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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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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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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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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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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