Constants and conversion factors useful in
nanotechnology
The following constants and conversion factors are useful
in calculations about
molecular manufacturing
systems and various applications of such systems. In general,
SI units are preferred in nanotechnology.
This page is provided as is, with no warranty expressed or implied. It might
have typppographical erors, etc.
Other web pages on constants, units, and conversion factors:
Yahoo has links to web pages of constants and units.
The National Institute of Standards and Technology (NIST) has a page on the fundamental physical constants, a page on SI units, and a page with chemistry
data for chemical species.
Tech Expo has a page on fundamental constants
Various astronomical constants.
Conversion of units.
Conversion of units.
Yahoo
links to web pages that convert units.
Note that the absence of Greek letters on the web means some of the following
symbols aren't quite right. Superscripts are prefixed with "^" to insure they
can be interpreted correctly even if your browser does not support superscripts.
SI prefixes:
- Y: 10^24 yotta
- Z: 10^21 zetta
- E: 10^18 exa
- P: 10^15 peta
- T: 10^12 tera
- G: 10^9 giga
- M: 10^6 mega
- k: 10^3 kilo
- h: 10^2 hecto
- da: 10^1 deka
- d: 10^-1 deci
- c: 10^-2 centi
- m: 10^-3 milli
- mu: 10^-6 micro
- n: 10^-9 nano
- p: 10^-12 pico
- f: 10^-15 femto
- a: 10^-18 atto
- z: 10^-21 zepto
- y: 10^-24 yocto
Fundamental units:
- m: meters (length)
- kg: kilogram (mass)
- s: seconds (time)
- A: ampere (electric current)
- K: kelvin (thermodynamic temperature)
- mol: mole (amount of substance)
- cd: candela (luminous intensity)
Derived units:
- J: joules (work, energy, heat) N*m, Kg*m^2/s^2
- N: newton, (force) kg*m/(s^2)
- Pa: pascal, (pressure, stress) N/m^2
- W: watt, (power) J/s
- C: coulomb, (electric charge) A*s
- V: volt (electric potential, emf) J/C, W/A
- Greek omega: ohm (resistance) V/A
- S: siemens (conductance) A/V
- Wb: weber (magnetic flux) V*s
- H: henry (inductance) Wb/A
- F: farad (capacitance) C/V
- T: Tesla (magnetic flux density) Wb/m^2, N/(A*m)
- Bq: becquerel (radioactivity) 1/s
Constants:
- c: 299,792,458 m/s; speed of light in vacuum[1]
- mu0: 12.566 370 614... x 10^-7 N/A^2; Permeability
of vacuum[1]
- e0: 8.854 187 817 x 10^-12 F/m, or 1/(mu0 * c^2);
permittivity of vacuum[1]
- G: 6.672 59 x 10^-11 m^3/(kg*s^2); Newtonian
constant of gravitation[1]
- h: 6.626 075 5 x 10^-34 J*s; Planck's constant[1]
- e: 1.602 176 565 x 10^-19 C; elementary charge on proton, electron[http://physics.nist.gov/cgi-bin/cuu/Value?e]
- a0: 0.529 177 249 x 10^-10 m; Bohr radius [1]
- Eh: 4.359 748 2 x 10^-18 J; Hartree (energy)[1]
- me: 9.109 389 7 x 10^-31 kg; mass of the electron[1]
- mp: 1.672 623 1 x 10^-27 kg; mass of the proton[1]
- mn: 1.674 928 6 x 10^-27 kg; mass of the neutron[1]
- NA: 6.022 141 29 x 10^23 mol^-1; Avogadro's
number [http://physics.nist.gov/cgi-bin/cuu/Value?na]
- mu: 1.660 540 2 x 10^-27 kg; atomic mass constant, amu[1]
- R: 8.314 510 J/(mol*K); molar gas constant[1]
- k: 1.380 658 x 10^-23 J/K; Boltzmann's constant R/NA[1]
- Vm: 0.022 414 10 m^3/mol; molar volume of ideal gas,
R*T/p at 273.15 K, 101,325 Pa[1]
- Volume occupied by one gas molecule at STP: ~37.22 nm^3 (Vm
/ NA)
- lattice spacing of diamond (300 K): 0.356 683 nm[5]
- lattice spacing of silicon (300 K): 0.543 095 nm[5]
- lattice spacing of germanium (300 K): 0.564 613 nm[5]
- lattice spacing of grey tin (300 K): 0.648 920 nm[5]
- C-C bond length in diamond: 0.154 448 nm it's the lattice spacing * sqrt(3)/4
- Number of carbon atoms/nm3 of diamond: 176
- C-C bond length in graphite: 0.142 nm [9]
- 1-3 distance in graphite: 0.246 nm; C-C bond length * sqrt(3)
- density of carbon atoms in a monoatomic sheet of graphite: 38.2 atoms/nm2;
4/( (C-C bond length)2*3*sqrt(3)))
(or 38.5 atoms/nm2 from [10])
- Number of carbon atoms/nm3 of graphite: 114
- Distance between adjacent sheets in graphite: 0.335 nm [9]
- Basal surface energy of graphite: 0.234 J/m2 [9]
- bandgap of diamond: 5.47 eV[5]
- bandgap of silicon: 1.12 eV[5]
- mobility of electron in diamond: 1800 cm^2/(V*s)[5]
- mobility of electron in silicon: 1500 cm^2/(V*s)[5]
- gn: 9.806 65 m/s^2; acceleration of gravity[1]
- Solar constant: 1,367.5 W/m^2; number of watts in sunlight near
Earth's orbit, variable with Earth's distance from the sun and solar activity[8]
- Solar output: 3.87 x 10^26 W (computed from solar constant)[3]
- Typical power consumption of a human being: ~100 W
- Energy used by the United States in 1990: 8.6 x 10^19 J[6]
- Energy used per person per year in the US in 1990: 3.5 x 10^11
J[6]
- Power used per person in the US in 1990: 11,000 W (computed from above)
- Energy used by the world in 1990: 1.4 x 10^20 J[6]
- Power consumption of the world in 1990: 4.4 x 10^12 W (computed
from above)
- Energy used per person per year in the world in 1990: 2.7 x 10^10
J[6]
- Power used per person in the world in 1990: 850 W (computed from above)
- Total world population in 1990: 5.3 x 10^9 [6]
- Earth's equatorial radius: 6,378,160 m [3]
- Earth's surface area (4 pi r^2, r from above): 5.1 x 10^14
m^2
- Solar power intercepted by the Earth: 1.74 x 10^17 W (derived
from above)
- Earth's mass: 5.975 x 10^24 kg[3]
- Earth's distance from sun (average): 1.5 x 10^11 m[3]
- Fraction of nitrogen in Earth's atmosphere (by volume): 0.780 84[3]
- Fraction of oxygen in Earth's atmosphere (by volume): 0.209 46[3]
- Fraction of water in Earth's atmosphere: variable. Arctic air might have
0.01% water by weight while tropical air might have 3%.
- Fraction of argon in Earth's atmosphere (by volume): 0.00934[3]
- Fraction of CO2 in Earth's atmosphere (by volume): 0.00031[3]
- More information about the earth
- Stiffness of carbon-carbon single bond: 440 N/m[4]
- Energy required to break carbon-carbon single bond: 0.556 aJ[4]
- Young's modulus of diamond: 1.05 x 10^12 Pa
- Strength of diamond: 5 x 10^10 Pa (an underestimate)[4]
- Density of diamond: 3500 kg/m^3[4]
A few useful conversion factors:
- one atmosphere (atm) is 101,325 Pa[1]
- one calorie (cal) is 4.184 J[2]
- one joule (J) is 0.0002390057361 kcal (derived from above)
- one joule is (J) 1.439325215 x 10^20 kcal/mole (derived from
above)
- one eV is 96.48533646 kJ/mol (derived from above)
- one kcal/mole is 6.947700141 x 10^-21 J (derived from above)
- one Hartree is 627.5095 Kcal/mol is 27.2116 eV is 4.3597482 x 10^-18
J[2]
- one electron volt (eV) is 1.602 176 565 x 10^-19 J[http://physics.nist.gov/cgi-bin/cuu/Value?e]
- 1,000 kg of crude oil is about 7.3 barrels
- one barrel is 158.9873 liters [7]
References:
1. The Fundamental Physical Constants, by E. Richard
Cohen and Barry N. Taylor, Physics Today, August 1995,
page BG9.
2. Exploring Chemistry with Electronic Structure Methods:
a guide to using Gaussian, by James B. Foresman and Aeleen Frish,
1993.
3. McGraw-Hill Concise Encyclopedia of Science & Technology,
Sybil P. Parker, Editor in Chief, 1982.
4. Nanosystems: molecular machinery, manufacturing, and computation
by K. Eric Drexler, Wiley 1992.
5. Physics of Semiconductor Devices 2nd edition, S. M. Sze,
Wiley 1981.
6. The Universal Almanac, 1993, John W. Wright,
published by Andrews and McMeel.
7. Http://www.chemie.fu-berlin.de/chemistry/general/units_en.html.
8. Science, September 26 1997, Vol. 277, No. 5334, pp 1963-1965;
Total solar irradiance trend during solar cycles 21 and 22.
9. Physics of Graphite, 1981, B.T. Kelly, Applied Science
Publishers.
10. Scientific Background on the Nobel Prize in Physics 2010: GRAPHENE