Konstantin Tsiolkovsky

Welcome to lifeform.org and lifeform.net, home of the Tsiolkovsky Group,
a space for Individuals dedicated to the realization of Hydrogen and Oxygen
powered, single stage to orbit, manned Space Colonization and development.

Save the Earth - Develop Space

Save the Earth - Develop Space

Rocket Science

Calvin and Hobbes

History of Rocket Science
Konstantin Tsiolkovsky Russia 1903 Original Space Flight Concepts
Robert Goddard America 1917 Initial Theory and Experiments
Hermann Oberth Germany 1923 Initial Theory
Werner von Braun Germany 1939 First Operational Rocket/V2
America 1961 F1/J2/Saturn/Apollo Program
Sergey Korolyov Russia 1957 R-7/Vostok/Soyuz
Krafft Ehricke America 1961 RL-10/Centaur Upper Stage
Paul Castenholz America 1971 SSME/Space Shuttle Main Engine

Present Rocket Science Assets - 2005
Space Shuttle Main Engine SSME 1981 350+ SSME Flights
Space Transportation System STS 1981 Space Shuttle Infrastructure
International Space Station/Soyuz ISS 2001 Operational and Functional
Boeing Delta IV Medium Upper Stage
Rocketdyne RS-68
Pratt & Whitney RL-10B-2 		2001 Hydrogen Powered
Two Stage to Orbit
Launch Vehicle

Future Rocket Science Goals - 2010
Human rate the Boeing Delta IV medium rocket.
Build two human rated launch pads at SLC-37A/B.
Convert Space Shuttle VAB and launch pad for
single space shuttle main engines in a straight stack.
Demonstrate the first single stage to orbit flight
using single space shuttle main engines - SSTO.
Demonstrate the first fully reusable launch vehicle
using single space shuttle main engines - RLV.
Demonstrate full flow staged combustion engine -
integrated powerhead demonstrator program - IPD.

Hydrogen/Oxygen Engine Comparison
Cryogenic Engine SSME (109%) RS-68 ET (Ideal)
Launcher Usage Space Shuttle Delta IV SSTO/RLV
Engine Weight 7,480 lbs. 14,560 lbs. 7,500 lbs.
Sea Level Thrust 418,660 lbf. 650,000 lbf. 650,000 lbf.
Vacuum Thrust 512,950 lbf. 745,000 lbf. 750,000 lbf.
Chamber Pressure 3,008 psia. 1,410 psia. 3,000 psia.
Specific Impulse - Isp 452 seconds 410 seconds 450 seconds
Nozzle Area Ratio 69 : 1 25.1 : 1 70 : 1
Thrust to Weight Ratio 68.6 : 1 51 : 1 100 : 1

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Instant Human - Just Add Coffee

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Stupendous Man

Space Shuttle Main Engine - SSME

Save the Earth - Develop Space

Save the Earth - Develop Space
n H 2e Compounds p 2h H He
He Li Be Molecules B C N O F Ne
Ne Na Mg Solutions Al Si P S Cl Ar
Ar K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr
Kr Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe
Xe Cs Ba La Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi

                        Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu     

a' a b' b c d' d e' e f g' g

Infrared - Pink - Red - Orange - Tan (Brown) - Yellow - Lime
Green - Aqua (Cyan) - Marine - Blue - Purple - Magenta - Ultraviolet

Radio Waves - Microwaves - Infrared - Optical - Ultraviolet - X-Rays - Gamma Rays

Cosmic Rays

Hydrogen

Phonons Photons

Heat Light Energy

Proton Neutron Electron

Water Oxygen Hydrogen Water

Elements Molecules Compounds Solutions

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Inert Gases Helium Neon Argon Krypton Xenon

Organics Hydrogen Carbon Oxygen Nitrogen Phosphorus

Alkali Metals Lithium Sodium Potassium Rubidium Cesium
Alkaline Earth Metals Beryllium Magnesium Calcium Strontium Barium
Rare Earth Metals Scandium Yttrium Lanthanum Cerium Lanthanides
Transition Metals Titanium Vanadium Chromium Manganese Refractories
Industrial Metals Iron Cobalt Nickel Copper Zinc
Technical Metals Aluminum Gallium Indium Tin Lead
Noble Metals Nickel Palladium Platinum Silver Gold
Heavy Metals Cadmium Mercury Thallium Lead Bismuth

Refractories Zirconium Niobium Molybdenum Ruthenium Rhodium
Hafnium Tantalum Tungsten Rhenium Osmium Iridium

Lanthanides Lanthanum Cerium Praseodymium Neodymium
Samarium Europium Gadolinium Terbium Dysprosium
Holmium Erbium Thulium Ytterbium Lutetium

Group III Elements Boron Aluminum Gallium Indium Thallium
Group IV Elements Carbon Silicon Germanium Tin Lead
Group V Elements Nitrogen Phosphorus Arsenic Antimony Bismuth
Semiconductors Silicon Germanium Arsenic Boron Phosphorus
Chalcogenides Oxygen Sulfur Selenium Tellurium Electron
Halide Salts Hydrogen Fluorine Chlorine Bromine Iodine

Organics Hydrogen Carbon Nitrogen Oxygen Phosphorus

Inert Gases Helium Neon Argon Krypton Xenon

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Hydrides
Water - H2O Ammonia - NH3 Methane - CH4

Molecular Gases
Hydrogen - H2 Oxygen - O2 Nitrogen - N2 Argon - Arn

Oxides
Carbonate - CO3 Silicate - SiO2 Borate - BO3
Carbon Dioxide - CO2 Silicon Dioxide - SiO2 Boric Acid - H3BO3

Nutrients
Nitrate - NO3- Phosphate - PO43- Sulfate - SO42-
Nitric Acid - HNO3 Phosphoric Acid - H3PO4 Sulfuric Acid - H2SO4
Potassium Nitrate - KNO3 Potassium Phosphate - KH2PO4 Potassium Sulfate - K2SO4

Calcium Nitrate - Ca(NO3)2. 4(H2O) Magnesium Sulfate - MgSO4. 7(H2O)

Potassium Hydroxide - KOH

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Bismuth (I) Iodide - BiI

The Bismuth - Iodide System

Table 5. The computed Spectroscopic properties of BiI (the excitation energy, Te, the equilibrium bond length, re, and the vibrational frequency, we) together with corresponding experimental data.

State Te (cm-1) re (Å) we (cm-1)
Calc. Exp. Calc. Exp. Calc. Exp.
C13S-0+ 0 0 2.886 2.805 156 164
C23S-1 5096 6182 2.878 - 152 169
a1D2 12336 - 2.861 - 155 -
B0+ (III) 24148 23389 2.898 - 170 198
0+ (IV) 25691 - 3.095 - 217 -

Potential Energy Curves of the Excited Electronic States of BiI

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The Sodium - Ammonia System

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Character Map Symbol Fonts
Greek Alphabet Metric Prefixes
Electromagnetic Spectrum Microwave Bands
SI International System of Units Fundamental Physical Constants
SI Defined Units SI Derived Units SI Accepted Units SI Derived Quantities
Earth Constants Universal Constants Planck Constants Electromagnetic Constants
Bohr Magneton Nuclear Magneton Fine Structure Constant Rydberg Constant
Physical Constants Chemical Constants Boltzmann Constant Physicochemical Constants
Electron Constants Proton Constants Neutron Constants Deuteron Constants
Energy Equivalence Factors Energy Conversion Factors
Energy Equivalence I Energy Equivalence II Energy Equivalence III Energy Equivalence IV
Energy Conversion I Energy Conversion II Energy Conversion III Energy Conversion IV
Natural Units (n.u.) Atomic Units (a.u.)
Other (SI Derived) Units

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Symbols and Terminology of Condensed Matter Physics
Space and Time Classical Mechanics
Electromagnetism Quantum Mechanics
Atoms and Molecules Statistical Mechanics
Electromagnetic Radiation
Spectroscopy
Solid State Physics
General Chemistry Thermodynamics
Thermodynamic Functions and Relations
Notation for Chemical and Physical Changes
Chemical Kinetics Electrochemistry
Surface Properties Transport Properties
Dimensionless Quantities

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Scientific and Technical Acronyms, Symbols and Abbreviations

A Mental Note : These tables are not yet Unicoded. In order to properly view these tables, you must have your Symbol Fonts enabled. Thus this page is best viewed in Firefox 2.0.0.20, whereas in Firefox 3.0+ the symbol fonts are completely borked.

Character Map - Times New Roman
# 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 #
32   ! " # $ % & ' ( ) * + , - . / 0 1 2 3 4 5 6 7 8 9 : ; < = > ? 63
64 @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z [ \ ] ^ _ 95
96 ` a b c d e f g h i j k l m n o p q r s t u v w x y z { | } ~  127
128   ‚ ƒ „ … † ‡ ˆ ‰ Š ‹ Œ     ‘ ’ “ ” • – — ˜ ™ š › œ   Ÿ 160
160  ¡ ¢ £ ¤ ¥ ¦ § ¨ © ª « ¬ ­ ® ¯ ° ± ² ³ ´ µ · ¸ ¹ º » ¼ ½ ¾ ¿ 191
192 À Á Â Ã Ä Å Æ Ç È É Ê Ë Ì Í Î Ï Ð Ñ Ò Ó Ô Õ Ö × Ø Ù Ú Û Ü Ý Þ ß 223
224 à á â ã ä å æ ç è é ê ë ì í î ï ð ñ ò ó ô õ ö ÷ ø ù ú û ü ý þ ÿ 255
# 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 #

Character Map - Symbol
# 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 #
32   ! " # $ % & ' ( ) * + , - . / 0 1 2 3 4 5 6 7 8 9 : ; < = > ? 63
64 @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z [ \ ] ^ _ 95
96 ` a b c d e f g h i j k l m n o p q r s t u v w x y z { | } ~  127
128                                 160
160  ¡ ¢ £ ¤ ¥ ¦ § ¨ © ª « ¬ ­ ® ¯ ° ± ² ³ ´ µ · ¸ ¹ º » ¼ ½ ¾ ¿ 191
192 À Á Â Ã Ä Å Æ Ç È É Ê Ë Ì Í Î Ï Ð Ñ Ò Ó Ô Õ Ö × Ø Ù Ú Û Ü Ý Þ ß 223
224 à á â ã ä å æ ç è é ê ë ì í î ï  ñ ò ó ô õ ö ÷ ø ù ú û ü ý þ  255
# 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 #

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Greek Alphabet
Greek Symbol Letter Greek Symbol Letter
Alpha A a A a Nu N n N n
Beta B b B b Xi X x X x
Gamma G g G g Omicron O o O o
Delta D d D d Pi P p P p
Epsilon E e E e Rho R r R r
Zeta Z z Z z Sigma S s S s
Eta H h H h Tau T t T t
Theta Q q Q q Upsilon U u U u
Iota I i I i Phi F f F f
Kappa K k K k Chi C c C c
Lambda L l L l Psi Y y Y y
Mu M m M m Omega W w W w

Metric Prefixes
Prefix Symbol ´ Value Prefix Symbol ´ Value
- - 100 one - - 100 one
deka da 101 ten deci d 10-1 tenth
hecto h 102 hundred centi c 10-2 hundredth
kilo k 103 thousand milli m 10-3 thousandth
mega M 106 million micro m 10-6 millionth
giga G 109 billion nano n 10-9 billionth
tera T 1012 trillion pico p 10-12 trillionth
peta P 1015 quadrillion femto f 10-15 quadrillionth
exa E 1018 zillion atto a 10-18 zillionth
zetta Z 1021 bizillion zepto z 10-21 bizillionth
yotta Y 1024 godzillion yocto y 10-24 godzillionth
lotta X 1027 wholelotta little x 10-27 reallittle
Other euphemisms are possible, i.e. - mongo, mutha, eensyteensy, ittybitty, nada, zip, zilch ...

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Frequency (Hz) = n = c/l = ck
Wavelength (m) = l = c/n = 1/k
Wavenumber (m-1) = k = n/c = 1/l
Speed of Light in Vacuum = c0 = 299 792 458 m s-1 (exact)
A Frequency and Wavenumber of 0 and a Wavelength of ¥ is called Direct Current.
Wait a Second, 0 ´ ¥ = 0/0 = ¼ God, my brain hurts ¼

Electromagnetic Spectrum
Frequency Wavelength Wavenumber Band Energy
3 Hz - 30 Hz 108 m - 107 m 10-8 m-1 - 10-7 m-1 ELF 1, ITU 1 n/a
30 Hz - 300 Hz 107 m - 106 m 10-7 m-1 - 10-6 m-1 SLF, ELF 2, ITU 2 n/a
300 Hz - 3 kHz 106 m - 105 m 10-6 m-1 - 10-5 m-1 ULF, ELF 3, ITU 3 n/a
3 kHz - 30 kHz 105 m - 104 m 10-5 m-1 - 10-4 m-1 VLF, ITU 4, CW n/a
30 kHz - 300 kHz 104 m - 103 m 10-4 m-1 - 10-3 m-1 LF, ITU 5, CW n/a
300 kHz - 3 MHz 1 km - 100 m 10-3 m-1 - 10-2 m-1 MF, ITU 6, AM n/a
3 MHz - 30 MHz 100 m - 10 m 10-2 m-1 - 10-1 m-1 HF, ITU 7, SSB n/a
30 MHz - 300 MHz 10 m - 1 m 10-1 m-1 - 1 m-1 VHF, ITU 8, FM n/a
Frequency Wavelength Wavenumber Band Energy
300 MHz - 3 GHz 1 m - 10 cm 1 m-1 - 10 m-1 UHF, ITU 9, FM, TV, Wireless, Microwave 1 meV - 10 meV
3 GHz - 30 GHz 10 cm - 1 cm 10 m-1 - 100 m-1 SHF, ITU 10, Microwave 10 meV - 100 meV
30 GHz - 300 GHz 1 cm - 1 mm 100 m-1 - 1000 m-1 EHF, ITU 11, Millimeter 100 meV - 1 meV
300 GHz - 3 THz 1 mm - 100 mm 10 cm-1 - 100 cm-1 ITU 12, Submillimeter 1 meV - 10 meV
3 THz - 30 THz 100 mm - 10 mm 100 cm-1 - 1000 cm-1 Far Infrared 10 meV - 100 meV
30 THz - 300 THz 10 mm - 1 mm 1000 cm-1 - 10000 cm-1 Infrared 100 meV - 1 eV
Frequency Wavelength Wavenumber Band Energy
3 ´ 1014 Hz - 3 ´ 1015 Hz 1 mm - 100 nm 10000 cm-1 - 105 cm-1 Near Infrared, Visible (Limit at ~ 3 eV), Near Ultraviolet 1 eV - 10 eV
3 ´ 1015 Hz - 3 ´ 1016 Hz 100 nm - 10 nm 10 mm-1 - 100 mm-1 Far Ultraviolet 10 eV - 100 eV
3 ´ 1016 Hz - 3 ´ 1017 Hz 10 nm - 1 nm 100 mm-1 - 1 nm-1 Soft X-rays 100 eV - 1 keV
3 ´ 1017 Hz - 3 ´ 1018 Hz 1 nm - 1 Å 1 nm-1 - 10 nm-1 X-rays 1 keV - 10 keV
3 ´ 1018 Hz - 3 ´ 1019 Hz 10-10 m - 10-11 m 1010 m-1 - 1011 m-1 Hard X-rays, Soft g Rays 10 keV - 100 keV
3 ´ 1019 Hz - 3 ´ 1020 Hz 10-11 m - 10-12 m 1011 m-1 - 1012 m-1 Soft g Rays, Hard g Rays (Limit at ~ 511 keV) 100 keV - 1 MeV
3 ´ 1020 Hz - 3 ´ 1021 Hz 10-12 m - 10-13 m 1012 m-1 - 1013 m-1 Hard "Cosmic" g Rays 1 MeV - 10 MeV
3 ´ 1021 Hz - 3 ´ 1022 Hz 10-13 m - 10-14 m 1013 m-1 - 1014 m-1 g Rays Produced by Cosmic Rays 10 MeV - 100 MeV
Frequency Wavelength Wavenumber Band Energy

Frequencies and Energies greater than this are in the realm of Nuclear Physics, High Energy Physics, Ungodly Physics and Godly Physics, in order of increasing Energy, respectively.

Microwave Bands
Frequency Wavelength Wavenumber Band
1 GHz - 2 GHz 30 cm - 15 cm 3.3 m-1 - 6.7 m-1 L-Band
2 GHz - 4 GHz 15 cm - 7.5 cm 6.7 m-1 - 13.3 m-1 S-Band
4 GHz - 8 GHz 7.5 cm - 3.7 cm 13.3 m-1 - 26.7 m-1 C-Band
8 GHz - 12 GHz 3.7 cm - 2.5 cm 26.7 m-1 - 40 m-1 X-Band
12 GHz - 18 GHz 2.5 cm - 1.7 cm 40 m-1 - 60 m-1 Ku-Band
18 GHz - 27 GHz 1.7 cm - 1.1 cm 60 m-1 - 90 m-1 K-Band
27 GHz - 40 GHz 1.1 cm- 0.75 cm 90 m-1 - 133 m-1 Ka-Band

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SI International System of Units

SI Defined Units
Quantity Name Symbol
length (distance) meter m
mass kilogram kg
time second s
temperature Kelvin K
current Ampere A (C s-1)
quantity mole mol
luminosity candela cd

SI Derived Units
Quantity Name Symbol Units
frequency Hertz Hz s-1
wavenumber - k m-1
velocity - - m s-1
acceleration - - m s-2
force Newton N kg m s-2
pressure (stress) Pascal Pa N m-2 = kg m-1 s-2
Energy (work, Heat) Joule J N m = kg m2 s-2 = W s
momentum (impulse) Fritz I N s = kg m s-1
power Watt W J s-1 = kg m2 s-3 = V A
electric charge Coulomb C A s
electric potential (emf) Volt V J C-1 = W A-1 = kg m2 s-3 A-1 = J s-1 A-1
resistance Ohm W V A-1 = kg m2 s-3 A-2 = J s-1 A-2 = W A-2
conductance Siemens S A V-1 = W-1 = kg-1 m-2 s3 A2 = J-1 s A2 = A2 W-1
magnetic flux Weber Wb V s = kg m2 s-2 A-1 = J A-1
inductance Henry H Wb A-1 = kg m2 s-2 A-2 = J A-2
capacitance Farad F C V-1 = kg-1 m-2 s4 A2 = J-1 s2 A2 = C2 J-1
electric field strength - - V m-1 = N C-1
electric displacement - - C m-2
magnetic field strength - - A m-1
magnetic flux density Tesla T Wb m-2 = N A-1 m-1 = kg s-2 A-1
plane angle radian rad 2p (circle)
solid angle steradian sr 4p (sphere)
luminous flux lumen lm cd sr
illuminance lux lx lm m-2

SI Accepted Units
Quantity Name Symbol Units
length Ångstrom Å, å 1 Å = 10-10 m
volume Liter L, l 1 L = 10-3 m3
mass metric ton t 1 t = 1000 kg
pressure bar bar 1 bar = 105 Pa = 105 N m-2
time minute min 1 min = 60 s
time hour h 1 h = 60 min = 3600 s
time day d 1 d = 24 h = 1440 min = 86 400 s
nautical distance nautical mile (nm) 1 nautical mile = 1852 m
nautical speed knot (kt) 1 nautical mile per hour = (1852/3600) m/s
plane angle degree o 1o = (p/180) rad
plane angle minute ' 1' = (1/60)o = (p/10 800) rad
plane angle second " 1" = (1/60)' = (1/3600)o = (p/648 000) rad

SI Derived Quantities
Name Quantity Units
area square meter m2
volume cubic meter m3
mass density kilogram per cubic meter kg/m3
molar concentration mole per cubic meter mol/m3
specific volume cubic meter per kilogram m3/kg
molar mass kilogram per mole kg/mol
molar volume cubic meter per mole m3/mol
dynamic viscosity Pascal second Pa•s
moment of force Newton meter, (Joule) N•m, (J)
surface tension Newton per meter, Joule per meter squared N/m, J/m2
angular velocity radian per second rad/s
angular acceleration radian per second squared rad/s2
heat flux density, irradiance Watt per square meter W/m2
thermal conductivity Watt per meter Kelvin W/(m•K)
heat capacity, entropy Joule per Kelvin J/K
specific heat capacity, specific entropy Joule per kilogram Kelvin J/(kg•K)
specific energy Joule per kilogram J/kg
energy density Joule per cubic meter J/m3
molar energy Joule per mole J/mol
molar entropy, molar heat capacity Joule per mole Kelvin J/(mol•K)
electric field strength Volt per meter V/m
electric charge density Coulomb per cubic meter C/m3
electric flux density Coulomb per square meter C/m2
resistivity Ohm meter W•m
conductivity Siemens per meter, (inverse Ohm meter) S/m, (W-1 m-1)
permittivity Farad per meter F/m
permeability Henry per meter H/m, (N/A2)
exposure (X-Rays and g-Rays) Coulomb per kilogram C/kg
radiant intensity Watt per steradian W/sr
radiance Watt per square meter steradian W/(m2•sr)
luminance candela per square meter cd/m2

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Fundamental Physical Constants
Updated to 1998 CODATA Recommended Values

Earth Constants
Constant Symbol Value
Standard Atmosphere atm 101 325 Pa (exact)
Rounded Atmosphere bar 100 000 Pa (exact)
Standard Acceleration of Gravity ga, gn 9.806 65 m s-2 (exact)
Astronomical Unit (Earth - Sun) au 1.495 978 706 91 (30) ´ 1011 m

Universal Constants
Constant Symbol Value
Speed of Light in Vacuum = (m0e0)-1/2 c, c0 299 792 458 m s-1 (exact)
Magnetic Constant (Permeability of Vacuum)
= 4p ´ 10-7 N A-2 (4p ´ 10-7 H m-1) = 1/e0c2 		m0 12.566 370 614 ¼ ´ 10-7 N A-2 (H m-1)
Electric Constant (Permittivity of Vacuum) = 1/m0c2 e0 8.854 187 817 ¼ ´ 10-12 F m-1
Characteristic Impedance of Vacuum = (m0/e0)1/2 = m0c = 1/e0c Z0 376.730 313 461 ¼ W
Newtonian Constant of Gravitation G 6.673 (10) ´ 10-11 m3 kg-1 s-2
Newtonian Constant of Gravitation G/hc 6.707 (10) ´ 10-39 (GeV/c2)-2
electron Volt (in Joules) = {e/C} J eV 1.602 176 462 (63) ´ 10-19 J
(unified) atomic mass unit = m(12C)/12 = 10-3 kg mol-1/NA u 1.660 538 73 (13) ´ 10-27 kg = 1 Dalton (Da)

Planck Constants
Constant Symbol Value
Planck Constant (in Joules) h 6.626 068 76 (52) ´ 10-34 J s (I m)
Planck Constant = h/{e} (in electron Volts) h/{e} 4.135 667 27 (16) ´ 10-15 eV s
Reduced Planck Constant = h/2p (in Joules) h (h bar) 1.054 571 596 (82) ´ 10-34 J s (I m)
Reduced Planck Constant = h/2p{e} (in electron Volts) h/{e} 6.582 118 89 (26) ´ 10-16 eV s
Planck Mass = (hc/G)1/2 mP 2.176 7 (16) ´ 10-8 kg
Planck Length = h/mPc = (hG/c3)1/2 lP 1.616 0 (12) ´ 10-35 m
Planck Time = lP/c = (hG/c5)1/2 tP 5.390 6 (40) ´ 10-44 s

Electromagnetic Constants
Constant Symbol Value
Electronic Charge Quantum = e e 1.602 176 462 (63) ´ 10-19 C
Quantized Electronic Charge = e/h e/h 2.417 989 491 (95) ´ 1014 A J-1
Magnetic Flux Quantum = h/2e F0 2.067 833 636 (81) ´ 10-15 Wb
Conductance Quantum = 2e2/h G0 7.748 091 696 (28) ´ 10-5 S
Inverse Conductance Quantum = h/2e2 G0-1 12 906.403 786 (95) W
Josephson Constant = 2e/h KJ 0.483 597 898 (19) ´ 1015 Hz V-1
Josephson Constant (conventional value) KJ-90 483 597.9 GHz V-1 (exact)
von Klitzing Constant = h/e2 = m0c/2a RK 25 812.807 592 (95) W
von Klitzing Constant (conventional value) RK-90 25 812.807 W (exact)
Mental Note : Conventional values are the internationally adopted exact values, used for realizing representations of the Volt using the Josephson effect, and the Ohm using the quantum Hall effect (QHE).

Bohr Magneton
Constant Symbol Value
Bohr Magneton = eh/2me mB 9.274 008 99 (37) ´ 10-24 J T-1
Bohr Magneton = mB/{e} (in electron Volts) mB/e 5.788 381 749 (43) ´ 10-5 eV T-1
Bohr Magneton = mB/h (in Hertz) mB/h 1.399 624 624 (56) ´ 1010 Hz T-1
Bohr Magneton = mB/hc (in wavenumbers) mB/hc 46.686 452 1 (19) m-1 T-1
Bohr Magneton = mB/k (in Kelvins) mB/k 0.671 713 1 (12) K T-1

Nuclear Magneton
Constant Symbol Value
Nuclear Magneton = eh/2mp mN 5.050 783 17 (20) ´ 10-27 J T-1
Nuclear Magneton = mN/{e} (in electron Volts) mN/e 3.152 451 238 (24) ´ 10-8 eV T-1
Nuclear Magneton = mN/h (in Hertz) mN/h 7.622 593 964 (31) MHz T-1
Nuclear Magneton = mN/hc (in wavenumbers) mN/hc 2.542 623 66 (10) ´ 10-2 m-1 T-1
Nuclear Magneton = mN/k (in Kelvins) mN/k 3.658 263 8 (64) ´ 10-4 K T-1

(Inverse) Fine Structure Constant
Constant Symbol Value
Fine Structure Constant = m0ce2/2h = e2/2he0c a 7.297 352 533 (27) ´ 10-3
Inverse Fine Structure Constant = 2h/e2m0c = e0c2h/e2 1/a = a-1 137.035 999 76 (50)

Rydberg Constant
Constant Symbol Value
Rydberg Constant = meca2/2h = Eh/2hc R¥ 10 973 731.568 549 (83) m-1
Rydberg Constant = R¥c (in Hertz) R¥c 3.289 841 960 368 (25) ´ 1015 Hz
Rydberg Constant = R¥hc (in Joules) R¥hc 2.179 871 90 (17) ´ 10-18 J
Rydberg Constant = R¥hc/{e} (in electron Volts) R¥hc/{e} 13.605 691 72 (53) eV

Physical Constants
Constant Symbol Value
Bohr Radius = a/4pR¥ = 4pe0h2/mee2 a0 0.529 177 208 3 (19) ´ 10-10 m
Hartree Energy = e2/4pe0a0 = 2R¥hc = a2mec2 = h2/mea02 Eh 4.359 743 81 (34) ´ 10-18 J
Hartree Energy = Eh/{e} (in electron Volts) Eh/{e} 27.211 383 4 (11) eV
Quantum of Circulation = h/2me h/2me 3.636 947 516 (27) ´ 10-4 m2 s-1
Quanta of Circulation = h/me h/me 7.273 895 032 (53) ´ 10-4 m2 s-1

Chemical Constants
Constant Symbol Value
Avogadro's Number (Avogadro Constant) NA, L 6.022 141 99 (47) ´ 1023 mol-1
Atomic Mass Constant = m(12C)/12 = 10-3 kg mol-1/NA mu 1.660 538 73 (13) ´ 10-27 kg = 1 Dalton (Da)
Atomic Mass Constant = muc2 (in Joules) muc2 1.492 417 78 (12) ´ 10-10 J
Atomic Mass Constant = muc2/{e} (in electron Volts) muc2/{e} 931.494 013 (37) MeV
Faraday Constant = NAe F 96 485.341 5 (39) C mol-1
Faraday Constant = NAe (conventional value) F 96 485.343 2 (76) C mol-1
Molar Planck Constant = NAh NAh 3.990 312 689 (30) ´ 10-10 J s mol-1
Molar Planck Constant = NAhc NAhc 0.119 626 564 92 (91) J m mol-1
Molar Gas Constant R 8.314 472 (15) J mol-1 K-1
Molar Volume = RT / p (Ideal Gas at T = 273.15 K, p = 101 325 Pa - Standard Atmosphere) Vm 22 413.996 (39) cm3 mol-1 ( p = 101 325 Pa)
Molar Volume = RT / p (Ideal Gas at T = 273.15 K, p = 100 000 Pa - Rounded Atmosphere) Vm 22 710.981 (40) cm3 mol-1 ( p = 100 000 Pa)
Loschmidt Constant = NA/Vm n0 2.686 777 5 (47) ´ 1025 m-3

Boltzmann Constant
Constant Symbol Value
Boltzmann Constant = R/NA k, kB 1.380 650 3 (24) ´ 10-23 J K-1
Boltzmann Constant = k/{e} (in electron Volts) k/{e} 8.617 342 (15) ´ 10-5 eV K-1
Boltzmann Constant = k/h (in Hertz) k/h 2.083 664 4 (36) ´ 1010 Hz K-1
Boltzmann Constant = k/hc (in wavenumbers) k/hc 69.503 56 (12) m-1 K-1

Physicochemical Constants
Constant Symbol Value
Stefan-Boltzmann Constant = (p2/60)k4/h3c2 s 5.670 400 (40) ´ 10-8 W m-2 K-4
First Radiation Constant = 2phc2 c1 3.741 771 07 (93) ´ 10-16 W m2
First Radiation Constant (Spectral Radiance) = 2hc2 c1L 1.191 042 722 (29) ´ 10-16 W m2 sr-1
Second Radiation Constant = hc/k c2 0.014 387 752 (25) m K
Wien Displacement Law Constant = lmaxT = c2 / 4.965 114 231 ¼ b 2.897 768 6 (51) m K
Sackur-Tetrode Constant (absolute entropy constant) =
5/2 + ln[(2pmu kT1 / h2)3/2 kT1 / p0], T1 = 1 K, p0 = 101.325 kPa - Standard Atmosphere 		- – 1.164 867 8 (44)
Sackur-Tetrode Constant (absolute entropy constant) =
5/2 + ln[(2pmu kT1 / h2)3/2 kT1 / p0], T1 = 1 K, p0 = 100 kPa - Rounded Atmosphere 		S0/R – 1.151 704 8 (44)
Mental Note : The entropy of an ideal monoatomic gas of relative atomic mass Ar is given by :
S = S0 + 3/2 R ln Ar – R ln ( p / p0) + 5/2 R ln (T / K).

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Electron Constants
Constant Symbol Value
Electron Mass me 9.109 381 88 (72) ´ 10-31 kg
Electron Mass (in atomic mass units) me 5.485 799 110 (12) ´ 10-4 u (amu)
Electron Mass = mec2 (in Joules) mec2 8.187 104 14 (64) ´ 10-14 J
Electron Mass = mec2/{e} (in electron Volts) mec2/{e} 0.510 998 902 (21) MeV
Electron - Proton Mass Ratio = me/mp me/mp 5.446 170 232 (12) ´ 10-4
Electron - Neutron Mass Ratio = me/mn me/mn 5.438 673 462 (12) ´ 10-4
Electron - Deuteron Mass Ratio = me/md me/md 2.724 437 117 0 (58) ´ 10-4
Electron Charge to Mass Ratio = – e/me – e/me – 1.758 820 174 (71) ´ 1011 C kg-1
Electron Molar Mass = NAme M(e), Me 5.485 799 110 (12) ´ 10-7 kg mol-1
Electron Compton Wavelength = h/mec lC(e) 2.426 310 215 (18) ´ 10-12 m
Electron Compton Wavelength = lC(e)/2p = aa0 = a2/4pR¥ lC(e) 3.861 592 642 (28) ´ 10-13 m
Electron Classical Radius = a2 a0 re 2.817 940 285 (31) ´ 10-15 m
Thomson Cross Section = (8p/3)re2 se 0.665 245 854 (15) ´ 10-28 m2
Electron Magnetic Moment me – 928.476 362 (37) ´ 10-26 J T-1
Electron Magnetic Moment = me/mB (in Bohr magnetons) me/mB – 1.001 159 652 186 9 (41)
Electron Magnetic Moment = me/mN (in Nuclear magnetons) me/mN – 1 838.281 966 0 (39)
Electron Magnetic Moment Anomaly = me/mB – 1 ae 1.159 652 186 9 (41) ´ 10-3
Electron g-factor = 2(1 + ae) ge – 2.002 319 304 373 7 (82)
Electron - Proton Magnetic Moment Ratio = me/mp me/mp – 658.210 687 5 (66)
Electron - Neutron Magnetic Moment Ratio = me/mn me/mn 960.920 50 (23)
Electron - Deuteron Magnetic Moment Ratio = me/md me/md – 2 143.923 498 (23)
Electron Gyromagnetic Ratio = 2|me|/h ge 1.760 859 794 (71) ´ 1011 s-1 T-1
Electron Gyromagnetic Ratio = ge/2p = 2|me|/h ge/2p 28 024.954 0 (11) MHz T-1

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Proton Constants
Constant Symbol Value
Proton Mass mp 1.672 621 58 (13) ´ 10-27 kg
Proton Mass (in atomic mass units) mp 1.007 276 466 88 (13) u (amu)
Proton Mass = mpc2 (in Joules) mpc2 1.503 277 31 (12) ´ 10-10 J
Proton Mass = mpc2/{e} (in electron Volts) mpc2/{e} 938.271 998 (38) MeV
Proton - Electron Mass Ratio = mp/me mp/me 1836.152 667 5 (39)
Proton - Neutron Mass Ratio = mp/mn mp/mn 0.998 623 478 55 (58)
Proton Charge to Mass Ratio = e/mp e/mp 9.578 834 08 (38) ´ 107 C kg-1
Proton Molar Mass = NAmp M(p), Mp 1.007 276 466 88 (13) ´ 10-3 kg mol-1
Proton Compton Wavelength = h/mpc lC(p) 1.321 409 847 (10) ´ 10-15 m
Proton Compton Wavelength = lC(p)/2p lC(p) 2.103 089 089 (16) ´ 10-16 m
Proton Magnetic Moment mp 1.410 606 633 (58) ´ 10-26 J T-1
Proton Magnetic Moment = mp/mB (in Bohr magnetons) mp/mB 1.521 032 203 (15) ´ 10-3
Proton Magnetic Moment = mp/mN (in Nuclear magnetons) mp/mN 2.792 847 337 (29)
Proton - Neutron Magnetic Moment Ratio = mp/mn mp/mn – 1.459 898 05 (34)
Proton g-factor = 2mp/mN gp 5.585 694 675 (57)
Proton Gyromagnetic Ratio = 2|mp|/h gp 2.675 222 12 (11) ´ 108 s-1 T-1
Proton Gyromagnetic Ratio = gp/2p = 2|mp|/h gp/2p 42.577 482 5 (18) MHz T-1

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Neutron Constants
Constant Symbol Value
Neutron Mass mn 1.674 927 16 (13) ´ 10-27 kg
Neutron Mass (in atomic mass units) mn 1.008 664 915 78 (55) u (amu)
Neutron Mass = mnc2 (in Joules) mnc2 1.505 349 46 (12) ´ 10-10 J
Neutron Mass = mnc2/{e} (in electron Volts) mnc2/{e} 939.565 330 (38) MeV
Neutron - Electron Mass Ratio = mn/me mn/me 1838.683 655 0 (40)
Neutron - Proton Mass Ratio = mn/mp mn/mp 1.001 378 418 87 (58)
Neutron Molar Mass = NAmn M(n), Mn 1.008 664 915 78 (55) ´ 10-3 kg mol-1
Neutron Compton Wavelength = h/mnc lC(n) 1.319 590 898 (10) ´ 10-15 m
Neutron Compton Wavelength = lC(n)/2p lC(n) 2.100 194 142 (16) ´ 10-16 m
Neutron Magnetic Moment mn – 0.966 236 40 (23) ´ 10-26 J T-1
Neutron Magnetic Moment = mn/mB (in Bohr magnetons) mn/mB – 1.041 875 63 (25) ´ 10-3
Neutron Magnetic Moment = mn/mN (in Nuclear magnetons) mn/mN – 1.913 042 72 (45)
Neutron - Electron Magnetic Moment Ratio = mn/me mn/mB 1.040 668 82 (25) ´ 10-3
Neutron - Proton Magnetic Moment Ratio = mn/mp mn/mp – 0.684 979 34 (16)
Neutron g-factor = 2mn/mN gn – 3.826 085 45 (90)
Neutron Gyromagnetic Ratio = 2|mn|/h gn 1.832 471 88 (44) ´ 108 s-1 T-1
Neutron Gyromagnetic Ratio = gn/2p = 2|mn|/h gn/2p 29.164 695 8 (70) MHz T-1

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Deuteron Constants
Constant Symbol Value
Deuteron Mass md 3.343 583 09 (26) ´ 10-27 kg
Deuteron Mass (in atomic mass units) md 2.013 553 212 71 (35) u (amu)
Deuteron Mass = mdc2 (in Joules) mdc2 3.005 062 62 (24) ´ 10-10 J
Deuteron Mass = mdc2/{e} (in electron Volts) mdc2/{e} 1 875.612 762 (75) MeV
Deuteron - Electron Mass Ratio = md/me md/me 3 670.482 955 0 (78)
Deuteron - Proton Mass Ratio = md/mp md/mp 1.999 007 500 83 (41)
Deuteron Molar Mass = NAmd M(d), Md 2.013 553 212 71 (35) ´ 10-3 kg mol-1
Deuteron Magnetic Moment md 0.433 073 457 (18) ´ 10-26 J T-1
Deuteron Magnetic Moment = md/mB (in Bohr magnetons) md/mB 0.466 975 4556 (50) ´ 10-3
Deuteron Magnetic Moment = md/mN (in Nuclear magnetons) md/mN 0.857 438 2284 (94)
Deuteron - Electron Magnetic Moment Ratio = md/me md/mB – 4.664 345 537 (50) ´ 10-4
Deuteron - Proton Magnetic Moment Ratio = md/mp md/mp 0.307 012 2083 (45)
Deuteron - Neutron Magnetic Moment Ratio = md/mn md/mn – 0.448 206 52 (11)

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Energy Equivalence Factors
E = mc2 = hc/l = hn = kT

Next Energy Equivalence I Previous
Units J (Joule) kg (kilogram)
1 J (Joule) = 1 J (Joule) 1.112 650 056 ´ 10-17 kg
1 kg (kilogram) = 8.987 551 787 ´ 1016 J 1 kg (kilogram)
1 m-1 (wavenumber) = 1.986 445 44 (16) ´ 10-25 J 2.210 218 63 (17) ´ 10-42 kg
1 Hz (Hertz) = 6.626 068 76 (52) ´ 10-34 J 7.372 495 78 (58) ´ 10-51 kg
1 K (Kelvin) = 1.380 650 3 (24) ´ 10-23 J 1.536 180 7 (27) ´ 10-40 kg
1 eV (electron Volt) = 1.602 176 462 (63) ´ 10-19 J 1.782 661 731 (70) ´ 10-36 kg
1 u (atomic mass unit) = 1.492 417 78 (12) ´ 10-10 J 1.660 538 73 (13) ´ 10-27 kg
1 Hartree (atomic energy unit) = 4.359 743 81 (34) ´ 10-18 J 4.850 869 19 (38) ´ 10-35 kg

Next Energy Equivalence II Previous
Units m-1 (wavenumber) Hz (Hertz)
1 J (Joule) = 5.034 117 62 (39) ´ 1024 m-1 1.509 190 50 (12) ´ 1033 Hz
1 kg (kilogram) = 4.524 439 29 (35) ´ 1041 m-1 1.356 392 77 (11) ´ 1050 Hz
1 m-1 (wavenumber) = 1 m-1 (wavenumber) 299 792 458 Hz
1 Hz (Hertz) = 3.335 640 952 ´ 10-9 m-1 1 Hz (Hertz)
1 K (Kelvin) = 69.503 56 (12) m-1 2.083 664 4 (36) ´ 1010 Hz
1 eV (electron Volt) = 806 544.77 (32) m-1 2.417 989 491 (95) ´ 1014 Hz
1 u (atomic mass unit) = 7.513 006 658 (57) ´ 1014 m-1 2.252 342 733 (17) ´ 1023 Hz
1 Hartree (atomic energy unit) = 21 947 463.137 10 (17) m-1 6.579 683 920 735 (50) ´ 1015 Hz

Next Energy Equivalence III Previous
Units K (Kelvin) eV (electron Volt)
1 J (Joule) = 7.242 964 (13) ´ 1022 K 6.241 509 74 (24) ´ 1018 eV
1 kg (kilogram) = 6.509 651 (11) ´ 1039 K 5.609 589 21 (22) ´ 1035 eV
1 m-1 (wavenumber) = 0.014 387 752 (25) K 1.239 841 857 (49) ´ 10-6 eV
1 Hz (Hertz) = 4.799 237 4 (84) ´ 10-11 K 4.135 667 27 (16) ´ 10-15 eV
1 K (Kelvin) = 1 K (Kelvin) 8.617 342 (15) ´ 10-5 eV
1 eV (electron Volt) = 11 604.506 K 1 eV (electron Volt)
1 u (atomic mass unit) = 1.080 952 8 (19) ´ 1013 K 931.494 013 (37) ´ 106 eV
1 Hartree (atomic energy unit) = 3.157 746 5 (55) ´ 105 K 27.211 383 4 (11) eV

Next Energy Equivalence IV Previous
Units u (atomic mass unit) Hartree (atomic energy unit)
1 J (Joule) = 6.700 536 62 (53) ´ 109 u 2.293 712 76 (18) ´ 1017 Hartree
1 kg (kilogram) = 6.022 141 99 (47) ´ 1026 u 2.061 486 22 (16) ´ 1034 Hartree
1 m-1 (wavenumber) = 1.331 025 042 (10) ´ 10-15 u 4.556 335 252 750 (35) ´ 10-8 Hartree
1 Hz (Hertz) = 4.439 821 637 (34) ´ 10-24 u 1.519 829 846 003 (12) ´ 10-16 Hartree
1 K (Kelvin) = 9.251 098 (16) ´ 10-14 u 3.166 815 3 (55) ´ 10-6 Hartree
1 eV (electron Volt) = 1.073 544 206 (43) ´ 10-9 u 0.036 749 326 0 (14) Hartree
1 u (atomic mass unit) = 1 u (atomic mass unit) 3.423 177 709 (26) ´ 107 Hartree
1 Hartree (atomic energy unit) = 2.921 262 304 (22) ´ 10-8 u 1 Hartree (atomic energy unit)

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Energy Conversion Factors
E = mc2 = hc/l = hn = kT

Next Energy Conversion I Previous
Units J (Joule) kg (kilogram)
1 J (Joule) ´ factor =
energy equivalent = 		1 J (Joule) ´ 1 =
1 J (Joule) 		1 J (Joule) ´ {1/c2} =
1.112 650 056 ´ 10-17 kg
1 kg (kilogram) ´ factor =
energy equivalent = 		1 kg (kilogram) ´ {c2} =
8.987 551 787 ´ 1016 J 		1 kg (kilogram) ´ 1 =
1 kg (kilogram)
1 m-1 (wavenumber) ´ factor =
energy equivalent = 		1 m-1 (wavenumber) ´ {hc} =
1.986 445 44 (16) ´ 10-25 J 		1 m-1 (wavenumber) ´ {h/c} =
2.210 218 63 (17) ´ 10-42 kg
1 Hz (Hertz) ´ factor =
energy equivalent = 		1 Hz (Hertz) ´ {h} =
6.626 068 76 (52) ´ 10-34 J 		1 Hz (Hertz) ´ {h/c2} =
7.372 495 78 (58) ´ 10-51 kg
1 K (Kelvin) ´ factor =
energy equivalent = 		1 K (Kelvin) ´ {k} =
1.380 650 3 (24) ´ 10-23 J 		1 K (Kelvin) ´ {k/c2} =
1.536 180 7 (27) ´ 10-40 kg
1 eV (electron Volt) ´ factor =
energy equivalent = 		1 eV (electron Volt) ´ {e} =
1.602 176 462 (63) ´ 10-19 J 		1 eV (electron Volt) ´ {e/c2} =
1.782 661 731 (70) ´ 10-36 kg
1 u (atomic mass unit) ´ factor =
energy equivalent = 		1 u (atomic mass unit) ´ {muc2} =
1.492 417 78 (12) ´ 10-10 J 		1 u (atomic mass unit) ´ {mu} =
1.660 538 73 (13) ´ 10-27 kg
1 Hartree (atomic energy unit) ´ factor =
energy equivalent = 		1 Hartree ´ {2R¥hc} =
4.359 743 81 (34) ´ 10-18 J 		1 Hartree ´ {2R¥h/c} =
4.850 869 19 (38) ´ 10-35 kg

Next Energy Conversion II Previous
Units m-1 (wavenumber) Hz (Hertz)
1 J (Joule) ´ factor =
energy equivalent = 		1 J (Joule) ´ {1/hc} =
5.034 117 62 (39) ´ 1024 m-1 		1 J (Joule) ´ {1/h} =
1.509 190 50 (12) ´ 1033 Hz
1 kg (kilogram) ´ factor =
energy equivalent = 		1 kg (kilogram) ´ {c/h} =
4.524 439 29 (35) ´ 1041 m-1 		1 kg (kilogram) ´ {c2/h} =
1.356 392 77 (11) ´ 1050 Hz
1 m-1 (wavenumber) ´ factor =
energy equivalent = 		1 m-1 (wavenumber) ´ 1 =
1 m-1 (wavenumber) 		1 m-1 (wavenumber) ´ {c} =
299 792 458 Hz
1 Hz (Hertz) ´ factor =
energy equivalent = 		1 Hz (Hertz) ´ {1/c} =
3.335 640 952 ´ 10-9 m-1 		1 Hz (Hertz) ´ 1 =
1 Hz (Hertz)
1 K (Kelvin) ´ factor =
energy equivalent = 		1 K (Kelvin) ´ {k/hc} =
69.503 56 (12) m-1 		1 K (Kelvin) ´ {k/h} =
2.083 664 4 (36) ´ 1010 Hz
1 eV (electron Volt) ´ factor =
energy equivalent = 		1 eV (electron Volt) ´ {e/hc} =
806 544.77 (32) m-1 		1 eV (electron Volt) ´ {e/h} =
2.417 989 491 (95) ´ 1014 Hz
1 u (atomic mass unit) ´ factor =
energy equivalent = 		1 u (atomic mass unit) ´ {muc/h} =
7.513 006 658 (57) ´ 1014 m-1 		1 u (atomic mass unit) ´ {muc2/h} =
2.252 342 733 (17) ´ 1023 Hz
1 Hartree (atomic energy unit) ´ factor =
energy equivalent = 		1 Hartree ´ {2R¥} =
21 947 463.137 10 (17) m-1 		1 Hartree ´ {2R¥c} =
6.579 683 920 735 (50) ´ 1015 Hz

Next Energy Conversion III Previous
Units K (Kelvin) eV (electron Volt)
1 J (Joule) ´ factor =
energy equivalent = 		1 J (Joule) ´ {1/k} =
7.242 964 (13) ´ 1022 K 		1 J (Joule) ´ {1/e} =
6.241 509 74 (24) ´ 1018 eV
1 kg (kilogram) ´ factor =
energy equivalent = 		1 kg (kilogram) ´ {c2/k} =
6.509 651 (11) ´ 1039 K 		1 kg (kilogram) ´ {c2/e} =
5.609 589 21 (22) ´ 1035 eV
1 m-1 (wavenumber) ´ factor =
energy equivalent = 		1 m-1 (wavenumber) ´ {hc/k} =
0.014 387 752 (25) K 		1 m-1 (wavenumber) ´ {hc/e} =
1.239 841 857 (49) ´ 10-6 eV
1 Hz (Hertz) ´ factor =
energy equivalent = 		1 Hz (Hertz) ´ {h/k} =
4.799 237 4 (84) ´ 10-11 K 		1 Hz (Hertz) ´ {h/e} =
4.135 667 27 (16) ´ 10-15 eV
1 K (Kelvin) ´ factor =
energy equivalent = 		1 K (Kelvin) ´ 1 =
1 K (Kelvin) 		1 K (Kelvin) ´ {k/e} =
8.617 342 (15) ´ 10-5 eV
1 eV (electron Volt) ´ factor =
energy equivalent = 		1 eV (electron Volt) ´ {e/k} =
11 604.506 K 		1 eV (electron Volt) ´ 1 =
1 eV (electron Volt)
1 u (atomic mass unit) ´ factor =
energy equivalent = 		1 u (atomic mass unit) ´ {muc2/k} =
1.080 952 8 (19) ´ 1013 K 		1 u (atomic mass unit) ´ {muc2/e} =
931.494 013 (37) ´ 106 eV
1 Hartree (atomic energy unit) ´ factor =
energy equivalent = 		1 Hartree ´ {2R¥hc/k} =
3.157 746 5 (55) ´ 105 K 		1 Hartree ´ {2R¥hc/e} =
27.211 383 4 (11) eV

Next Energy Conversion IV Previous
Units u (atomic mass unit) Hartree (atomic energy unit)
1 J (Joule) ´ factor =
energy equivalent = 		1 J (Joule) ´ {1/muc2} =
6.700 536 62 (53) ´ 109 u 		1 J (Joule) ´ {1/2R¥hc} =
2.293 712 76 (18) ´ 1017 Hartree
1 kg (kilogram) ´ factor =
energy equivalent = 		1 kg (kilogram) ´ {1/mu} =
6.022 141 99 (47) ´ 1026 u 		1 kg (kilogram) ´ {c/2R¥h} =
2.061 486 22 (16) ´ 1034 Hartree
1 m-1 (wavenumber) ´ factor =
energy equivalent = 		1 m-1 (wavenumber) ´ {h/muc} =
1.331 025 042 (10) ´ 10-15 u 		1 m-1 (wavenumber) ´ {1/2R¥} =
4.556 335 252 750 (35) ´ 10-8 Hartree
1 Hz (Hertz) ´ factor =
energy equivalent = 		1 Hz (Hertz) ´ {h/muc2} =
4.439 821 637 (34) ´ 10-24 u 		1 Hz (Hertz) ´ {1/2R¥c} =
1.519 829 846 003 (12) ´ 10-16 Hartree
1 K (Kelvin) ´ factor =
energy equivalent = 		1 K (Kelvin) ´ {k/muc2} =
9.251 098 (16) ´ 10-14 u 		1 K (Kelvin) ´ {k/2R¥hc} =
3.166 815 3 (55) ´ 10-6 Hartree
1 eV (electron Volt) ´ factor =
energy equivalent = 		1 eV (electron Volt) ´ {e/muc2} =
1.073 544 206 (43) ´ 10-9 u 		1 eV (electron Volt) ´ {e/2R¥hc} =
0.036 749 326 0 (14) Hartree
1 u (atomic mass unit) ´ factor =
energy equivalent = 		1 u (atomic mass unit) ´ 1 =
1 u (atomic mass unit) 		1 u (atomic mass unit) ´ {muc/2R¥h} =
3.423 177 709 (26) ´ 107 Hartree
1 Hartree (atomic energy unit) ´ factor =
energy equivalent = 		1 Hartree ´ {2R¥h/muc} =
2.921 262 304 (22) ´ 10-8 u 		1 Hartree (atomic energy unit) ´ 1 =
1 Hartree (atomic energy unit)

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Next Natural Units (n.u.) Previous
Unit Description Symbol Value
n.u. of velocity Speed of Light in vacuum c, c0 299 792 458 m s-1 (exact)
n.u. of action Reduced Planck Constant = h = h/2p h = h/2p 1.054 571 596 (82) ´ 10-34 J s (I m)
n.u. of mass Electron Rest Mass (in kilograms) me 9.109 381 88 (72) ´ 10-31 kg
n.u. of energy electron energy equivalent (in Joules) mec2 8.187 104 14 (64) ´ 10-14 J
n.u. of energy electron energy equivalent (in electron Volts) mec2/{e} 0.510 998 902 (21) MeV
n.u. of momentum electron momentum equivalent mec 2.730 923 98 (21) ´ 10-22 I (Fritz, N s, kg m s-1)
n.u. of momentum electron momentum equivalent (in electron Volts/c) mec/{e} 0.510 998 902 (21) MeV/c
n.u. of length electron Compton wavelength = h/mec lC 386.159 264 2 (28) ´ 10-15 m
n.u. of time electronic transition equivalent h/mec2 1.288 088 655 5 (95) ´ 10-21 s

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Next Atomic Units (a.u.) Previous
Unit Symbol Value
a.u. of mass (Electron Rest Mass) me 9.109 381 88 (72) ´ 10-31 kg
a.u. of charge (Electronic Charge) e 1.602 176 462 (63) ´ 10-19 C
a.u. of action (Reduced Planck Constant) h = h/2p 1.054 571 596 (82) ´ 10-34 J s (I m)
a.u. of length (Bohr Radius) a0 = 4pe0h2/mee2 = a/4pR¥ 0.529 177 208 3 (19) ´ 10-10 m
a.u. of energy (Hartree Energy) Eh = e2/4pe0a0 = 2R¥hc = a2mec2 = h2/mea02 4.359 743 81 (34) ´ 10-18 J
a.u. of time h/Eh 2.418 884 326 500 (18) ´ 10-17 s
a.u. of velocity a0Eh/h = ac 2.187 691 252 9 (80) ´ 106 m s-1
c/a.u. of velocity ch/a0Eh = a-1 137.035 989 5 (61)
a.u. of force Eh/a0 8.238 721 81 (64) ´ 10-8 N
a.u. of momemtum h/a0 1.992 851 51 (16) ´ 10-24 I (Fritz, N s, kg m s-1)
a.u. of current eEh/h 6.623 617 53 (26) ´ 10-3 A
a.u. of charge density ea03 1.081 202 285 (43) ´ 1012 C m-3
a.u. of electric potential Eh/e 27.211 383 4 (11) V
a.u. of electric field Eh/ea0 5.142 206 24 (20) ´ 1011 V m-1
a.u. of electric field gradient Eh/ea02 9.717 361 53 (39) ´ 1021 V m-2
a.u. of electric dipole moment ea0 8.478 352 67 (33) ´ 10-30 C m
a.u. of electric quadrupole moment ea02 4.486 551 00 (18) ´ 10-40 C m2
a.u. of polarizability e2a02/Eh 1.648 777 251 (18) ´ 10-41 C2 m2 J-1
a.u. of first hyperpolarizability e3a03/Eh2 3.206 361 57 (14) ´ 10-53 C3 m3 J-2
a.u. of second hyperpolarizability e4a04/Eh3 6.235 381 12 (51) ´ 10-65 C4 m4 J-3
a.u. of magnetic flux density h/ea02 2.350 517 349 (94) ´ 105 T
a.u. of magentic dipole moment Eh/me = 2mB 1.854 801 799 (75) ´ 10-23 J T-1
a.u. of magnetizability e2a02/me 7.891 036 41 (14) ´ 10-29 J T-1
a.u. of permittivity (107/c2) e2/a0Eh 1.112 650 056 ¼ ´ 10-10 F m-1

A Note on Notation : Units in theoretical calculations are usually renormalized to h = c = 1.

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Next Other (SI Derived) Units Previous
Quantity Unit Symbol Value in SI Units
Force (Newton) dyne dyn 10-5 N
Pressure (Pascal) Rounded Atmosphere bar 100 000 Pa
Standard Atmosphere atm 101 325 Pa
torr (mmHg) Torr 133 322 Pa
Energy (Joule) erg erg 10-7 J
thermochemical calorie calth 4.184 J
Magnetic Flux Density Gauss (gauss) G 10-4 T
Electric Dipole Moment Debye (debye) D 3.335 64 ´ 10-30 C m
Dynamic Viscosity Poise (poise) P 10-1 N s m-2, (10-1 Pa s)
Kinematic Viscosity Stokes (stokes) St 10-4 m2 s-1

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Symbols and Terminology of Condensed Matter Physics
Physical and Chemical Quantities

Space and Time
Name Symbol Definition SI Units
cartesian space coordinates x, y, z - m
spherical space coordinates r, q, f - m, 1, 1
unit vectors, (orthonormal vectors) i, j, k i • i = j • j = k • k = 1
i • j = j • k = k • i = 0 		m, 1
position vector r r = x i + y j + z k m
generalized coordinates q, qi - (varies)
Distance d - m
Length l - m
height h - m
width w - m
breadth b - m
thickness d, d - m
radius r - m
diameter d - m
path s - m
length of arc s - m
Area A, As, S - m2
Volume V, v - m3
Plane Angle a, b, g, q, f a = s/r 1, rad
Solid Angle w, W - 1, sr
Time t - s
period, (duration) T T = t/N s
Frequency n, f n = 1/T Hz
angular frequency, circular frequency w w =2pn rad s-1, s-1
characteristic
-- time interval
-- relaxation time
-- time constant 		t, T t = |dt/dlnx| s
Angular Velocity w w = df/dt rad s-1, s-1
Angular Acceleration w• w• = dw/dt rad s-2, s-2
Velocity v, u, w, c, r•, r´ (r dot, r prime) v = dr / dt (r•, r´) m s-1
speed v, u, w, c v = |v| m s-1
Acceleration a, (g) a = dv/dt m s-2

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Classical Mechanics
Name Symbol Definition SI Units
Mass m standard kg
reduced mass m m = m1m2 / (m1 + m2) kg
Density, mass density r r = m/V kg m-3
relative density d d = r/r* 1
surface density rA , rS rA = m / A kg m-2
Specific Volume u u = V/m = 1/r m3 kg-1
moment of inertia I , J I = å mi ri2 kg m2
Momentum p p = mv I, Fritz, N s, kg m s-1
angular momentum, action L L = r ´ p J s, kg m2 s-1, I m
Force F F = d p/dt = ma N, kg m s-2
Moment of Force, torque T , M T = r ´ F N m, (J)
Energy E kg m2 s-2 J
potential energy Ep , V , F Ep = – ò F • ds J
kinetic energy Ek , T , K Ek = ½mv2 J
work W , w W = ò F • ds J
Hamilton function H H (q, p) = T (q, p) + V (q) J
Lagrange function L L (q, q•) = T (q, q•) – V (q) J
Pressure p, P p = F / A Pa, N m-2
Surface Tension g, s g = dW / dA N m-1, J m-2
weight G , (W , P ) G = mg N
Gravitational Constant G F = Gm1m2/r2 N m2 kg-2
normal stress s s = F / A Pa
shear stress t t = F / A Pa
linear strain, relative elongation e, e e = Dl/l 1
modulus of elasticity, Young's Modulus E E = s/e Pa
shear strain g g = Dx/d 1
shear modulus G G = t/g Pa
volume strain, bulk strain q q = DV/V0 1
bulk modulus, compression modulus K K = – V0(d p/d V) Pa
Viscosity, dynamic viscosity h, m tx,z = h(dvx/dz) Pa s
fluidity f f = 1/h m kg-1 s
Kinematic Viscosity n n = h/r m2 s-1
friction coefficient m, f Ffrict = mFnorm 1
Power P P = dW / dt W
sound energy flux P, Ps P = dE / dt W
acoustic reflection factor r P = Pt / P0 1
acoustic absorption factor as, a as = 1 – r 1
acoustic transmission factor t t = Ptr / P0 1
acoustic dissipation factor d d = as – t 1

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Electromagnetism
Name Symbol Definition SI Units
Electric Charge, quantity of electricity Q - C
charge density r r = Q / V C m-3
surface charge density s s = Q / A C m-2
Electric Potential V , f V = dW / dQ V, J C-1
electric potential difference U , DV , Df U = V 1 – V 2 V
Electromotive Force (emf) E E = ò F/Q • ds V
Electric Field Strength E E = F/Q = – grad V V m-1
electric flux Y Y = ò D • dA C
Electric Displacement D D = eE C m-2
Capacitance C C = Q/U F
Permittivity e D = eE F m-1
Permittivity of Vacuum e0 e0 = m0-1c0-2
= 8.854 187 817 ¼ ´ 10-12 F m-1 		F m-1
relative permittivity er er = e/e0 1
dielectric polarization, dipole moment per volume P P = D – e0E C m-2
electric susceptibility ce ce = er – 1 1
electric dipole moment p, m p = Q r C m
Electric Current I I = dQ/dt A
electric current density j, J I = ò j • dA A m-2
polarizability (of a particle) a - m2 C V-1
Magnetic Flux Density, magnetic induction B F = Q v ´ B T
Magnetic Flux F F = ò B • dA Wb
Magnetic Field Strength H B = mH A m-1
Permeability m B = mH H m-1, (N A-2)
Permeability of Vacuum m0 m0 = 4p ´ 10-7 H m-1 (N A-2)
= 12.566 370 614 ¼ ´ 10-7 H m-1 (N A-2) 		H m-1, (N A-2)
relative permeability mr mr = m/m0 1
magnetization, magnetic dipole moment per volume M M = B/m0 – H A m-1
magnetic susceptibility c, k, cm c = mr – 1 1
molar magnetic susceptibility cm cm = Vm c m3 mol-1
magnetic dipole moment m, m Ep = – m • B A m2, J T-1
Electrical Resistance R R = U / I W
Electrical Conductance G G = 1/R S
loss angle d d = (p/2) + fI – fU 1, rad
reactance X X = ( U / I ) sin d W
impedance, complex impedance Z Z = R + iX W
admittance, complex admittance Y Y = 1/Z S
suseptance B Y = G + iB S
Electrical Resistivity r r = E / j W m
Electrical Conductivity k, g, s k = 1/r S m-1, (W-1 m-1)
(self) Inductance L E = – L (dI /dt) H
mutual inductance M, L1 2 E1 = – L1 2 dI2/dt H
magnetic vector potential A B = Ñ ´ A Wb m-1
Poynting vector S S = E ´ H W m-2

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Quantum Mechanics
Name Symbol Definition SI Units
momentum operator pˆ pˆ = – ihÑ m-1 J s
(I, Fritz, N s, kg m s-1)
kinetic energy operator T ˆ T ˆ = – (h2/2m)Ñ2 J
hamiltonian operator Hˆ Hˆ = T ˆ + V J
wave function, state function Y, y, f Hˆy = Ey m-3/2
probability density P P = y*y m-3
charge density of electrons r r = – eP C m-3
probability current density S S = – ih(y*Ñy – yÑy*)/2me m-2 s-1
electric current, density of electrons j j = – eS A m-2
matrix elements of operator  Aij , ái |  | jñ Aij = ò yi*Âyj dt (varies)
expectation value of operator  á A ñ, A– á A ñ = ò y*Ây dt (varies)
hermitian conjugate of operator  † ( † )ij = ( Aji )* (varies)
commutator of  and Ê [Â, Ê], [Â, Ê]- [Â, Ê] = Â Ê – Ê Â (varies)
anticommutator of  and Ê [Â, Ê]+ [Â, Ê] = Â Ê + Ê Â (varies)
spin wavefunction a, b - 1
coulomb integral HAA HAA = ò yA*HˆyA dt J
resonance integral HAB HAB = ò yA*HˆyB dt J
overlap integral SAB SAB = ò yA*yB dt 1

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Atoms and Molecules
Name Symbol Definition SI Units
number of Entities
(atoms, molecules, ions, formula units …) 		N N = {1, 2, 3 … N , N + 1, N + 2, N + 3 …
2N … N 2 … N N … N N N … …} 		1
nucleon number, mass number A - 1
Proton number, atomic number Z - 1
Neutron number N N = A – Z 1
Electron Rest Mass me me = 9.109 381 88 (72) ´ 10-31 kg kg
mass of atom, atomic mass ma, m - kg
Atomic Mass Constant mu mu = ma(12C)/12 = 10-3 kg mol-1/NA
= 1.660 538 73 (13) ´ 10-27 kg = 1 Dalton (Da) 		kg
mass excess D D = ma – Amu kg
Elementary Charge, Proton Charge e e = 1.602 176 462 (63) ´ 10-19 C C
Planck Constant h h = 6.626 068 76 (52) ´ 10-34 J s (I m) J s (I m)
Reduced Planck Constant (h bar), Planck Constant/2p h = h/2p h = 1.054 571 596 (82) ´ 10-34 J s (I m) J s (I m)
Bohr Radius a0 a0 = a/4pR¥ = 4pe0h2/mee2
= 0.529 177 208 3 (19) ´ 10-10 m 		m
Hartree Energy Eh Eh = e2/4pe0a0 = 2R¥hc = a2mec2
= h2/mea02 = 4.359 743 81 (34) ´ 10-18 J 		J
Rydberg Constant R¥ R¥ = meca2/2h = Eh/2hc
= 10 973 731.568 549 (83) m-1 		m-1
Fine Structure Constant a a = m0ce2/2h = e2/2he0c
= 7.297 352 533 (27) ´ 10-3 		1
Inverse Fine Structure Constant a-1 a-1 = 2h/e2m0c = e0c2h/e2
= 137.035 999 76 (50) 		1
ionization energy Ei , I - J
electron affinity Eea - J
dissociation energy Ed, D - J
-- from ground state Do - J
-- from the potential minimum De - J
principal quantum number (Hydrogen atom) n E = – hcR/n2 1
Angular Momentum Quantum Numbers See Under Spectroscopy
magnetic dipole moment of a molecule m, m Ep = – m • B J T-1, A m2
magnetizability of a molecule x m = xB J T-2
Bohr Magneton mB mB = eh/2me
= 9.274 008 99 (37) ´ 10-24 J T-1 		J T-1
Nuclear Magneton mN mN = (me/mp)mB = eh/2mp
= 5.050 783 17 (20) ´ 10-27 J T-1 		J T-1
magnetogyric ratio, gyromagnetic ratio g g = m/L (L = angular momentum) s-1 T-1, C kg-1
g - factor g - 1
Larmor circular frequency wL wL = (e/2m)B s-1
Larmor frequency nL nL = wL/2p Hz
longitudinal relaxation time T1 - s
transverse relaxation time T2 - s
electric dipole moment of a molecule p, m Ep = – p • E C m
quadrupole moment of a molecule Q, Q Ep = ½Q : V ² = 1/3Q C m2
quadrapole moment of a nucleus eQ eQ = 2 á Qzz ñ C m2
electric field gradient tensor q qab = – 2V/ab V m-2
quadrapole interaction energy tensor c cab = eQqab J
electric polarizability of a molecule a p (induced) = aE C m2 V-1
activity (of a radioactive substance) A A = dNB/dt Bq
decay (rate) constant, disintegration (rate) constant l A = lNB s-1
half life t½, T½ - s
mean life t - s
level width G G = h/t J
disintegration energy Q - J
cross section (of a nuclear reaction) s - m2

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Statistical Mechanics
Name Symbol Definition SI Units
number of Entities
(atoms, molecules, ions, formula units …) 		N N = {1, 2, 3 … N , N + 1, N + 2, N + 3 …
2N … N 2 … N N … N N N … …} 		1
number density of Entities, number concentration n, C n = N /V m-3
Avogadro Constant, Avogadro's Number L, NA NA = 6.022 141 99 (47) ´ 1023 mol-1 mol-1
Boltzmann Constant k, kB R/NA = 1.380 650 3 (24) ´ 10-23 J K-1 J K-1
Molar Gas Constant R R = NAk = 8.314 472 (15) J K-1 mol-1 J K-1 mol-1
molecular position vector r (x, y, z) - m
molecular velocity vector c (cx, cy, cz),
u (ux, uy, uz) 		c = dr / dt (r•, r´) (r dot, r prime) m s-1
molecular momentum vector p (px, py, pz) p = m c I, N s, kg m s-1
velocity distribution function (Maxwell) f (cx) f (cx) = (m/2pkT )½
´ exp(– mcx2/2kT ) 		m-1 s
speed distribution function (Maxwell-Boltzmann) F (c) F (c) = (m/2pkT )3/2
´ 4pc2exp(– mc2/2kT ) 		m-1 s
average speed c˜, u˜, ácñ, áuñ c~ = ò c F(c) dc m s-1
generalized coordinate q - (m)
generalized momentum p p = L / q• (q dot) (I, N s, kg m s-1)
volume in phase space W W = (1/h)ò p dq 1
probability P - 1
statistical weight, degeneracy g, d, W , w, b - 1
density of (energy) states r(E) r(E) = dN / dE J-1
partition function, sum over states Symbol Definition SI Units
-- for a single molecule q, z q = åi gi exp( – ei/kT ) 1
-- for a canonical ensemble (system or assembly) Q , Z - 1
microcanonical ensemble W - 1
grand canonical ensemble X - 1
symmetry number s, s - 1
reciprocal temperature b b = 1/kT J-1
charateristic temperature Q - K

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Electromagnetic Radiation
Name Symbol Definition SI Units
Wavelength l - m
Speed of Light in vacuum c0 c0 = 299 792 458 m s-1 (exact) m s-1
Speed of Light in a medium c c = c0/n m s-1
Wavenumber in vacuum n˜ n˜ = n/c0 = 1/nl m-1
Wavenumber in a medium s, (k) s = 1/l m-1
Frequency n n = c/l Hz
circular frequency, pulsatance w w = 2pn s-1, rad s-1
refractive index n n = c0/c 1
Planck Constant h h = 6.626 068 76 (52) ´ 10-34 J s (I m) J s (I m)
Reduced Planck Constant h (Planck Constant/2p, h bar) h = h/2p = 1.054 571 596 (82) ´ 10-34 J s (I m) J s (I m)
radiant energy Q, W - J
radiant energy density r, w r = Q / V J m-3
spectral radiant energy density Symbol Definition SI Units
-- in terms of frequency rn, wn r = dr/dn J m-3 Hz-1
-- in terms of wavenumber rn˜, wn˜ r = dr/dn˜ J m-2
-- in terms of wavelength rl, wl r = dr/dl J m-4
Einstein transition probabilities Symbol Definition SI Units
-- spontaneous emission Anm dNn / dt = – Anm Nn s-1
-- stimulated emission Bnm dNn / dt = – rn˜ (n˜nm) ´ Bnm Nn s kg-1
-- stimulated absorption Bnm dNn / dt = rn˜ (n˜nm) ´ Bnm Nn s kg-1
radiant power, radiant energy per time F, P F = dQ/dt W
radiant intensity I I = dF/dW W sr-1
radiant exitance (emitted radiant flux) M M = dF/dAsource W m-2
irradiance E, (I ) E = dF/dA W m-2
emittance, emissivity e e = M / Mbb 1
Stefan-Boltzmann Constant s Mbb = sT 4 = (p2/60)k4/h3c2
= 5.670 400 (40) ´ 10-8 W m-2 K-4 		W m-2 K-4
First Radiation Constant c1 c1 = 2phc02 = 3.741 771 07 (93) ´ 10-16 W m2 W m2
Second Radiation Constant c2 c2 = hc0/k = 0.014 387 752 (25) m K m K
transmittance, transmission factor t, T t = Ftr/F0 1
absorptance, absorbtion factor a a = Fabs/F0 1
reflectance, reflection factor r r = Frefl/F0 1
(decadic) absorbance A A = – lg(1 – ai) 1
naperian absorbance B B = – ln(1 – ai) 1
absorption coefficients Symbol Definition SI Units
-- (linear) decadic a, K a = A/l m-1
-- (linear) naperian a a = B/l m-1
-- molar (decadic) e e = a/c = A/cl m2 mol-1
-- molar naperian k k = a/c = B/cl m2 mol-1
complex refractive index nˆ nˆ = n + ik 1
molar refraction R, Rm R = [(n2 – 1)/(n2 + 2)] ´ Vm m3 mol-1
angle of optical rotation a - 1, rad

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Spectroscopy
Name Symbol Definition SI Units
total term T T = Etot/hc m-1
transition wavenumber n˜, (n) n˜ = T ¢ – T ² m-1
transition frequency n n = (E¢ – E²)/h Hz
electronic term Te Te = Ee/hc m-1
vibrational term G G = Evib/hc m-1
rotational term F F = Erot/hc m-1
spin orbit coupling constant A Ts.o. = AáLˆ • Sˆñ m-1
principle moments of inertia IA ; IB ; IC IA £ IB £ IC kg m2
rotational constants (in wavenumbers) Ã ; B˜; C˜ Ã = h/8p2cIA m-1
rotational constants (in frequency) A, B, C A = h/8p2IA Hz
inertial defect D D = IC – IA – IB kg m2
asymmetry parameter k k = (2B – A – C)/(A – C) 1
centrifugal distortion constants Symbol Definition SI Units
-- S reduction DJ ; DJK ; DK ; d1; d2 - m-1
-- A reduction DJ ; DJK ; DK ; dJ ; dK - m-1
harmonic vibration number we, wr - m-1
vibrational anharmicity constant wexe ; xrs ; gn´ - m-1
vibrational quantum numbers ur ; lt - 1
Coriolis zeta constant zrsa - 1
Angular Momentum Quantum Numbers : see additional Information below
degeneracy, statistical weight g, d, b - 1
electric dipole moment of a molecule p, m Ep = – p • E C m
transition dipole moment of a molecule M, R M = ò y¢ p y² dt C m
molecular geometry, interatomic distances Symbol Definition SI Units
-- equilibrium distance re - m
-- zero-point average distance rx - m
-- ground state distance r0 - m
-- substitution structure distance rs - m
vibrational coordinates Symbol Definition SI Units
-- internal coordinates R i, ri, q j, etc. - (varies)
-- symmetry coordinates S i - (varies)
-- normal coordinates Symbol Definition SI Units
---- mass adjusted Q r - kg½ m
---- dimensionless qr - 1
vibrational force constants Symbol Definition SI Units
-- diatomic ƒ, (k) ƒ = 2V / r 2 J m-2
-- polyatomic Symbol Definition SI Units
---- internal coordinates ƒij ƒij = 2V / ri rj (varies)
---- symmetry coordinates Fij Fij = 2V / S i S j (varies)
---- dimensionless normal coordinates frst…, krst… - m-1
Nuclear Magnetic Resonance (NMR) Symbol Definition SI Units
-- magnetogyric ratio g g = m / I h s-1 T-1, C kg-1
-- shielding constant sA BA = (1 – sA) B 1
-- chemical shift, d scale d d = 106 (n – n0) / n0 1
-- (indirect) spin-spin coupling constant JAB Hˆ/ h = JAB Î A • Î B Hz
-- direct (dipolar) coupling constant DAB - Hz
longitudinal relaxation time T1 - s
transverse relaxation time T2 - s
Electron Spin Resonance (ESR)
Electron Paramagnetic Resonance (EPR) 		Symbol Definition SI Units
-- magnetogyric ratio g g = m / s h s-1 T-1, C kg-1
-- g factor g hn = gmBB 1
-- hyperfine coupling constant Symbol Definition SI Units
---- in liquids a, A Hˆhfs / h = a Sˆ• Î Hz
---- in solids T Hˆhfs / h = Sˆ• T • Î Hz

Angular Momentum Quantum Numbers
Angular Momentum Operator
Symbol 		Quantum Number Symbol
Total Z-axis z-axis
electron orbital Lˆ L ML L
-- one electron only lˆ l ml l
electron spin Sˆ S MS S
-- one electron only sˆ s ms s
electron orbital + spin Lˆ + Sˆ - - W = L + S
nuclear orbital (rotational) Rˆ R - KR , kR
nuclear spin Î I MI -
internal vibrational - - - -
-- spherical top lˆ l (lz) - Kl
-- other jˆ, pˆ - - l (lz)
sum of R + L (+ j) Nˆ N - K , k
sum of N + S Jˆ J MJ K , k
sum of J + I Fˆ F MF -

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Solid State Physics
Name Symbol Definition SI Units
lattice vector R, R0 - m
fundamental translation vectors for the crystal lattice a1; a2; a3,
a, b, c 		R = n1a1 + n2a2 + n3a3 m
(circular) reciprocal lattice vector G G • R = 2pm m-1
(circular) fundamental translation vectors of the reciprocal lattice b1; b2; b3,
a*; b*; c* 		ai • bk = 2pdik m-1
lattice plane spacing d - m
Bragg angle q nl = 2d sin q 1, rad
order of reflection n - 1
order parameters Symbol Definition SI Units
-- short range s - 1
-- long range s - 1
Burgers vector b - m
particle position vector r, R j - m
equilibrium position vector of an ion R0 - m
displacement vector of an ion u u = R – R0 m
Debye-Waller factor B, D - 1
Debye circular wavenumber qD - m-1
Debye circular frequency wD - s-1
Grüneisen parameter g, G g = aV/kCv 1
Madelung constant a, M Ecoul = aNAz+z–e2/4pe0pR0 1
density of states NE dN(E)/dE J-1 m-3
(spectral) density of vibrational modes Nw, g Nw = dN(w)/dw s m-3
resistivity tensor rik E = r • j W m
conductivity tensor sik s = r-1 S m-1, (W-1 m-1)
thermal conductivity tensor lik Jq = – l • grad T W m-1 K-1
residual resistivity rR - W m
relaxation time t t = l / vF s
Lorenz coefficient L L = l / sT V2 K-2
Hall coefficient AH, RH E = r • j + RH (B ´ j ) m3 C-1
Peltier coefficient P - V
Thomson coefficient m, (t) - V K-1
work function F F = E¥ – EF J
number density, number concentration n, (r) - m-3
gap energy Eg - J
donor ionization energy Ed - J
acceptor ionization energy Ea - J
Fermi energy EF, eF - J
Fermi temperature TF EF = kBTF K
circular wave vector, propogation vector k, q k = 2p/l m-1
Bloch function uk(r) y(r) = uk(r) exp(k • r) m-3/2
charge density of electrons r r(r) = – ey*(r)y(r) C m-3
effective mass m* - kg
mobility m m = vdrift / E m2 V-1 s-1
mobility ratio b b = mn/mp 1
diffusion coefficient D dN/dt = – D A(dn/dx) m2 s-1
diffusion length L L = (Dt)½ m
characteristic (Weiss) temperature q, qW - K
Curie temperature TC - K
Néel temperature TN - K
superconducting critical transition temperature Tc - K

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General Chemistry
Name Symbol Definition SI Units
number of Entities
(atoms, molecules, ions, formula units …) 		N N = {1, 2, 3 … N , N + 1, N + 2, N + 3 …
2N … N 2 … N N … N N N … …} 		1
amount of substance, chemical amount n nB = NB/L (L = Avogadro's Constant) mol
Avogadro Constant, Avogadro's Number L, NA L = 6.022 141 99 (47) ´ 1023 mol-1 mol-1
mass of atom, atomic mass ma, m - kg
mass of entity, molecule or formula unit mf , m - kg
Atomic Mass Constant mu mu = ma(12C)/12 = 10-3 kg mol-1/NA
= 1.660 538 73 (13) ´ 10-27 kg = 1 Dalton (Da) 		kg
Molar Mass M MB = m/nB kg mol-1
relative molecular mass, (relative molar mass, molecular weight) Mr Mr, B = mB/mu 1
relative atomic mass, (atomic weight) Ar Ar = ma/mu 1
Molar Volume Vm Vm, B = V / nB m3 mol-1
mass fraction w wB = mB / åi mi 1
volume fraction f fB = VB / åi Vi 1
mole fraction, amount fraction, number fraction x, y xB = nB / åi ni 1
(total) Pressure p, P - Pa
partial pressure of substance B pB pB = yB p Pa
mass concentration (Mass Density) g, r gB = mB / V kg m-3
number concentration, number density of Entities C, n CB = NB / V m-3
amount concentration (concentration of substance B) c, cB, [B] cB = nB / V mol m-3
solubility s sB = cB (saturated solution) mol m-3
molality (of a solute) m, (b) mB = nB/mA mol kg-1
surface concentration G GB = nB / A mol m-2
stoichiometric number n - 1
extent of reaction, advancement x Dx = nB/nB mol
degree of dissociation a - 1

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Thermodynamics
Name Symbol Definition SI Units
Heat q, Q - J
work w, W - J
internal Energy U DU = q + w J
enthalpy H H = U + pV J
thermodynamic Temperature T - K
Celsius Temperature q, t q / ºC = T / K – 273.15 ºC
Entropy S dS ³ dq/T J K-1
Helmholtz energy (Helmholtz function) A A = U – T S J
Gibbs energy (Gibbs function) G G = H – T S = U + p V – T S J
Massieu function J J = – A / T J K-1
Planck function Y Y = – G / T J K-1
Surface Tension g, s g = ( G / As )T , p J m-2, N m-1
molar quantity X X m X m = X / n (varies)
specific quantity X x x = X / m (varies)
pressure coefficient b b = (p / T )V Pa K-1
relative pressure coefficient a p a p = (1 / p)(p / T )V K-1
isothermal compressibility kT kT = – (1/V )( V / p )T Pa-1
isentropic compressibility kS kS = – (1/V )( V / p )S Pa-1
linear expansion coefficient al al = (1 / l )( l / T ) K-1
cubic expansion coefficient a, aV , g a = (1/V )(V / T ) p K-1
Heat Capacity (at constant pressure) Cp Cp = (H / T ) p J K-1
Heat Capacity (at constant volume) CV CV = (H / T )V J K-1
ratio of heat capacities g, (k) g = Cp / CV 1
Joule-Thomson coefficient m, mJT m = (T / p )H K Pa-1
second virial coefficient B pVm = RT (1 + B/Vm + …) m3 mol-1
compression factor (compressibility factor) Z Z = pVm / RT 1
partial molar quantity X XB, (X ¢B) XB = ( X / nB )T , p , n j ¹ B (varies)
chemical potential (partial molar Gibbs energy) m B = ( G / nB )T , p , n j ¹ B J mol-1
absolute activity l lB = exp(mB / RT ) 1
standard chemical potential mo, mo - J mol-1
standard partial molar enthalpy HBo HBo = mBo + T SBo J mol-1
standard partial molar entropy SBo SBo = – (mBo/ T ) p J mol-1 K-1
standard reaction Gibbs energy (function) Dr G o Dr G o = åB nBmBo J mol-1
affinity of reaction A, A A = ( G / x )T , p = – åB nBmB J mol-1
standard reaction enthalpy Dr H o Dr H o = åB nBHBo J mol-1
standard reaction entropy Dr S o Dr S o = åB nBSBo J mol-1 K-1
equilibrium constant K o, K K o = exp(Dr G o / RT ) 1
-- pressure basis Kp Kp = ÕB pBnB Pa Sn
-- concentration basis Kc Kc = ÕB cBnB (mol m-3) Sn
-- molality basis Km Km = ÕB mBnB (mol kg-1) Sn
fugacity f, p~ fB = lB limp ® 0 ( pB/lB)T Pa
fugacity coefficient f fB = fB / pB 1
activity and activity coefficient referenced to Raoult's law
-- (relative) activity a aB = exp[(mB – mB*) / RT] 1
-- activity coefficient f fB = aB / xB 1
activity and activity coefficient referenced to Henry's law
-- (relative) activity Symbol Definition SI Units
---- molality basis am am, B = exp[(mB – mBo) / RT ] 1
---- concentration basis ac ac, B = exp[(mB – mBo) / RT ] 1
---- mole fraction basis ax ax, B = exp[(mB – mBo) / RT ] 1
-- activity coefficient Symbol Definition SI Units
---- molality basis gm am, B = gm, B mB / mo 1
---- concentration basis gc ac, B = gc, B cB / co 1
---- mole fraction basis gx ax, B = gx, B xB 1
ionic strength Symbol Definition SI Units
-- molality basis I m, I I m = ½ åB mB zB2 mol kg-1
-- concentration basis I c, I I c = ½ åB cB zB2 mol m-3
osmotic coefficient Symbol Definition SI Units
-- molality basis fm fm = (mA* – mA) / ( RT MA å mB ) 1
-- mole fraction basis fx fx = (mA – mA*) / ( RT ln xA ) 1
osmotic opressure P P = cB RT (ideal dilute solution) Pa

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Thermodynamic Functions and Relations
Name Symbol Relation
amount of substance - i ni mol (mole), integer - n
mole fraction of substance - i xi xi = ni / å j n j
Volume V m3
Pressure p Pa (Pascal), N m-2
Temperature T K (Kelvin)
Energy U J (Joule), kg m2 s-2
Entropy S dS ³ dq/T (J/K)
Enthalpy H H = U + p V
Helmholtz energy A A = U – T S
Gibbs energy G G = U + p V – T S = H – T S
isobaric heat capacity Cp Cp = ( H / T ) p
isochoic heat capacity CV CV = ( U / T )V
isobaric expansivity a a = V -1 ( V / T ) p
isothermal compressibility kT kT = – V -1 ( V / p )T
isentropic compressibility kS kS = – V -1 ( V / p )S
- - Cp – CV = T a2 V / kT
- - kT – kS = T a2 V / Cp
Gibbs - Helmholtz equation - H = G – T ( G / T ) p
Maxwell relations - ( S / p )T = – ( V / T ) p
( S / V )T = – ( p / T )V
Joule - Thomson expansion mJT mJT = ( T / p )H = – [ V – T ( V / T ) p ] / Cp
Joule - Thomson expansion fJT fJT = ( H / p )T = V – T ( V / T ) p
partial molar quantity X i X i = ( X / n i )T , p , n j ¹ i
chemical potential mi mi = ( G / n i )T , p , n j ¹ i
perfect gas pg pV = å i n i RT
perfect gas pg mpg = mio + RT ln (xi p / po)
(Superscript o in above indicates standard state.)
fugacity fi fi = (xi p ) exp [mi – mipg / RT ]
activity coefficient gi gi = fi / xi fio
(Superscript o in above indicates standard state.)
Gibbs - Duhem relation - 0 = S dT – V d p + å i n i dmi

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Notation for Chemical and Physical Changes
Recommended Subscripts
(X = H , S , G , etc.)
Chemical Change Subscript Symbol
chemical reaction r Dr X
Formation from Elements f Df X
combustion c Dc X
melting, fusion (solid « liquid) fus Dfus X
vaporization, evaporation (liquid ® gas) vap Dvap X
sublimation (solid ® gas) sub Dsub X
phase transition trs Dtrs X
solution (of a solute in a solvent) sol Dsol X
mixing (of two fluids) mix Dmix X
dilution (of a solution) dil Ddil X
adsorption ads Dads X
displacement dpl Ddpl X
immersion imm Dimm X
atomization at Dat X

Recommended Superscripts
Chemical State Superscript
standard state o, o
pure substance *
infinite dilution ¥
ideal id
activated complex, transition state ‡
excess quantity E

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Chemical Kinetics
Name Symbol Definition SI Units
rate of change of quantity X X• X• = dX/dt (varies)
rate of conversion x• x• = dx/dt mol s-1
rate of concentration change of substance B (due to chemical reaction) rB, vB rB = dcB/dt mol m-3 s-1
rate of reaction (based on amount concentration) v v = x•/V = nB-1 dcB/dt mol m-3 s-1
partial order of reaction nB v = k ÕB cBnB 1
overall order of reaction n n = åB nB 1
rate constant, rate coefficient k v = k ÕB cBnB (m3 mol-1) n - 1 s-1
Boltzmann Constant k, kB kB = R/NA = 1.380 650 3 (24) ´ 10-23 J K-1 J K-1
half life t½ c(t½) = c0/2 s
relaxation time t t = 1/(k1 + k-1) s
energy of activation, activation energy Ea, E Ea = RT 2 d ln k/dT J mol-1
pre-exponential factor A k = A exp( – Ea/RT ) (m3 mol-1) n - 1 s-1
volume of activation D‡V D‡V = – RT ( ln k/ p)T m3 mol-1
collision diameter d dAB = rA + rB m
collision cross section s sAB = pdAB m2
collision frequency ZA - s-1
collision number ZAB, ZAA - m-3 s-1
collision frequency factor zAB, zAA zAB = ZAB/LcAcB m3 mol-1 s-1
standard enthalpy of activation D‡H o, DH ‡ - J mol-1
standard entropy of activation D‡S o, DS ‡ - J mol-1 K-1
standard Gibbs energy of activation D‡G o, DG ‡ - J mol-1
quantum yield, photochemical yield f - 1

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Electrochemistry
Name Symbol Definition SI Units
Elementary Charge, Proton Charge e e = 1.602 176 462 (63) ´ 10-19 C C
Faraday Constant F F = eL = 96 485.341 5 (39) C mol-1 C mol-1
charge number of an ion z zB = QB/e 1
ionic strength Symbol Definition SI Units
-- concentration basis I c, I I c = ½ åi ci zi2 mol m-3
-- molality basis I m, I I m = ½ åi mi zi2 mol kg-1
mean ionic activity a± a± = m± g± / mo 1
mean ionic molality m± m±n+ + n– = m+n+ m–n– mol kg-1
mean ionic activity coefficient g± g±n+ + n– = g+n+ g–n– 1
charge number of electrochemical cell reaction n, (z) - 1
electric potential difference (of a galvanic cell) DV , E, U DV = V R – V L V
Electromotive Force, emf, electrode potential E E = limI ® 0 DV V
standard emf, standard potential of the electrochemical cell reaction Eo Eo = – DrG o/nF = (RT/nF) ln K o V
standard electrode potential Eo - V
emf of the cell, potential of the electrochemical cell reaction E E = Eo – [(RT/nF) åi ni ln ai] V
pH pH pH » – lg [c(H +) / mol dm-3] 1
inner electric potential f Ñf = – E V
outer electric potential y y = Q/4pe0r V
surface electric potential c c = f – y V
Galvani potential difference Df Dfab = fb – fa V
Volta potential difference Dy Dyab = yb – ya V
electrochemical potential m~ m~Ba = ( G / nBa ) J mol-1
Electric Current I I = dQ/dt A
(electric) current density j j = I / A A m-2
(surface) charge density s s = Q / A C m-2
electrode reaction rate constant k kox = Ia / nFA Õi cini (varies)
mass transfer coefficient, diffusion rate constant kd kd, B = | vB | Il, B / nFcA m s-1
thickness of a diffusion layer d dB = DB / kd, B m
transfer coefficient (electrochemical) a ac = – (|v|RT/nF)( ln |Ic| / E ) 1
overpotential h h = EI – EI = 0 – I Ru V
electrokinetic potential (zeta potantial) z - V
Conductivity k, (s) k = j / E S m-1, (W-1 m-1)
conductivity cell constant Kcell Kcell = k R m-1
molar conductivity (of an electrolyte) L L = k / cB S m2 mol-1
ionic conductivity, molar conductivity of an ion l l = | zB | F uB S m2 mol-1
electric mobility u, (m) uB = vB / E m2 V-1 s-1
transport number t tB = jB / åi ji 1
reciprocal radius of ionic atmosphere k k = (2F 2I / eRT)½ m-1

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Surface Properties
Name Symbol Definition SI Units
specific surface area a, as, s a = A/m m2 kg-1
surface amount of B, adsorbed amount of B nBs, nBa - mol
surface excess of B nBs - mol
surface excess concentration of B GB, (GBs ) GB = nBs / A mol m-2
total excess surface concentration G , (G s ) G = åiGi mol m-2
area per molecule a, s aB = A/NBs m2
area per molecule in a filled monolayer am, sm am, B = A/Nm, B m2
surface coverage q q = NBs/Nm, B 1
contact angle q - 1, rad
film thickness t, h, d - m
thickness of (surface or interficial) layer t, d, t - m
Surface Tension, interficial tension g, s g = ( G / As )T , p N m-1, J m-2
film tension Sf Sf = 2gf N m-1
reciprocal thickness of the double layer k k = (2F 2Ic / eRT)½ m-1
average molar masses Symbol Definition SI Units
-- number-average Mn Mn = åi niMi / åi ni kg mol-1
-- mass-average Mm Mm = åi niMi2 / åi niMi kg mol-1
-- Z-average MZ MZ = åi niMi3 / åi niMi2 kg mol-1
sedimentation coefficient s s = v/a s
van der Waals constant l - J
retarded van der Waals constant b, B - J
van der Waals - Hamaker constant AH - J
surface pressure ps, p ps = g 0 – g N m-1

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Transport Properties
Name Symbol Definition SI Units
flux (of a quantity X ) JX, J JX = A-1 dX/dt (varies)
volume flow rate qV, V• qv = dV/dt m3 s-1
mass flow rate qm, m• qm = dm/dt kg s-1
mass transfer coefficient kd - m s-1
heat flow rate f f = dq/dt W
heat flux Jq Jq = f / A W m-2
thermal conductance G G = f / DT W K-1
thermal resistance R R = 1/G K W-1
thermal conductivity l, k l = Jq / (dT / dl) W m-1 K-1
coefficient of heat transfer h, (k, K, a) h = Jq / DT W m-2 K-1
thermal diffusivity a a = l / rcp m2 s-1
diffusion coefficient D D = Jn / (dc/dl) m2 s-1

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The following symbols are used in the definition of the Dimensionless Quantities :

Mass (m), Time (t), Length ( l ), Area (A), Volume (V ), Density (r), Speed (v), Viscosity (h), Pressure (p), Temperature (T ), Surface Tension (g), Acceleration of Free Fall (g), Speed of Sound (c), Mean Free Path (l), Frequency ( f ), Specific Heat Capacity at Constant Pressure (Cp), Cubic Expansion Coefficient (a), Mole Fraction (x), Permeability (m), Electrical Conductivity (k), Magnetic Flux Density (B), Thermal Conductivity (k), Thermal Diffusivity (a), Diffusion Coefficient (D), Coefficient of Heat Transfer (h), and Mass Transfer Coefficient (kd).

Dimensionless Quantities
Name Symbol Definition SI Units
Reynolds number Re Re = rvl/h 1
Euler number Eu Eu = D p/rv2 1
Froude number Fr Fr = v/(lg)½ 1
Grashof number Gr Gr = l 3gaDT r2/h2 1
Weber number We We = rv2l/g 1
Mach number Ma Ma = v/c 1
Knudsen number Kn Kn = l/l 1
Strouhal number Sr Sr = l f /v 1
Fourier number Fo Fo = at/l 2 1
Péclet number Pe Pe = vl/a 1
Rayleigh number Ra Ra = l 3gaDT r/ha 1
Nusselt number Nu Nu = hl / k 1
Stanton number St St = h/rvcp 1
Fourier number for mass transfer Fo* Fo* = Dt/l 2 1
Grashof number for mass transfer Gr* Gr* = l 3g(r / x)T, p (Dxr / h) 1
Péclet number for mass transfer Pe* Pe* = vl / D 1
Nusselt number for mass transfer Nu* Nu* = kd l / D 1
Stanton number for mass transfer St* St* = kd / v 1
Prandtl number Pr Pr = h/ra 1
Schmidt number Sc Sc = h/rD 1
Lewis number Le Le = a/D 1
Magnetic Reynolds number Rm, Rem Rm = vmk l 1
Alfvén number Al Al = v(r m)½ / B 1
Hartmann number Ha Ha = B l (k h)½ / B 1
Cowling number Co Co = B 2/mrv2 1

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Character Map Symbol Fonts
Greek Alphabet Metric Prefixes
Electromagnetic Spectrum Microwave Bands
SI International System of Units Fundamental Physical Constants
SI Defined Units SI Derived Units SI Accepted Units SI Derived Quantities
Earth Constants Universal Constants Planck Constants Electromagnetic Constants
Bohr Magneton Nuclear Magneton Fine Structure Constant Rydberg Constant
Physical Constants Chemical Constants Boltzmann Constant Physicochemical Constants
Electron Constants Proton Constants Neutron Constants Deuteron Constants
Energy Equivalence Factors Energy Conversion Factors
Energy Equivalence I Energy Equivalence II Energy Equivalence III Energy Equivalence IV
Energy Conversion I Energy Conversion II Energy Conversion III Energy Conversion IV
Natural Units (n.u.) Atomic Units (a.u.)
Other (SI Derived) Units

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Space and Time Classical Mechanics
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Spectroscopy
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Thermodynamic Functions and Relations
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