds Van der Waals Bonding You might think that two neutral molecules would not interact
7. Molecular Bonds Van der Waals Bonding The second type, the dipole–induced dipole force, results when a
8. Molecular Bonds Hydrogen Bonding Because hydrogen has only one electron, it is expected to form a
9. Energy States and Spectra of Molecules Rotational Motion of Molecules the reduced mass of the molecule
10. Energy States and Spectra of Molecules Rotational Motion of Molecules J is the rotational quantum number
11. Energy States and Spectra of Molecules Rotational Motion of Molecules
12. Energy States and Spectra of Molecules Vibrational Motion of Molecules v is the vibrational quantum number
13. Energy States and Spectra of Molecules Vibrational Motion of Molecules
14. Energy States and Spectra of Molecules Molecular Spectra The energy levels of any molecule can be
15. Molecular Spectra Energy States and Spectra of Molecules When a molecule absorbs a photon with the
16. Molecular Spectra Energy States and Spectra of Molecules
17. Bonding in Solids Ionic Solids α is a dimensionless number known as the Madelung constant
18. Bonding in Solids Ionic Solids Total potential energy versus ion separation distance for an ionic solid,
19. Bonding in Solids Covalent Solids
20. Bonding in Solids Covalent Solids
21. Bonding in Solids Metallic Solids Metallic bonds are generally weaker than ionic or covalent bonds. The
22. Free-Electron Theory of Metals The probability that a particular state having energy E is occupied by
23. Free-Electron Theory of Metals
24. Free-Electron Theory of Metals The function g(E) is called the density-of-states function.
25. Free-Electron Theory of Metals
26. Free-Electron Theory of Metals
27. Free-Electron Theory of Metals
28. Band Theory of Solids
29. Band Theory of Solids Energies of the 1s and 2s levels in sodium as a function
30. Band Theory of Solids Energy bands of a sodium crystal. Blue represents energy bands occupied by
31. Electrical Conduction in Metals, Insulators, and Semiconductors Metals Half-filled band of a metal, an electrical conductor.
32. Electrical Conduction in Metals, Insulators, and Semiconductors Insulators The lower, filled band is called the valence
33. Electrical Conduction in Metals, Insulators, and Semiconductors Semiconductors Semiconductors have the same type of band structure
34. Electrical Conduction in Metals, Insulators, and Semiconductors Semiconductors
35. Doped Semiconductors Electrical Conduction in Metals, Insulators, and Semiconductors
36. Electrical Conduction in Metals, Insulators, and Semiconductors Doped Semiconductors
37. Superconductivity There is a class of metals and compounds known as superconductors whose electrical resistance decreases
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Слайд 2

Molecular Bonds
A potential energy function that can be used to model

a molecule should account for two known features of molecular bonding:
1. The force between atoms is repulsive at very small separation distances. When two atoms are brought close to each other, some of their electron shells overlap, resulting in repulsion between the shells. This repulsion is partly electrostatic in origin and partly the result of the exclusion principle. Because all electrons must obey the exclusion principle, some electrons in the overlapping shells are forced into higher energy states and the system energy increases as if a repulsive force existed between the atoms.
2. At somewhat larger separations, the force between atoms is attractive. If that were not true, the atoms in a molecule would not be bound together.
Taking into account these two features, the potential energy for a system of two atoms can be represented by an expression of the form

Слайд 3

Molecular Bonds
Potential energy versus internuclear separation distance for a two-atom system

is graphed in Figure. At large separation distances between the two atoms, the slope of the curve is positive, corresponding to a net attractive force. At the equilibrium separation distance, the attractive and repulsive forces just balance. At this point, the potential energy has its minimum value and the slope of the curve is zero.

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Molecular Bonds
Ionic Bonding
Total energy versus
internuclear separation distance for
Na+ and Cl- ions.

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Molecular Bonds
Covalent Bonding
A covalent bond between two atoms is one in

which electrons supplied by either one or both atoms are shared by the two atoms.

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Molecular Bonds
Van der Waals Bonding
You might think that two neutral molecules

would not interact by means of the electric force because they each have zero net charge. They are attracted to each other, however, by weak electrostatic forces called van der Waals forces.

There are three types of van der Waals forces. The first type, called the dipole–dipole force, is an interaction between two molecules each having a permanent electric dipole moment. For example, polar molecules such as HCl have permanent electric dipole moments and attract other polar molecules.

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Molecular Bonds
Van der Waals Bonding
The second type, the dipole–induced dipole force,

results when a polar molecule having a permanent electric dipole moment induces a dipole moment in a nonpolar molecule. In this case, the electric field of the polar molecule creates the dipole moment in the nonpolar molecule, which then results in an attractive force between the molecules.
The third type is called the dispersion force, an attractive force that occurs between two nonpolar molecules. In this case, although the average dipole moment of a nonpolar molecule is zero, the average of the square of the dipole moment is nonzero because of charge fluctuations. Two nonpolar molecules near each other tend to have dipole moments that are correlated in time so as to produce an attractive van der Waals force.

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Molecular Bonds
Hydrogen Bonding
Because hydrogen has only one electron, it is expected

to form a covalent bond with only one other atom within a molecule. A hydrogen atom in a given molecule can also form a second type of bond between molecules called a hydrogen bond.

DNA molecules are held together by hydrogen bonds

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Energy States and Spectra of Molecules
Rotational Motion of Molecules
the reduced mass

of the molecule

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Energy States and Spectra of Molecules
Rotational Motion of Molecules
J is the

rotational quantum number

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Energy States and Spectra of Molecules
Rotational Motion of Molecules

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Energy States and Spectra of Molecules
Vibrational Motion of Molecules
v is the

vibrational quantum number

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Energy States and Spectra of Molecules
Vibrational Motion of Molecules

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Energy States and Spectra of Molecules
Molecular Spectra
The energy levels of any

molecule can be calculated from this expression, and each level is indexed by the two quantum numbers v and J.

In general, a molecule vibrates and rotates simultaneously. To a first approximation, these motions are independent of each other, so the total energy of the molecule for these motions is

Слайд 15

Molecular Spectra
Energy States and Spectra of Molecules
When a molecule absorbs a

photon with the appropriate energy, the vibrational quantum number v increases by one unit while the rotational quantum number J either increases or decreases

Therefore, the molecular absorption spectrum consists of two groups of lines:

Слайд 16

Molecular Spectra
Energy States and Spectra of Molecules

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Bonding in Solids
Ionic Solids
α is a dimensionless number known as the

Madelung constant

Слайд 18

Bonding in Solids
Ionic Solids
Total potential energy versus ion separation distance for

an ionic solid, where U0 is the ionic cohesive energy and r0 is the equilibrium separation distance between ions

This minimum energy U0 is called the ionic cohesive energy of the solid, and its absolute value represents the energy required to separate the solid into a collection of isolated positive and negative ions.

The atomic cohesive energy of NaCl is

Слайд 19

Bonding in Solids
Covalent Solids

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Bonding in Solids
Covalent Solids

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Bonding in Solids
Metallic Solids
Metallic bonds are generally weaker than ionic or

covalent bonds. The outer electrons in the atoms of a metal are relatively free to move throughout the material, and the number of such mobile electrons in a metal is large. The metallic structure can be viewed as a “sea” or a “gas” of nearly free electrons surrounding a lattice of positive ions

Слайд 22

Free-Electron Theory of Metals
The probability that a particular state having energy

E is occupied by one of the electrons in a solid is

f(E) is called the Fermi–Dirac distribution function and EF is called the Fermi energy.

Statistical physics can be applied to a collection of particles in an effort to relate microscopic properties to macroscopic properties. In the case of electrons, it is necessary to use quantum statistics, with the requirement that each state of the system can be occupied by only two electrons (one with spin up and the other with spin down) as a consequence of the exclusion principle.

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Free-Electron Theory of Metals

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Free-Electron Theory of Metals
The function g(E) is called the density-of-states function.

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Free-Electron Theory of Metals

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Free-Electron Theory of Metals

Слайд 27

Free-Electron Theory of Metals

Слайд 28

Band Theory of Solids

Слайд 29

Band Theory of Solids
Energies of the 1s and 2s levels in

sodium as a function of the separation distance r between atoms.

Слайд 30

Band Theory of Solids
Energy bands of a sodium crystal. Blue represents

energy bands occupied by the sodium electrons when the atom is in its ground state. Gold represents energy bands that are empty.

Band theory allows us to build simple models to understand the behavior of conductors, insulators, and semiconductors as well as that of semiconductor devices, as we shall discuss in the following sections.

Слайд 31

Electrical Conduction in Metals,
Insulators, and Semiconductors
Metals
Half-filled band of a metal, an

electrical conductor. At T=0 K, the Fermi energy lies in the middle of the band.

Слайд 32

Electrical Conduction in Metals,
Insulators, and Semiconductors
Insulators
The lower, filled band is called

the valence band, and the upper, empty band is the conduction band. (The conduction band is the one that is partially filled in a metal.) It is common to refer to the energy separation between the valence and conduction bands as the energy gap Eg of the material.

Слайд 33

Electrical Conduction in Metals,
Insulators, and Semiconductors
Semiconductors
Semiconductors have the same type of

band structure as an insulator, but the energy gap is much smaller, on the order of 1 eV.

Слайд 34

Electrical Conduction in Metals,
Insulators, and Semiconductors
Semiconductors

Слайд 35

Doped Semiconductors
Electrical Conduction in Metals,
Insulators, and Semiconductors

Слайд 36

Electrical Conduction in Metals,
Insulators, and Semiconductors
Doped Semiconductors

Слайд 37

Superconductivity
There is a class of metals and compounds known as superconductors

whose electrical resistance decreases to virtually zero below a certain temperature Tc called the critical temperature.

Molecules and solids

Содержание

Molecular BondsA potential energy function that can be used to model

Molecular BondsPotential energy versus internuclear separation distance for a two-atom system

Molecular BondsIonic BondingTotal energy versusinternuclear separation distance forNa+ and Cl- ions.

Molecular BondsCovalent BondingA covalent bond between two atoms is one in

Molecular BondsVan der Waals BondingYou might think that two neutral molecules

Molecular BondsVan der Waals BondingThe second type, the dipole–induced dipole force,

Molecular BondsHydrogen BondingBecause hydrogen has only one electron, it is expected

Energy States and Spectra of MoleculesRotational Motion of Moleculesthe reduced mass

Energy States and Spectra of MoleculesRotational Motion of MoleculesJ is the

Energy States and Spectra of MoleculesRotational Motion of Molecules

Energy States and Spectra of MoleculesVibrational Motion of Moleculesv is the

Energy States and Spectra of MoleculesVibrational Motion of Molecules

Energy States and Spectra of MoleculesMolecular SpectraThe energy levels of any

Molecular SpectraEnergy States and Spectra of MoleculesWhen a molecule absorbs a

Molecular SpectraEnergy States and Spectra of Molecules

Bonding in SolidsIonic Solidsα is a dimensionless number known as the

Bonding in SolidsIonic SolidsTotal potential energy versus ion separation distance for

Bonding in SolidsCovalent Solids

Bonding in SolidsCovalent Solids

Bonding in SolidsMetallic SolidsMetallic bonds are generally weaker than ionic or

Free-Electron Theory of MetalsThe probability that a particular state having energy

Free-Electron Theory of Metals

Free-Electron Theory of MetalsThe function g(E) is called the density-of-states function.

Free-Electron Theory of Metals

Free-Electron Theory of Metals

Free-Electron Theory of Metals

Band Theory of Solids

Band Theory of SolidsEnergies of the 1s and 2s levels in

Band Theory of SolidsEnergy bands of a sodium crystal. Blue represents

Electrical Conduction in Metals,Insulators, and SemiconductorsMetalsHalf-filled band of a metal, an

Electrical Conduction in Metals,Insulators, and SemiconductorsInsulatorsThe lower, filled band is called

Electrical Conduction in Metals,Insulators, and SemiconductorsSemiconductorsSemiconductors have the same type of

Electrical Conduction in Metals,Insulators, and SemiconductorsSemiconductors

Doped SemiconductorsElectrical Conduction in Metals,Insulators, and Semiconductors

Electrical Conduction in Metals,Insulators, and SemiconductorsDoped Semiconductors

SuperconductivityThere is a class of metals and compounds known as superconductors

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A potential energy function that can be used to model

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Potential energy versus internuclear separation distance for a two-atom system

Molecular Bonds
Ionic Bonding
Total energy versus
internuclear separation distance for
Na+ and Cl- ions.

Molecular Bonds
Covalent Bonding
A covalent bond between two atoms is one in

Molecular Bonds
Van der Waals Bonding
You might think that two neutral molecules

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Van der Waals Bonding
The second type, the dipole–induced dipole force,

Molecular Bonds
Hydrogen Bonding
Because hydrogen has only one electron, it is expected

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the reduced mass

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J is the

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v is the

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The energy levels of any

Molecular Spectra
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When a molecule absorbs a

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Bonding in Solids
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The probability that a particular state having energy

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The function g(E) is called the density-of-states function.

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Semiconductors have the same type of

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