Friday, February 25, 2011

Round-Number Handbook of Physics for Medicine and Biology

The 4th edition of Intermediate Physics for Medicine and Biology contains a list of fundamental constants in Appendix O. Russ Hobbie and I got the values of these constants from a 2002 study, but the National Institute of Science and Technology (NIST) website we cite no longer exists. A new NIST website,, gives the most up-to-date values for these constants, often including many significant figures.

For some applications, knowing the electron mass to, say, nine significant figures is important. But in biology and medicine, most quantities are not known with such precision. If a number is known to one percent, that is impressive. When I teach biological and medical physics, I would much rather see my students have an approximate feel for the size of important constants, without having them bother to memorize more than one or two significant figures. To know that the speed of light is 299,792,458 m/s is nice, but what I really want them to remember (forever!) is that the speed of light is about 3 × 108 m/s. If they need more precision, they can look it up.

Edward Purcell, one of the great ones, published his “Round-Number Handbook of Physics” in the January 1983 issue of the American Journal of Physics. He presented a list of important physical constants, but only to one or two significant figures. It was meant not as a reference to look up precise values, but as a list of approximate values that every physicist should know without needing to consult a reference. Unfortunately, Purcell used cgs units, which are becoming more and more obsolete.

Below I present my version of a “Round-Number Handbook of Physics for Medicine and Biology”. I take the constants from Appendix O and approximate them as round numbers in (mostly) mks units. These are the numbers you should remember.

cSpeed of light3 × 108 m/s
eElementary charge1.6 × 10-19 C
FFaraday constant105 C/mole
gAcceleration of gravity10 m/s2
hPlanck’s constant2π × 10-34 J s
Planck’s constant (reduced)10-34 J s
kBBoltzmann’s constant1.4 × 10-23 J/K
meElectron mass9 × 10-31 kg
mec2Electron rest energy0.5 MeV
mpProton mass1.7 × 10-27 kg
mpc2Proton rest energy1000 MeV
NAAvogadro’s number6 × 1023 1/mole
reClassical radius of the electron3 × 10-15 m
RGas constant8 J/(mole K)

2 cal/(mole °C)
ε0Electrical permittivity9 × 10-12 F/m
1/4πε0Coulomb’s law constant9 × 109 N m2/C2
σSB Stefan Boltzmann constant 6 × 10-8 W/(m2 K4)
λCCompton wavelength of the electron2.4 pm
μBBohr magneton10-23 J/T
μ0Magnetic permeability4π × 10-7 H/m
μNNuclear magneton5 × 10-27 J/T

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