this class closely follows the second chapter of callister

Materials 100A, Class 2, atomic stucture, periodic table, bonding . . .

Ram Seshadri MRL 2031, x6129

[email protected]; http://www.mrl.ucsb.edu/∼seshadri/teach.html

This class closely follows the second chapter of Callister

Atomic structure

Atoms are composed of protons (positively charged), neutrons (no charge) and electrons (negatively charged). The number ofelectrons in an atom (which is equal to the number of protons) is called the atomic number. The number of electrons (or protons)+ the number of neutrons is called the mass number. The atomic mass (which is numerically, a value close to the mass number)is the weighted average mass of a number of isotopes of the element, expressed in a system of units where the common isotope ofcarbon 12C has an atomic mass of precisely 12.00000. The unit of atomic mass in g is equal to 1.00000/(Avogadro Number) =1.00000/6.0221367×1023 = 1.66054×10−24 g. This is sometimes called the Lochschmidt number. One atom of 12C weighs 12 timesthis, 1.99265×1023 g. If instead of counting atom by atom, we count in bunches corresponding to the Avogadro number, we havemoles of something, and 1 mole of 12C weights precisely 12.00000 g. One mole of a normal carbon sample (which is a mixture ofisotopes with different mass numbers) actually weighs 12.011 g.

Atoms have protons and neutrons in the core, in a nucleus. The electrons whiz around the nucleus according to two models, asimple one called the Bohr model, and a more complicated one called the atomic orbital model.

In the Bohr model, electrons whiz around in different shells, the K shell, the L, shell, the M shell, the N shell, and so on. TheK shell can accommodate 2 electrons, M can accommodate 8, M can accommodate 18 and N 32. The more sophisticated atomicorbital model has four kinds of orbitals, s, p, d and f (and for extremely heavy elements, a g orbital), that arise as solutions ofthe Schrodinger equation for atoms. This equations forms the basis of quantum mechanics. One of the outcomes of the solving theSchrodinger equation is that every electron in an atom is associated with a set of 4 numbers called the quantum numbers. The firstnumber, the principle quantum number n takes on values as shown below and these correspond to the different shells of the Bohr atom.

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http://www.mrl.ucsb.edu/~seshadri/teach.html


n Shell Subshells States Electrons

1 K s 1 22 L s 1 2

p 3 63 M s 1 2

p 3 6d 5 10

4 N s 1 2p 3 6d 5 10f 7 14

In an atom, the electrons will always attempt to go to states with the lowest energy. This is the aufbau (or building-up) principle.However, you cannot fill states beyond a certain point. For example, if you finish filling 3d states with 10 electrons, you have to moveon to 4s. This is a consequence of the Pauli exclusion principle which states that no two electrons in an atom can share identical setsof the four quantum numbers. The scheme below shows the rules for filling up electrons in an atom. First all the “core” electronsfill up. Towards the end, the “valence” electrons start filling up. It is the valence electrons that usually decide the properties of theatom, such as its reactivity towards other elements.

2

3

4

5

6

n=1

s p d f g

The periodic table:

The rules for filling up electrons in an atom result in the periodic table. Note that elements in the periodic table are separated intovarious categories. You must learn to understand these different categories: Alkali metals, alkaline earth metals, transition metals,

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main group elements (consisting of metalloids and non-metals) and the noble gases. Also, there are the lanthanide and actinideelements.

1.00791 4.00262

20.1801014.0077

39.9481835.45317

18.998915.9998

83.8036

131.2954

(222)86

12.0116

C

10.811

B

5

26.982

Al

13 28.086

Si

14 30.97415 32.065

S

16

6.941

Li

3 9.0122

Be

4

22.99011 24.305

Mg

12

39.09819 40.078

Ca

20 44.956

Sc

21 47.867

Ti

22 50.942

V

23 51.996

Cr

24 54.938

Mn

25 55.845

Fe

26 58.933

Co

27 58.693

Ni

28 63.546

Cu

29 65.39

Zn

30 69.72331 72.64

Ge

32 74.922

As

33 78.96

Se

34 79.90435

85.46837 87.62

Sr

38 88.906

Y

39 91.224

Zr

40 92.906

Nb

41 95.94

Mo

42

132.9155 137.33

Ba

56

138.91

La

La-Lu

57-71

57

178.49

Hf

72 180.95

Ta

73 183.84

W

74

(223)87 (226)

Ra

88

(227)

Ac

Ac-Lr

89-103

89

(98)

Tc

43 126.90

I

53101.07

Ru

44 102.91

Rh

45 106.42

Pd

46 107.87

Ag

47 112.41

Cd

48

186.21

Re

75 190.23

Os

76 192.22

Ir

77 195.08

Pt

78 196.97

Au

79 200.59

PNa

K Ga

Rb

Cs

Fr

Hg

80 204.38

Tl

81 207.2

Pb

82 208.98

Bi

83 (209)

Po

84 (210)

At

85

114.82

In

49 118.71

Sn

50 121.76

Sb

51 127.60

Te

52

H He

NeN

ArCl

FO

Kr

Xe

Rn

Br

IA

IIA

IIIB IVB VB VIB VIIB IB IIB

IVA VA VIA VIIA

VIIIB

VIIIA1

54

2

3

13 14 15 16 17

18

6 7 8 9 10 11 12

IIIA

174.97

Lu

71140.12

Ce

58

232.04

Th

90 231.04

Pa

91 238.03

U

92

140.91

Pr

59 144.24

Nd

60

(262)

Lr

103

(145)

Pm

61

(237)

Np

93 (244)

Pu

94 (243)

Am

95 (247)

Cm

96 (247)

Bk

97 (251)

Cf

98 (252)

Es

99 (257)

Fm

100 (258)

Md

101 (259)

No

102

150.36

Sm

62 151.96

Eu

63 157.25

Gd

64 158.93

Tb

65 162.50

Dy

66 164.93

Ho

67 167.26

Er

68 168.93

Tm

69 173.04

Yb

70

(264)

Bh

107(261)

Rf

104 (262)

Db

105 (266)

Sg

106 (277)

Hs

108 (268)

Mt

109

Copyright EniG. ([email protected])© 1998-2002

10.811

B

5

13

(281)

Uun

110 (272)

Uuu

111 (285)

Uub

112 (289)

Uuq

114

Ne

Ga

Fe

Tc

1

2

3

4

5

6

7

HYDROGEN HELIUM

NEONNITROGEN

ARGONCHLORINE

FLUORINEOXYGEN

KRYPTON

XENON

RADON

CARBONBORON

ALUMINIUM SILICON PHOSPHORUS SULPHUR

LITHIUM BERYLLIUM

SODIUM MAGNESIUM

POTASSIUM CALCIUM SCANDIUM TITANIUM VANADIUM CHROMIUM MANGANESE COBALT NICKEL COPPER ZINC GALLIUM GERMANIUM ARSENIC SELENIUM BROMINE

RUBIDIUM STRONTIUM YTTRIUM ZIRCONIUM NIOBIUM MOLYBDENUM

CAESIUM BARIUM

LANTHANUM

HAFNIUM TANTALUM TUNGSTEN

FRANCIUM RADIUM

ACTINIUM

TECHNETIUM IODINERUTHENIUM RHODIUM PALLADIUM SILVER CADMIUM

RHENIUM OSMIUM IRIDIUM PLATINUM GOLD THALLIUM LEAD BISMUTH POLONIUM ASTATINE

INDIUM TIN ANTIMONY TELLURIUM

PE

RIO

D

GROUP

IRON

MERCURY

LANTHANIDE

ACTINIDE

LUTETIUMCERIUM

THORIUM PROTACTINIUM URANIUM

PRASEODYMIUM NEODYMIUM

LAWRENCIUM

PROMETHIUM

NEPTUNIUM PLUTONIUM AMERICIUM CURIUM BERKELIUM CALIFORNIUM EINSTEINIUM FERMIUM MENDELEVIUM NOBELIUM

SAMARIUM EUROPIUM GADOLINIUM TERBIUM DYSPROSIUM HOLMIUM ERBIUM THULIUM YTTERBIUM

BOHRIUMRUTHERFORDIUM DUBNIUM SEABORGIUM HASSIUM MEITNERIUM

http://www.ktf-split.hr/periodni/en/

Lanthanide

Actinide

PERIODIC TABLE OF THE ELEMENTS

BORON

ATOMIC NUMBER

ELEMENT NAME

SYMBOL

(1) Pure Appl. Chem., , No. 4, 667-683 (2001)73

Editor: Aditya Vardhan ([email protected])

Relative atomic mass is shown with fivesignificant figures. For elements have no stablenuclides, the value enclosed in bracketsindicates the mass number of the longest-livedisotope of the element.

However three such elements (Th, Pa, and U)do have a characteristic terrestrial isotopiccomposition, and for these an atomic weight istabulated.

Metal

Alkali metal

Alkaline earth metal

Transition metals

Lanthanide

Actinide

Chalcogens element

Halogens element

Noble gas

Semimetal Nonmetal

- gas

- liquid

- solid

- synthetic

STANDARD STATE (100 °C; 101 kPa)

UNUNNILIUM UNUNUNIUM UNUNQUADIUMUNUNBIUM

RELATIVE ATOMIC MASS (1)

GROUP CASGROUP IUPAC

Count the electrons in the noble gases. Note that they correspond to filled K shells (He), filled L shells (Ne), filled M shells (Ar). . . . These are stable configurations and the noble gases are rather unreactive. It is always useful to know how far an element is fromthe nearest noble gas. For instance, Br is just one electron away from Kr, and as a result, will grab an electron whenever it gets thechance. K has just one electron more than Ar and is always trying to get rid of it (the one electron). Another way of stating this isthat Br has 7 valence electrons (and tries to get one more to reach 8) while K has 1 valence electron and tries to get rid of it to reach zero.

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In general, atoms that can adopt the configuration of the nearest noble gas by gaining electrons, have a tendency to grab electronsfrom other atoms. This tendency is called electronegativity, and Pauling introduced a scale to describe this tendency. The scale runsto 4 (corresponding to F) which is an atom that always tries very hard to grab electrons. Atoms that have can gain a noble gasconfiguration by giving up electrons are electropositive, and their electronegativity values are small (usually below 1.5).

Bonding:

• There are four forces in nature. The strong and the weak interactions act between electrons, protons, neutrons and otherelementary particles and do not concern us. We do not know of any normal material whose properties (melting point, forexample) depend on the magnitude of these forces. The two other forces are gravitational and electromagnetic.

• Gravitational forces account for large scale phenomena such as tides, and seasons, and together with intermolecular forces, decidethe length of a giraffe’s neck. We shall not discuss gravitation.

• All interactions that are important for solids, should in principle, come out as solutions of the Schrodinger equation (SE).Unfortunately, solutions of the SE are hard to come by for many real systems, and even if they were available, their utility wouldnot be assured. We therefore continue to propagate the useful fiction that cohesive interactions in materials can be classified asbelonging to one of four categories – van der Waals, ionic, covalent or metallic.1 We keep in mind that these are not very easilydistinguished from one-another in many solids.

For a delightfully readable text on the nature of cohesion between molecules, and between molecules and surfaces, look at J. N.Israelachvili, Intermolecular and Surface Forces.

van der Waals

• The simplest solids are perhaps those obtained on cooling down a noble gas – He, Ne, Ar, Kr or Xe. He does not form a solidat ambient pressure. All the other noble gases do.

• The interactions between noble gas atoms (which have closed shells of electrons) is of the van der Waals type (note: van derWaals, not van der Waal’s !) which means that the interaction is between instantaneous dipoles formed because the atoms“breathe” and this breathing causes the centers of positive and negative charges to, from time to time, not coincide. The forcesare therefore also referred to as induced dipole-induced dipole interactions, or London dispersion forces (after F. W. London).

1Hydrogen bonds are somewhere between being ionic and covalent and we do not see a good reason to place them in a class by themselves.

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electron cloudnucleus

• If we were to believe the above scheme, it should come as no surprise that the largest noble gas atom should be the most polar-isable and therefore the most cohesive. The boiling points (often better indicators of cohesion than melting points) testify to this:

Atom TM (K) TB (K)

Ne 24 27Ar 84 87Kr 116 120Xe 161 165

• Other columns of elements in the periodic table don’t follow this simple trend. For example:

Atom TM (K) TB (K)

Cu 1353 2833Ag 1235 2433Au 1333 3133

Ionic

• As a good thumb rule, atoms at the two ends of the electronegativity scale either give up their valence electrons very easily toform stable cations (ions with small values of electronegativity) or take up electrons very easily to form anions (ions with largeelectronegativities).

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H . . .2.2 . . .Li Be . . . B C N O F1.0 1.6 . . . 2.0 2.6 3.0 3.4 4.0Na Mg . . . Al Si P S Cl0.9 1.3 . . . 1.6 1.9 2.2 2.6 3.2K Ca . . . Ga Ge As Se Br0.8 1.0 . . . 1.8 2.0 2.2 2.6 3.0Rb Sr . . . In Sn Sb Te I0.8 0.9 . . . 1.8 1.9 2.1 2.1 2.7Cs Ba . . . Tl Pb Bi Po At0.8 0.9 . . . 1.8 2.1 2.0 2.0 2.2

• The process of giving up electrons (in the case of cations) and of taking electrons (anions) permits the ion to achieve a stableelectronic configuration such as that of

– a noble gas: For example, Na+ and F− have the Ne configuration

– the d10 configuration: Ga3+ takes this up

– the s2 configuration: Pb2+ and Bi3+ take this up

• Once they have done this, they can pair up suitably to form ionic solids that are held together by Coulombic interactions

• For any ionic crystal, the attractive Coulombic part (per mole) is:

∆UAtt. = −(

LA|z+||z−|e2

4πε0r

)

L is the Avogadro number.

• The repulsive part arises because atoms and ions behave nearly like hard spheres. This is a consequence of the Pauli exclusionprinciple which says that no two electrons in a system can have all four quantum numbers the same.

• The repulsion can be approximated by the expression:

∆URep. =LB

rn

6


where B is called the repulsion coefficient and n is the Born exponent. n is normally around 8 or 9.

The two terms add:

∆U(0 K) = −LA|z+||z−|e2

4πε0r+

LB

rn

Covalent bonding

• Covalent bonds are formed between non-metallic (usually) atoms of similar electronegativity. s or p orbitals are used.

For example, the 1s orbitals on two hydrogen atoms combine to form the molecular orbitals σ(1s) which is bonding and σ∗(1s),which is antibonding. The two electrons occupy the bonding level and leave the antibonding level empty. In the followingdepiction, the circles are the 1s orbitals:

Ene

rgy

bonding molecular orbital

atomic orbital

antibonding molecular orbital

• Why is covalent bonding strongly directional ? The example of sp3 hybrids in diamond and Si:

s

pz

px py

Hybrid orbitals are obtained from linear combinations of atomic orbitals on the same atom. These hybrid orbitals can thenoverlap with similar hybrid orbitals on neighboring atoms, just as the 1s orbitals do in the hydrogen chain.

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Metallic bonding

This is a special case of covalent bonding where all the states are not filled up, and the electrons float around fixed nuclei in thesolid.

8

this class closely follows the second chapter of callister

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