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Fundamental Concepts

Atoms are composed of electrons, protons, and neutrons. Electron and protons are

negative and positive charges of the same magnitude, 1.6 × 10-19 Coulombs.

he mass of the electron is negligible !ith respect to those of the proton and the

neutron, !hich form the nucleus of the atom. he unit of mass is an atomic mass

unit "amu# $ 1.66 × 10-%& 'g, and e(uals 1)1% the mass of a carbon atom. he

Carbon nucleus has *$6, and A$6, !here * is the number of protons, and A the

number of neutrons. +eutrons and protons have ver similar masses, roughl e(ual

to 1 amu. A neutral atom has the same number of electrons and protons, *.

A mole is the amount of matter that has a mass in grams e(ual to the atomic mass

in amu of the atoms. hus, a mole of carbon has a mass of 1% grams. he number of

atoms in a mole is called the Avogadro number, +av $ 6.0% × 10%. +ote that +av

$ 1 gram)1 amu.

Calculating n, the number of atoms per cm in a piece of material of densit d

"g)cm#.

n $ +av × d )

!here is the atomic mass in amu "grams per mol#. hus, for graphite "carbon#

!ith a densit d $ 1./ g)cm, $1%, !e get 6 × 10% atoms)mol × 1./ g)cm ) 1%

g)mol# $ 9 × 10%% C)cm.

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or a molecular solid li'e ice, one uses the molecular mass, "%2# $ 1/. 3ith a

densit of 1 g)cm, one obtains n $ . × 10%% %2)cm. +ote that since the

!ater molecule contains atoms, this is e(uivalent to 9.9 × 10%% atoms)cm.

ost solids have atomic densities around 6 × 10%% atoms)cm. he cube root of

that number gives the number of atoms per centimeter, about 9 million. he mean

distance bet!een atoms is the inverse of that, or 0.%4 nm. his is an important

number that gives the scale of atomic structures in solids.

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Electrons in Atoms

he forces in the atom are repulsions bet!een electrons and attraction bet!een

electrons and protons. he neutrons pla no significant role. hus, * is !hat

characteri5es the atom.

he electrons form a cloud around the neutron, of radius of 0.04 % nanometers.

Electrons do not move in circular orbits, as in popular dra!ings, but in 7fu557

orbits. 3e cannot tell ho! it moves, but onl sa !hat is the probabilit of finding

it at some distance from the nucleus. According to (uantum mechanics, onl certain

orbits are allo!ed "thus, the idea of a mini planetar sstem is not correct#. he

orbits are identified b a principal (uantum number n, !hich can be related to the

si5e, n $ 0 is the smallest8 n $ 1, % .. are larger. "he are (uanti5ed or discrete,

being specified b integers#. he angular momentum l is (uanti5ed, and so is the

pro:ection in a specific direction m. he structure of the atom is determined b

the ;auli e<clusion principle, onl t!o electrons can be placed in an orbit !ith a

given n, l, m one for each spin. able %.1 in the te<tboo' gives the number of

electrons in each shell "given b n# and subshells "given b l#.

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The Periodic Table

Elements are categori5ed b placing them in the periodic table. Elements in a

column share similar properties. he noble gases have closed shells, and so the do

not gain or lose electrons near another atom. Al'alis can easil lose an electron and

become a closed shell8 halogens can easil gain one to form a negative ion, again

!ith a closed shell. he propensit to form closed shells occurs in molecules, !hen

the share electrons to close a molecular shell. E<amples are %, +%, and +aCl.

he abilit to gain or lose electrons is termed electronegativit or electro

positivit, an important factor in ionic bonds.

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Bonding Forces and Energies

he Coulomb forces are simple= attractive bet!een electrons and nuclei, repulsive

bet!een electrons and bet!een nuclei. he force bet!een atoms is given b a sum

of all the individual forces, and the fact that the electrons are located outside the

atom and the nucleus in the center.

3hen t!o atoms come ver close, the force bet!een them is al!as repulsive,

because the electrons sta outside and the nuclei repel each other. >nless both

atoms are ions of the same charge "e.g., both negative# the forces bet!een atoms

is al!as attractive at large internuclear distances r. ?ince the force is repulsive

at small r, and attractive at small r, there is a distance at !hich the force is 5ero.

his is the e(uilibrium distance at !hich the atoms prefer to sta.

he interaction energ is the potential energ bet!een the atoms. @t is negative if

the atoms are bound and positive if the can move a!a from each other. he

interaction energ is the integral of the force over the separation distance, so

these t!o (uantities are directl related. he interaction energ is a minimum at

the e(uilibrium position. his value of the energ is called the bond energ, and is

the energ needed to separate completel to infinit "the !or' that needs to be

done to overcome the attractive force.# he strongest the bond energ, the

hardest is to move the atoms, for instance the hardest it is to melt the solid, or to

evaporate its atoms.

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Primary Interatomic Bonds

@onic Aonding 

his is the bond !hen one of the atoms is negative "has an e<tra electron# and

another is positive "has lost an electron#. hen there is a strong, direct Coulomb

attraction. An e<ample is +aCl. @n the molecule, there are more electrons around

Cl, forming Cl- and less around +a, forming +aB. @onic bonds are the strongest

bonds. @n real solids, ionic bonding is usuall combined !ith covalent bonding. @n

this case, the fractional ionic bonding is defined as ionic $ 100 × D1 e<p"-0.%4

"A #%F, !here A and are the electro negativities of the t!o atoms, Aand , forming the molecule.

Covalent Aonding 

@n covalent bonding, electrons are shared bet!een the molecules, to saturate the

valence. he simplest e<ample is the % molecule, !here the electrons spend more

time in bet!een the nuclei than outside, thus producing bonding.

.etallic Aonding 

@n metals, the atoms are ioni5ed, loosing some electrons from the valence band.

hose electrons form a electron sea, !hich binds the charged nuclei in place, in a

similar !a that the electrons in bet!een the atoms in the % molecule bind the

protons.

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Secondary Bonding (Van der Waals

0luctuating @nduced Gipole Aonds 

?ince the electrons ma be on one side of the atom or the other, a dipole is

formed= the B nucleus at the center, and the electron outside. ?ince the electron

moves, the dipole fluctuates. his fluctuation in atom A produces a fluctuating

electric field that is felt b the electrons of an ad:acent atom, . Atom then

polari5es so that its outer electrons are on the side of the atom closest to the B

side "or opposite to the side# of the dipole in A. his bond is called van der 3aals

bonding.

;olar .olecule-@nduced Gipole Aonds 

A polar molecule li'e %2 "s are partiall B, 2 is partiall #, !ill induce a dipole

in a nearb atom, leading to bonding.

;ermanent Gipole Aonds 

his is the case of the hdrogen bond in ice. he end of the molecule is

positivel charged and can bond to the negative side of another dipolar molecule,

li'e the 2 side of the %2 dipole.

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!olecules

@f molecules formed a closed shell due to covalent bonding "li'e %, +%# then the

interaction bet!een molecules is !ea', of the van der 3aals tpe. hus, molecular

solids usuall have ver lo! melting points.