CBC Databook

7/25/2019 CBC Databook

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1

CONTENTSRelative Atomic Masses of the Elements 2

Units, Symbols and Constants

The International System of Units (SI) 4

Recommended Values of Physical Constants 7

Selected Spectroscopic Data

Infrared

Characteristic Wavenumbers of Absorptions of

Organic Functional Groups 8

Anions and Cations 11

Coordination Compounds 11Nuclear Magnetic Resonance

Properties of Selected NMR-Active Nuclides 12

Chemical Shifts of Common Functional Groups13C nuclei 131H nuclei attached to saturated linkages 141H nuclei attached to unsaturated linkages 151

H nuclei attached to heteroatoms 15Additivity Table for 1H Chemical Shifts of Methylene Groups 15

SpinSpin Coupling Constants: 1 1H H 16

Ultraviolet and Visible

Absorption Maxima of Substituted Benzene Rings 17

WoodwardFieser Rules for the Prediction of maxValues 18

Electronic Absorption Characteristics of Transition Metal Complexes 19

Spectrochemical andTrans

-Effect Series 19Mass Spectrometry

Common Fragmentations and Fragment Ions 20

Symbols and Abbreviations Commonly Encountered in Organic Chemistry 21

The Proteinogenic Amino Acids 22


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2

RELATIVE ATOMIC MASSESAr(E) ('ATOMIC WEIGHTS')

OF THE ELEMENTS

(Scaled toAr(12

C) = 12)

The atomic weights of many elements are not invariant but depend on the origin and treatment of thematerial. The footnote to this Table elaborates the types of variation to be expected for individualelements. The values ofAr(E) given here apply to elements as they exist naturally on Earth.

1 Hydrogen H 1.00794 a,b,c 21 Scandium Sc 44.955910

2 Helium He 4.002602 a,c 22 Titanium Yi 47.88

3 Lithium Li 6.941 a,b,c 23 Vanadium V 50.9415

4 Beryllium Be 9.01218 24 Chromium Cr 51.9961

5 Boron B 10.811 a,b,c 25 Manganese Mn 54.938056 Carbon C 12.011 c 26 Iron Fe 55.847

7 Nitrogen N 14.00674 a,c 27 Cobalt Co 58.93320

8 Oxygen O 15.9994 a,c 28 Nickel Ni 58.69

9 Fluorine F 18.9984032 29 Copper Cu 63.546 c

10 Neon Ne 20.1797 a,b 30 Zinc Zn 65.39

11 Sodium Na 22.989768 31 Gallium Ga 69.723

12 Magnesium 24.3050 32 Germanium Ge 72.61

13 Aluminium Al 26.98154 33 Arsenic As 74.9216

14 Silicon Si 29.0855 c 34 Selenium Se 78.96

15 Phosphorus P 30.973762 35 Bromine Br 79.904

16 Sulfur S 32.066 c 36 Krypton Kr 83.80 a,b

17 Chlorine Cl 35.4527 37 Rubidium Rb 85.4678 a

18 Argon Ar 39.948 a,c 38 Strontium Sr 87.62 a,c

19 Potassium K 39.0983 39 Yttrium Y 88.90585


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41 Niobium Nb 92.90638 73 Tantalum Ta 180.9479

42 Molybdenum Mo 95.94 74 Tungsten W 183.8543 Technetium* Tc 98.9062 e 75 Rhenium Re 186.207

44 Ruthenium Ru 101.07 a 76 Osmium Os 190.2 a

45 Rhodium Rh 102.90550 77 Iridium Ir 192.22

46 Palladium Pd 106.42 a 78 Platinum Pt 195.08

47 Silver Ag 107.8682 a 79 Gold Au 196.96654

48 Cadmium Cd 112.411 a 80 Mercury Hg 200.59

49 Indium In 114.82 81 Thallium Tl 204.3833

50 Tin Sn 118.710 82 Lead Pb 207.2 a,c

51 Antimony Sb 121.75 83 Bismuth Bi 208.9804

52 Tellurium Te 127.60 84 Polonium* Po 209 d

53 Iodine I 126.90447 a 85 Astatine* At 210 d

54 Xenon Xe 131.29 a,b 86 Radon* Rn 222 d

55 Caesium Cs 132.9054 87 Francium* Fr 223 d

56 Barium Ba 137.327 88 Radium Ra 226.0254 d

57 Lanthanum La 138.9055 a 89 Actinium* Ax 227 d

58 Cerium Ce 140.115 a 90 Thorium* Th 232.0381 a,c,e

59 Praseodymium Pr 140.90765 91 Protactinium* Pa 231.03588 e

60 Neodymium Nd 144.24 a 92 Uranium* U 238.0289 a,b,e

61 Promethium* Pm 145 d 93 Neptinium* Np 237.0482

62 Samarium Sm 150.36 a 94 Plutonium* Pu 244 d

63 Europium Eu 151.965 a 95 Americium* Am 243 d64 Gadolinium Gd 157.25 a 96 Curium* Cm 247 d

65 Terbium Tb 158.92534 97 Berkelium* Bk 247 d

66 Dysprosium Dy 162.50 a 98 Californium* Cf 251 d


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4

UNITS and CONSTANTS

The International System of Units (SI)

Physical Quantity Name of Unit Symbol Expression in terms of

SI base units

SI base units

length metre m

mass kilogram kg

time second s

electric current ampere Athermodynamic temperature kelvin K

amount of substance mole mol

SI derived units

energy, work, heat joule J m2kg s2

force newton N m kg s2= J m1pressure, stress pascal Pa m1kg s2= N m2= J m3

power watt W m2kg s3= J s1

electric charge coulomb C s A

electric potential volt V m2kg s3A1= J A1s1

electric resistance ohm m2

kg s3

A2

= V A1

electric conductance siemens S m2kg1s3A2= 1

electric capacitance farad F m2kg1s4A2= A s V1

magnetic flux weber Wb m2kg s2A1= V s2 2 2 1


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SI Prefixes

Fraction Prefix Symbol Multiple Prefix Symbol

101 deci d 10 deca da

102 102centi c hecto h

103 103milli m kilo k

106 106micro mega M

109 109nano n giga G

1012 1012pico p tera T

1015 1015femto f peta P

1018 1018atto exa E

Decimal Fractions and Multiples of SI Units Having Special Names

Physical Quantity Name of Unit Symbol Definition

length ngstrm 1010m = 101nm = 100 pm

area barn b 1028m2

volume litre l 1203m3= 1 dm3= 1000 cm3

force dyne dyn 105Npressure bar bar 105Pa

energy erg erg 107J

104m2s1kinematic viscosity stokes St


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Units Defined Exactly in Terms of the SI Units

Physical Quantity Name of Unit Symbol Definitiona

length inch in 0.0254 m

mass pound lb 0.453 592 37 kg

time minute min 60 s

time hour h 3600 s

plane angle degree (/180) rad

force kilogram-force kgf 9.806 65 N

pressure standard atmosphere atm 101 325 Pa

pressure conventional millimetreof mercuryb

mmHg 13.5951 9.806 65 Pa =133.322 Pa

pressure torr Torr (101 523/760) Pa = 133.322 Pa

pressure bar bar 105Pa

pressure pounds per square inch psi 6894.757 Pa

energy kilowatt hour kW h 3.6 106J

energy thermochemical calorie calth 4.184 J

electric dipole moment debye D 3.335 64 1030C m

aThese definitions are exact


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7

Recommended Values of Fundamental Constants

Fundamental Constant Symbol Value

6.022 1367 1023mol1L,NAAvogadro constant

8.314 510 J K1mol1Rgas constant

1.380 658 1023J K1k, kBBoltzmann constant

9.648 5309 104C mol10.025 693 V

F

(RT/F )Faraday constant at T= 298.15 K

1.602 177 33 1019

Ceelementary charge1.602 18 1019J

9.648 547 104J mol1eV

LeV =FVelectron volt

6.626 0755 1034J s1.054 5726 1034J s

hPlanck constanth = h/2

speed of light in vacuuma 2.997 924 58 108m s1c

permeability of a vacuuma 4107A2o

permittivity of a vacuuma 8.854 187 816 1012F m1o

9.109 3897 1031kgmerest mass of electron

1.672 6231 1027kgmprest mass of proton

4.359 7482 1018JEhHartree energy

5.291 772 49 1011ma0Bohr radius

9.274 0154 1024J T1Bohr magneton B= eh/4 me

5.050 7866 1027J T1nuclear magneton = eh/4mp

109 737.315 34 cm1Rydberg constant R


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SPECTROSCOPIC DATA

INFRARED

Characteristic Wavenumbers, ~ , of Fundamental Absorptions of Organic Functional Groups

~/cm1

1. OH stretching

free sharp 36503590intramolecular hydrogen-bonded single bridges(excluding chelates)

sharp 36003450

intermolecular hydrogen bonded polymeric associations broad 34003200

intermolecular chelates and carboxylic acids broad 32002500

2. NH stretching(hydrogen bonding lowers as in OH stretching)

primary amides two bands ~3500 and 3400

primary amines two bands 35003300

secondary amides 34603400

secondary amines 34503300

3. CH stretching

alkynes 3300

alkenes and aryls 30403010

methyls and methylenes two or three bands 29602850

aldehydes 29002700

4. CX stretching

nitriles 22602220alkynes 22602100

5. X=Y=Z stretching

allenes C=C=C ~1950


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Characteristic wavenumbers,~ , of fundamental absorptions of organic functional groups (continued)

~C=O stretching continued /cm

1

(b) Ketones

four ring ~1780

five ring 17501740

17251705saturated acyclic, alicyclic six-ring and larger, and ,-unsaturated five ring

aryl 17001680

16851660,-unsaturated(c) Carboxylic acids

saturated 17251700

17151690,-unsaturated

aryl 17001680

most carboxylate anions 16101550

(d) Esters and lactones

esters of phenols or enols 18001750

five-ring lactones 17801760

17701740,-unsaturated five-ring lactones

saturated esters and six-ring and larger lactones 17501735

17301715esters of aromatic or ,-unsaturated acids(e) Amides and lactams

primary amides two bands ~1690 and 1600

primary amides (solid phase) two bands 1650 and 1640

secondary amides two bands 17001670 and 15501510

secondary amides (solid phase) two bands 16801630 and 15701515

tertiary amides 16701630

four-ring lactams ~1745

five-ring lactams ~1700

six ring and large lactams ~1670


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Characteristic wavenumbers,~ , of fundamental absorptions of organic functional groups (continued)

~/cm1

8. C=C stretching

isolated variable 16801620

conjugated one or two bands 16501590

aromatic two bands ~1600 and 1500

aromatic weak or absent when ring is not further conjugated 1580

9. N=O stretching

Nitro compounds asymmetric 15551540

symmetric 13851350

10. Carbonhalogen stretching

CF 14001000

CCl 800 600CBr 600500

CI 500

11. CH deformations

i-propyl 13851380 13701365

11751165 11701140

t-butyl 13951385 1365

12551245 12501200

RCH=CH2 995985 915905

RCH=CHR (trans) 970960

R2C=CH 895885

R2C=CHR 840790

RCH=CHR (cis) ~690

~630RCCH

12. NH bend


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~Characteristic Wavenumbers, , of Fundamental Absorptions of Anions and Cations

~/cm1

[NH4]+ammonium 33003030 14301390

[CN]cyanide 22002000

[SCN]thiocyanate 21502050CN stretch

[CH3CO2]

COO antisymmetric stretch 15801550acetate[CH3CO2]

acetate COO symmetric stretch 14301410

[CO3]2carbonate 14901410

[NO3]nitrate 13801350

[ClO4]perchlorate 11701050

[SO4]2sulfate 11301080

[PO4]3phosphate 11001000

[CrO4]2chromate 885

N-bonded thiocyanate CS stretch 860780

S-bonded thiocyanate CS stretch 720690

~Characteristic Wavenumbers, , of Fundamental Absorptions in Coordination Compounds

~/cm1

Transition metal carbonyls:Wavenumber ranges of these CO stretchingvibrations apply only to unsubstituted, neutral species. Actual values dependalso on the compound and the nature of other ligands attached to the metal.

terminal CO 21501900

bridging CO 19001750


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NUCLEAR MAGNETIC RESONANCE

Properties of Selected NMR-Active Nuclides

Nuclide Natural Abundance

C

I / 107rad T1s1 Relative Receptivityvalues for I= nuclei

are 3C

1H 99.985% 1/2 26.75 1.002H, D 0.015% 1 4.11 1.45 106

10B 19.58% 3 2.87 3.93 10311B 80.42% 3/2 8.58 0.133

13C 1.108% 1 6.73 1.76 10414N 99.63% 1 1.93 1.00 10315N 0.37% 1/2 2.71 3.85 10617O 0.037% 5/2 3.63 1.08 10519F 100% 1/2 25.18 0.834

23

Na 100% 3/2 7.08 9.27 102

27Al 100% 5/2 6.98 0.20729Si 4.70% 1/2 5.32 3.69 10431P 100% 1/2 10.84 0.067

77Se 7.58% 1/2 5.12 5.30 104103Rh 100% 1/2 0.85 3.16 105107Ag 51.82% 1/2 1.09 3.48 105109Ag 48.18% 1/2 1.25 4.92 105117Sn 7.61% 1/2 9.58 3.49 103119Sn 8.58% 1/2 10.02 4.51 103


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Chemical Shifts of Common Functional Groups

Positions of 1H- and 13C-NMR signals in the following tables are given as chemical shifts, ,expressed as parts per million, ppm, relative to tetramethylsilane, TMS. Usual ranges of values

for 1H-NMR are 015, except that most MH shifts are < 0. For 1H-NMR, values are usually

within 0.2 of those quoted unless inductive, anisotropic or steric effects associated with functional

groups operate. Chemical shifts for13C-NMR are usually 0250.

Chemical Shifts of13

C Nuclei in Common Functional Groups

Alkanes Ethers

Cyclopropanes 08 CH3O 4560

Cycloalkanes 525 RCH2O 4270RCH3 525 R2CHO 6577

RCH2R 2245 R3CO 7083

R2CHR 3058

AminesR3CR 2850

CH3N 1045Carbonyls RCH2N 4555

RCOOR 160177 R2CH2N 5070

RCOOH 162183 R3CN 6075

RCHO 185205

Other HeteroatomsRCOR 190220 RCH2S 2242

Halogens RCH2P 1025

CH3X 525 ArP 120130


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Chemical Shifts of Methyl, Methylene and Methine Protons Attached to Saturated Linkages

Methyl Methylene Methine

CH3C 0.9

CH3CC=C 1.1

CH3CO 1.4 CH2C 1.4 >CHC 1.5

CH3C=C 1.6 CH2CC=C 1.7

CH3CONR 2.0 CH2CO 1.9 >CHCO

CH3C=CCO 2.0CH3COOR 2.0

CH3S 2.1

CH3COR 2.2 CH2COOR 2.2

CH3I 2.2 CH2CONR 2.2

CH3CHO 2.2 CH2CHO 2.2

CH3Ar 2.3 CH2C=C 2.2

CH3N 2.3 CH2CN 2.3

CH3COOAr 2.4 CH2COR 2.4

CH2S 2.4 >CHCHO 2.4

CH2C=CCO 2.4

CH2N 2.5

CH3COAr 2.6 CH2Ar 2.6

CH3Br 2.6

>CHCOR 2.7

>CHCN 2.7

>CHN 2.8

CH3NCOR 2.9

CH3NAr 3.0

CH3Cl 3.0 >CHAr 3.0

CH2I 3.2 >CHS 3.2

CH3OR 3.3 >CHCOAr 3.3

CH3N+ 3.3

CH OH 3 4 CH OR 3 4


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Chemical Shift Ranges of Protons Attached to Unsaturated Linkages

Proton Proton

CCH 1.83.1 C=CHO 6.08.1

CH=CN 3.75.0 Aromatic protons 6.09.0

CH=C=O 4.05.0 CH=CCO 6.57.8

C=CH 4.56.0 HCOO, HCON 8.08.2

C=CHN 5.78.0 RCHO, ArCHO 9.410.5

C=CHCO 5.86.7

Chemical Shift Ranges of MH, OH and NH Protons

Group Range

MH (M = Transition metal) 300 Diagnostic of metal hydride

ROH 210 H-bonded enols usually in range 1116

RNH2RNHR' 25 Position depends strongly on solvent

ArNH2, ArNHR' 3.56 or larger

RCONH2 58.5 Often very broad (sometimes unobservable)

RCONHCOR' 9ca. 12 Often very broad

RCO2H 10ca. 13

Additivity Table for Estimation of the1H Chemical Shifts of Methylene Groups

(CH2X1X2) = 1.25 + X1+ X2

substituent Xn substituent Xn sustituent Xn

alkyl 0.0 OCOR 2.7 SH, SR 1.0

vinyl 0.8 NH2, NR2 1.0 SO2R 1.7

alkynyl 0.9 NO2 3.0 -CHO 1.2


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1H1H SpinSpin Coupling Constants

J/ Hz J/ Hz

C

H

H

CH CH O8 to 18a 03

CH CH CH C CH68b 13

68b 46H3C CH2 CH C CH

CH

H3C

H3C

CH C C CH68b 02

Ha

Heq

Ha

Heq

H

H

orthoaa 813 69

metaae 26 13

paraee 26 01

HH

C CH CH 512411 cis

H

C CH CH C trans613 1218


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ULTRAVIOLET and VISIBLE

Absorption band intensities are expressed in terms of the molar absorption coefficient

lc

A=

whereA= dimensionless absorbance, c= molar concentration, and l= path length of the

absorbing species. Units of may therefore be mol1dm3cm1or 103cm2mol1.Absorption bands with maxima, max, below 215 nm are observable only as end absorption.

Compounds containing unconjugated -bands show only end absorption. Saturated aldehydesand ketones do, however, show a low-intensity band with max= 1030 mol1dm3cm1in therange 275295 nm.

Absorption Maxima of Substituted Benzenes PhR

solvent: H2O or MeOH

R max/ nm

max/ mol1

dm3cm1

max/ nm

max/ mol1

dm3cm1

max/ nm

max/ mol1

dm3cm1

H 203 7400 254 204+NH3 203 7500 254 160

Me 206 7000 261 225

Cl, Br 210 7700 262 190

OH 210 6200 270 1450

OMe 217 6400 269 1480SO2NH2 217 9700 264 740

CN 224 13000 271 1000

CO2 224 8700 268 560


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WoodwardFieser Rules for the Prediction of maxValues for * Transitions

of Dienes, Polyenes and ,-Unsaturated Aldehydes, Ketones and Acids

Basic Chromophore:Diene max(EtOH) / nm214Diene

Increment/ nm

Each additional double bond extending the conjugation 30

Each homoannular dienea 39

The exocyclic nature of any double bondb 5

Each alkyl group or ring residue 5Each auxochrome: OAcyl 0

OAlkyl 6

SAlkyl 30

Cl, Br 5

NAlkyl2 60

Basic Chromophore:, -unsaturated Aldehydes, Ketones and Acids max(EtOH) / nm215Six-ring or acyclic ,-unsaturated ketone

202Five-ring ,-unsaturated ketone

209,-unsaturated aldehyde

197,-unsaturated acid

Increment/ nm

Each additional double bond extending the conjugation 30Each homoannular dienea 39

The exocyclic nature of any double bondb 5

Each alkyl group or ring residue 10

12

for aldehydes and ketones only 18

Each auxochrome: OH 35

3050

OAcyl 6, ,

OAlkyl 35

30


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Typical Electronic Absorption Intensities of Transition Metal Complexes

max / mol1dm3cm1Type of Transition

Spin-forbidden, Laporte forbidden 0.011.0

Spin-allowed, Laporte forbidden 1.0100

Spin-allowed, Laporte forbidden, but with dp mixing (Tdsymmetry)and/or intensity stealing

1001000

Spin-allowed, Laporte allowed; charge transfer > 1000

Spectrochemical Series

Common Ligands

I < Br


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MASS SPECTROMETRY

Common Fragmentations and Fragment Ions in Mass Spectrometry

Common Fragmentations

m / z Fragment Lost Inference

M 3 toM 14 highest mass peak observed is itself a fragment and not a molecular ion

M 15 CH3

M 17 OH alcohol or carboxylic acid

NH3 primary amine, odd molecular weight

M 18 H2O alcohol, aldehyde, ketone

M 26 C2H2

CN nitrile, odd molecular weight

M 31 CH3O methyl ester or etherM 35 orM 37 Cl a molecular ion consisting of two peaks of intensity 3:1, two mass

units apart, indicates a monochloro compound

M 43 CH3CO methyl ketone

M 58 CH2=C(OH)CH3 McLafferty rearrangement, methyl ketone with -hydrogen

M 77 C6H5 monosubstituted

M 79 orM 81 Br a molecular ion consisting of two peaks of equal intensity, two massunits apart, indicates a monobromo compound

M 91 C7H7 benzylic

M 105 C6H5CO aromatic ketone or ester

M 127 I

Fragment Ions

m / z Fragment Inference

18 H2O+

28 CO+, C2H4+, N2

+


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SYMBOLS AND ABBREVIATIONS COMMONLY ENCOUNTERED IN ORGANIC CHEMISTRY

Groups

R alkyl generalised alkyl group

Me methyl CH3

Et ethyl CH2CH3

Pr propyl CH2CH2CH3

i-Pr isopropyl CH(CH3)2

Bu, n-Bu butyl CH2CH2CH2CH3

i-Bu isobutyl CH2CH(CH3)2

s-Bu, sec-Bu sec-butyl CH(CH3)CH2CH3

t-Bu, tert-Bu tert-butyl C(CH3)3

Ar aryl generalised aromatic ring

Ph () phenyl C6H5

Ac acetyl (ethanoyl) COCH3

Bn benzyl CH2C6H5

Boc, BOC or t-Boc t-butoxycarbonyl COOC(CH3)3

Bz benzoyl COC6H5

Ms mesyl (methanesulfonyl) SO2CH3

Tf triflyl (trifluoromethanesulfonyl) SO2CF3

Ts tosyl (toluenesulfonyl) SO2C6H4CH3(para)

TMS trimethylsilyl (or tetramethylsilane in NMR) Si(CH3)3

TBDPS tert-butyldiphenylsilyl SiPh2C(CH3)3

TBS tert-butyldimethylsilyl (also seen as TBDMS) Si(CH3)2C(CH3)3

THP tetrahydropyranyl

Z benzyloxycarbonyl or Cbz C6H5CH2OCO

Reagents, Solvents and Others

aq. aqueous HMPA hexamethylphosphoramide

B Li nB Li b t llithi h li ht


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THE PROTEINOGENIC AMINO ACIDS

For the generalised L-amino acid structure:H2N CO2H

HRor in zwitterionic form

H3N CO2

HR

All have Sabsolute configuration except cysteine which isR

Amino Acid R Amino Acid R

Glycine (Gly or G)H-

Cysteine (Cys or C)

HS

Alanine (Ala or A) CH3- Methionine (Met or M)H3CS

Valine (Val or V)H3C CH3

Histidine (His or H)

HN

N

Leucine (Leu or L)

CH3

H3C

Lysine (Lys or K) H2N

Isoleucine (Ile or I) H3C H

CH3

Arginine (Arg or R)

HNH2N

NH

Phenylalanine (Phe or F) Aspartic acid (Asp or D)HO2C

Tryptophan (Trp or W)

HN

Glutamic acid (Glu or E) HO2C

Serine (Ser or S)HO

Asparagine (Asn or N)

H2N

O

Threonine (Thr or T)H OH

CH3

Glutamine (Gln or Q)H2N

23


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24


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GROUP THEORY

Character Tables

CS= Ch E hA' 1 1 x,y,Rz x

2,y2,z2,xy

A" 1 1 z,Rx,Ry yz,xz

C2v E C2 v(xz) 'v(yz)

A1 1 1 1 1 z x2,y2,z2

A2 1 1 1 1 Rz xy

B1 1 1 1 1 x,Ry xz

B2 1 1 1 1 y,Rx yz

C3v E 2C3 3v

A1 1 1 1 z x2+y2,z2

A2 1 1 1 RzE 2 1 0 (x,y), (Rx,Ry) (x

2y2,xy) (xz,yz)

C4v E 2C4 C2 2v 2d

A1 1 1 1 1 1 z x2+y2,z2

A2 1 1 1 1 1 Rz

B1 1 1 1 1 1 x2y2

B2 1 1 1 1 1 xy

E 2 0 2 0 0 ( ) (R R ) ( )

25


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D2h E C2(z) C2(y) C2(x) i v(xy) v(xz) v(yz)

Ag 1 1 1 1 1 1 1 1 x2,y2,z2

B1g 1 1 1 1 1 1 1 1 Rz xy

B2g 1 1 1 1 1 1 1 1 Ry xz

B3g 1 1 1 1 1 1 1 1 Rx yzAu 1 1 1 1 1 1 1 1

B1u 1 1 1 1 1 1 1 1 z

B2u 1 1 1 1 1 1 1 1 y

B3u 1 1 1 1 1 1 1 1 x

D3h E 2C3 3C2 h 2S3 3v

A'1 1 1 1 1 1 1 x2+y2,z2

A'2 1 1 1 1 1 1 Rz

E' 2 1 0 2 1 0 (x,y) (x2y2, 2xy)

A"1 1 1 1 1 1 1

A"2 1 1 1 1 1 1 z

E" 2 1 0 2 1 0 (Rx,Ry) (xz,yz)

D4h E 2C4 C2 2C'2 2C"2 i 2S4 h 2v 2d

A1g 1 1 1 1 1 1 1 1 1 1 x2+y2,z2

A2g 1 1 1 1 1 1 1 1 1 1 Rz

26


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26

D2d= Vd E 2S4 C2 2C'2 2d

A1 1 1 1 1 1 x2+y2,z2

A2 1 1 1 1 1 Rz

B1 1 1 1 1 1 x2y2B2 1 1 1 1 1 z xy

E 2 0 2 0 0 (x,y), (Rx,Ry) (xz,yz)

Cv E C2 2C v

A1+ 1 1 1 1 z x2+y2,z2A2 1 1 1 1 RzE1 2 2 2 cos 0 (x,y), (Rx,Ry) (xz,yz)E2 2 2 2 cos 2 0 (x2y2,xy)

E3 2 2 2 cos 3 0

Dh E 2C

v i 2S C2

g+ 1 1 1 1 1 1 x2+y2,z2g 1 1 1 1 1 1 Rzg 2 2 cos 0 2 2 cos 0 (Rx,Ry) (xz,yz) 2 2 2 0 2 2 2 0 ( 2 2 2 )

27


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PHYSICAL DEFINITIONS AND FORMULAE

Classical Mechanics

amF= Newtons Second Law F= force, m= mass, a= acceleration

xFW= W= work done, F= force,x= distance movedvmp = p= momentum, m= mass, v= velocity

m

pvmT

2

22

21 == T= kinetic energy, m= mass, v= velocity,

p= momentum

A

FP = P= pressure, F= force,A= area

A

gmP = P= pressure, m= mass,

g= acceleration due to gravity,A= area

V

m= = density, m= mass, V= volume

P= pressure exerted by a column of density and

height hwhere g= acceleration due to gravity,A= area, V= volumehgA

gV

A

gm

P =

==

Electrical Energy

RIV= Ohms Law V= electrical potentialI= current,R= resistance

tRI

R

tVtIVE 2

2

=== E= energy, V= electrical potentialI= current,

t= time,R= resistance

t

EW= W= power,E= energy, t= time

Electrostatics


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PERIODIC TABLE OF THE ELEMENTS1

H2

He3

Li4

Be 5

B6

C7

N8

O9

F10

Ne11

Na

12

Mg

13

Al

14

Si

15

P

16

S

17

Cl

18

Ar19K

20

Ca21

Sc22

Ti23

V24

Cr25

Mn26

Fe27

Co28

Ni29

Cu30

Zn31

Ga32

Ge33

As34

Se35

Br36

Kr37

Rb38

Sr39

Y40

Zr41

Nb42

Mo43

Tc44

Ru45

Rh46

Pd47

Ag48

Cd49

In50

Sn51

Sb52

Te53

I54

Xe55

Cs56

Ba57

La72

Hf73

Ta74

W75

Re76

Os77

Ir78

Pt79

Au80

Hg81

Tl82

Pb83

Bi84

Po85

At86

Rn87

Fr88

Ra89

Ac104

Rf105

Db106

Sg107

Bh108

Hs109

Mt

58

Ce59

Pr60

Nd61

Pm62

Sm63

Eu64

Gd65

Tb66

Dy67

Ho68

Er69

Tm70

Yb71

Lu90

Th91

Pa92

U93

Np94

Pu95

Am96

Cm97

Bk98

Cf99

Es100

Fm101

Md102

No103

Lr

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