Physical Constants
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Fundamental Constants_____________________________________________________________________________________________
------------------------------------------------------------------------------------------------------ c 2.99792458E+08 m / s speed of light* h 6.62606876E-34 J s Planck constant 4.13566727E-15 eV s hbar 1.054571596E-34 J s h/(2*Pi) 6.58211889E-16 eV s k 1.3806503E-23 J / K Boltzmann constant (R/NA) 8.617342E-05 eV / K 1.9872065 cal mol ^-1 K ^-1 Na 6.022140857E+23 mol ^-1 Avogadro's number R 8.314472 J mol ^-1 K ^-1 molar gas constant (NA*k) g 9.80665 m s ^-2 standard gravity cal 4.184 J calorie* eV 1.602176462E-19 J electron volt Eh 4.35974381E-18 J Hartree energy a0 0.5291772083E-10 m Bohr radius A 1.8897261339 a0 angstrom e 1.602176462E-19 C elementary charge (in Coulombs) e0 8.854187817..E-12 C ^2 J ^-1 m^-1 vacuum permittivity* (u0 ^-1 c^-2) u0 4 * Pi E -07 N s ^2 C ^-2 vacuum permeability* 12.56637061..E-07 N s ^2 C ^-2 F 96485.3415 C / mol Faraday constant (NA*e) uB 9.27400899E-24 J / T Bohr magneton uN 5.05078317E-27 J / T nuclear magneton ge 2.0023193043737 electron g-value u 1.66053873E-27 kg atomic mass unit me 9.10938188E-31 kg electron mass mp 1.67262158E-27 kg proton mass mn 1.67492716E-27 kg neutron mass mu 1.88353109E-28 kg muon mass Pi 3.14159265358979.. pi constant e 2.71828182845905.. natural log base------------------------------------------------------------------------------------------------------ *exact value Source: physics.nist.gov/constants; 1998
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Nuclear Magnetogyric Ratios__________________________________________________________________________________
-------------------------------------------------------- spin gamma natural nuclei (I) (rad/sec-G) abundance (%) -------------------------------------------------------- photon 1 pion 0 electron 1/2 neutron 1/2 -18320.0 1H* 1/2 26752.2128 99.985 2H* 1 4106.62791 0.015 3H 1/2 28534.9779 0 3He 1/2 ~0 4He 0 ~100 12C 0 98.93 13C* 1/2 6728.284 1.07 14N 1 1933.7792 99.63 15N* 1/2 -2712.61804 0.37 16O 0 99.76 17O 5/2 -3628. 0.038 18O 0 0.205 19F* 1/2 25181.48 100 31P* 1/2 10839.4 100 35Cl 3/2 75.78 37Cl 3/2 24.22 -------------------------------------------------------- *nuclei commonly used in biological NMR
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Unit Conversions__________________________________________________________________________________
-------------------------------------------------------------------------------- 1 N = 1 kg m s^-2 Newton force 1 J = 1 N m Joule energy 1 W = 1 J / s watt power 1 V = 1 J / C volt electrostatic potential 1 A = 1 C / s Ampere current 1 OMEGA = 1 V / A ohm resistance 1 F = 1 C / V Farad capacitance 1 T = 1 N A^-1 m^-1 Tesla magnetic field strength = 1E+4 G 1 G = 1E-4 T Gauss magnetic field strength
1 A = 1E-10 m angstrom length 1 u = 1E-6 m micron ( um ) length 1 L = 1E-3 m^3 liter volume 1 erg = 1E-7 J erg energy 1 dyn = 1E-5 N dyne force 1 Pa = 1 N m^-2 Pascal pressure 1 bar = 1E5 Pa bar pressure = 0.986923 atm* 1 atm = 101.325 kPa* atm pressure = 760 Torr 1 Torr = 1/760 atm Torr ( mmHg ) pressure 1 D = 3.33564E-30 C m Debye dipole moment 1 p = 1E-1 N s m^-2 Poise viscosity 1 eu = 1 cal mol^-1 K^-1 entropy unit entropy -------------------------------------------------------------------------------- *exact value
------------------------------------------------------ ---------------------- Useful Relations ----------------------------------------------------------------------------
Capacitance: C = Q / V Ohm's law: V = I * R Joule heating law: P = V * I E = h v = h c / lambda lambda = c / v ~v = 1 / lambda ( cm ^-1 ) hc = 1239.841856 eV nm ~ 1240. eV nm Celsius temp* ( from Kelvin ): T ( degr C ) = T ( K ) - 273.15 ---------------------------------------------------------------------------- *exact value
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The Electromagnetic Spectrum__________________________________________________________________________________
-------------------------------------------------------------------------------------------- v ( Hz ) Region E = h v E (kcal/mol) Type of transition excited -------------------------------------------------------------------------------------------- 10^21 Gamma rays 4.1 MeV -- nuclear 10^18 X-rays 4.1 keV -- bond breaking/ionization 10^16 Ultraviolet 41 eV 945 electronic 5*10^14 Visible 2.1 eV 48 electronic 10^13 Infrared 41 meV 0.95 vibrational 10^11 Microwave 0.41 meV 0.01 rotational 10^6 Radio 4.1 neV -- -- --------------------------------------------------------------------------------------------
Fundamental Constants_____________________________________________________________________________________________
------------------------------------------------------------------------------------------------------ c 2.99792458E+08 m / s speed of light* h 6.62606876E-34 J s Planck constant 4.13566727E-15 eV s hbar 1.054571596E-34 J s h/(2*Pi) 6.58211889E-16 eV s k 1.3806503E-23 J / K Boltzmann constant (R/NA) 8.617342E-05 eV / K 1.9872065 cal mol ^-1 K ^-1 Na 6.022140857E+23 mol ^-1 Avogadro's number R 8.314472 J mol ^-1 K ^-1 molar gas constant (NA*k) g 9.80665 m s ^-2 standard gravity cal 4.184 J calorie* eV 1.602176462E-19 J electron volt Eh 4.35974381E-18 J Hartree energy a0 0.5291772083E-10 m Bohr radius A 1.8897261339 a0 angstrom e 1.602176462E-19 C elementary charge (in Coulombs) e0 8.854187817..E-12 C ^2 J ^-1 m^-1 vacuum permittivity* (u0 ^-1 c^-2) u0 4 * Pi E -07 N s ^2 C ^-2 vacuum permeability* 12.56637061..E-07 N s ^2 C ^-2 F 96485.3415 C / mol Faraday constant (NA*e) uB 9.27400899E-24 J / T Bohr magneton uN 5.05078317E-27 J / T nuclear magneton ge 2.0023193043737 electron g-value u 1.66053873E-27 kg atomic mass unit me 9.10938188E-31 kg electron mass mp 1.67262158E-27 kg proton mass mn 1.67492716E-27 kg neutron mass mu 1.88353109E-28 kg muon mass Pi 3.14159265358979.. pi constant e 2.71828182845905.. natural log base------------------------------------------------------------------------------------------------------ *exact value Source: physics.nist.gov/constants; 1998
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Nuclear Magnetogyric Ratios__________________________________________________________________________________
-------------------------------------------------------- spin gamma natural nuclei (I) (rad/sec-G) abundance (%) -------------------------------------------------------- photon 1 pion 0 electron 1/2 neutron 1/2 -18320.0 1H* 1/2 26752.2128 99.985 2H* 1 4106.62791 0.015 3H 1/2 28534.9779 0 3He 1/2 ~0 4He 0 ~100 12C 0 98.93 13C* 1/2 6728.284 1.07 14N 1 1933.7792 99.63 15N* 1/2 -2712.61804 0.37 16O 0 99.76 17O 5/2 -3628. 0.038 18O 0 0.205 19F* 1/2 25181.48 100 31P* 1/2 10839.4 100 35Cl 3/2 75.78 37Cl 3/2 24.22 -------------------------------------------------------- *nuclei commonly used in biological NMR
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Unit Conversions__________________________________________________________________________________
-------------------------------------------------------------------------------- 1 N = 1 kg m s^-2 Newton force 1 J = 1 N m Joule energy 1 W = 1 J / s watt power 1 V = 1 J / C volt electrostatic potential 1 A = 1 C / s Ampere current 1 OMEGA = 1 V / A ohm resistance 1 F = 1 C / V Farad capacitance 1 T = 1 N A^-1 m^-1 Tesla magnetic field strength = 1E+4 G 1 G = 1E-4 T Gauss magnetic field strength
1 A = 1E-10 m angstrom length 1 u = 1E-6 m micron ( um ) length 1 L = 1E-3 m^3 liter volume 1 erg = 1E-7 J erg energy 1 dyn = 1E-5 N dyne force 1 Pa = 1 N m^-2 Pascal pressure 1 bar = 1E5 Pa bar pressure = 0.986923 atm* 1 atm = 101.325 kPa* atm pressure = 760 Torr 1 Torr = 1/760 atm Torr ( mmHg ) pressure 1 D = 3.33564E-30 C m Debye dipole moment 1 p = 1E-1 N s m^-2 Poise viscosity 1 eu = 1 cal mol^-1 K^-1 entropy unit entropy -------------------------------------------------------------------------------- *exact value
------------------------------------------------------ ---------------------- Useful Relations ----------------------------------------------------------------------------
Capacitance: C = Q / V Ohm's law: V = I * R Joule heating law: P = V * I E = h v = h c / lambda lambda = c / v ~v = 1 / lambda ( cm ^-1 ) hc = 1239.841856 eV nm ~ 1240. eV nm Celsius temp* ( from Kelvin ): T ( degr C ) = T ( K ) - 273.15 ---------------------------------------------------------------------------- *exact value
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The Electromagnetic Spectrum__________________________________________________________________________________
-------------------------------------------------------------------------------------------- v ( Hz ) Region E = h v E (kcal/mol) Type of transition excited -------------------------------------------------------------------------------------------- 10^21 Gamma rays 4.1 MeV -- nuclear 10^18 X-rays 4.1 keV -- bond breaking/ionization 10^16 Ultraviolet 41 eV 945 electronic 5*10^14 Visible 2.1 eV 48 electronic 10^13 Infrared 41 meV 0.95 vibrational 10^11 Microwave 0.41 meV 0.01 rotational 10^6 Radio 4.1 neV -- -- --------------------------------------------------------------------------------------------