[x] Close ad

PHYSICAL CONSTANTS

In science, a physical constant is a physical quantity whose value does not change. It can be contrasted with a mathematical constant, which is a fixed value that does not directly involve a physical measurement. Contrary to wide belief, physical constants do not depend on systems of units.

Contents

Examples

There are many physical constants in science, some of the most famous being the reduced Planck constant ħ, the gravitational constant G, the speed of light c, the electric constant ε0, and the elementary charge e. Constants can take many forms: the speed of light in a vacuum signifies a maximum speed limit of the universe; while the fine-structure constant α, which characterizes the interaction between electrons and photons, is dimensionless.

Fundamental Constants

Fundamental physical constants, are basic properties of nature, not depending on our culture. Another civilisation in another Galaxy would find the same values for those constants. All examples above are considered fundamental physical constants, whereas the length of the Eiffel tower or the earth's acceleration constant g are not fundamental. While some properties of materials and particles are constant, they do not show up on this page because they are specific to their respective materials or properties alone.

How constant are constants?

Beginning with Paul Dirac in 1937, some scientists have speculated that physical constants may actually decrease in proportion to the age of the universe. Scientific experiments have not yet pinpointed any definite evidence that this is the case, although they have placed upper bounds on the maximum possible relative change per year at very small amounts (roughly 10-5 per year for the fine structure constant α and 10-11 for the gravitational constant G). It is currently disputed [1] [2] that any changes in dimensionful physical constants such as G, c, ħ, or ε0 are operationally meaningless; however, a change in a dimensionless constant such as α is something that would definitely be noticed. If a measurement indicated that a dimensionful physical constant had changed, this would be the result or interpretation of a more fundamental dimensionless constant changing, which is the salient metric.

Anthroposiphic principle

Some people claim that if the physical constants had slightly different values, our universe would be so radically different that intelligent life would probably not have emerged, and that our universe therefore seems to be fine-tuned for intelligent life. The weak anthropic principle simply states that it's only because these fundamental constants acquired their respective values that there was sufficient order and richness in elemental diversity for life to have formed, which subsequently evolved the necessary intelligence toward observing that these constants have taken on the values they have.

Table of universal constants

Quantity Symbol Value Relative Standard Uncertainty
characteristic impedance of vacuum Z_0 = \mu_0 c \, 376.730 313 461... Ω defined
electric constant (permittivity of free space) \epsilon_0 = 1 / ( \mu_0 c^2 )\, 8.854 187 817... × 10-12F·m-1 defined
magnetic constant (permeability of free space) \mu_0 \, 4π × 10-7 N·A-2 = 1.2566 370 614... × 10-6 N·A-2 defined
Newtonian constant of gravitation G \, 6.6742(10) × 10-11m3·kg-1·s-2 1.5 × 10-4
Planck's constant h \, 6.626 0693(11) × 10-34 J·s 1.7 × 10-7
Dirac's constant \hbar = h / (2 \pi) 1.054 571 68(18) × 10-34 J·s 1.7 × 10-7
speed of light in vacuum c \, 299 792 458 m·s-1 defined

Table of electromagnetic constants

Quantity Symbol Value1 (SI units) Relative Standard Uncertainty
Bohr magneton \mu_B = e \hbar / 2 m_e 927.400 949(80) × 10-26 J·T-1 8.6 × 10-8
conductance quantum G_0 = 2 e^2 / h \, 7.748 091 733(26) × 10-5 S 3.3 × 10-9
Coulomb's constant \kappa = 1 / 4\pi\epsilon_0 \, 8.987 742 438 × 109 N·m2C-2 defined
elementary charge e \, 1.602 176 53(14) × 10-19 C 8.5 × 10-8
Josephson constant K_J = 2 e / h \, 483 597.879(41) × 109 Hz· V-1 8.5 × 10-8
magnetic flux quantum \phi_0 = h / 2 e \, 2.067 833 72(18) × 10-15 Wb 8.5 × 10-8
nuclear magneton \mu_N = e \hbar / 2 m_p 5.050 783 43(43) × 10-27 J·T-1 8.6 × 10-8
resistance quantum R_0 = h / 2 e^2 \, 12 906.403 725(43) Ω 3.3 × 10-9
von Klitzing constant R_K = h / e^2 \, 25 812.807 449(86) Ω 3.3 × 10-9

Table of atomic and nuclear constants

Quantity Symbol Value1 (SI units) Relative Standard Uncertainty
Bohr radius a_0 = \alpha / 4 \pi R_\infin \, 0.529 177 2108(18) × 10-10 m 3.3 × 10-9
Fermi coupling constant G_F / (\hbar c)^3 1.166 39(1) × 10-5 GeV-2 8.6 × 10-6
fine-structure constant \alpha = \mu_0 e^2 c / (2 h) = e^2 / (4 \pi \epsilon_0 \hbar c) \, 7.297 352 568(24) × 10-3 3.3 × 10-9
Hartree energy E_h = 2 R_\infin h c \, 4.359 744 17(75) × 10-18 J 1.7 × 10-7
quantum of circulation h / 2 m_e \, 3.636 947 550(24) × 10-4 m2 s-1 6.7 × 10-9
Rydberg constant R_\infin = \alpha^2 m_e c / 2 h \, 10 973 731.568 525(73) m-1 6.6 × 10-12
Thomson cross section (8 \pi / 3)r_e^2 0.665 245 873(13) × 10-28 m2 2.0 × 10-8
weak mixing angle \sin^2 \theta_W = 1 - (m_W / m_Z)^2 \, 0.222 15(76) 3.4 × 10-3

Table of physico-chemical constants

Quantity Symbol Value1 (SI units) Relative Standard Uncertainty
atomic mass constant (unified atomic mass unit) m_u = 1 \ u \, 1.660 538 86(28) × 10-27 kg 1.7 × 10-7
Avogadro's number N_A, L \, 6.022 1415(10) × 1023 1.7 × 10-7
Boltzmann constant k = R / N_A \, 1.380 6505(24) × 10-23 J·K-1 1.8 × 10-6
Faraday constant F = N_A e \, 96 485.3383(83)C·mol-1 8.6 × 10-8
first radiation constant c_1 = 2 \pi h c^2 \, 3.741 771 38(64) × 10-16 W·m2 1.7 × 10-7
for spectral radiance c_{1L} \, 1.191 042 82(20) × 10-16 W · m2 sr-1 1.7 × 10-7
Loschmidt constant at T=273.15 K and p=101.325 kPa n_0 = N_A / V_m \, 2.686 7773(47) × 1025 m-3 1.8 × 10-6
gas constant R \, 8.314 472(15) J·K-1·mol-1 1.7 × 10-6
molar Planck constant N_A h \, 3.990 312 716(27) × 10-10 J · s · mol-1 6.7 × 10-9
molar volume of an ideal gas at T=273.15 K and p=100 kPa V_m = R T / p \, 22.710 981(40) × 10-3 m3 ·mol-1 1.7 × 10-6
at T=273.15 K and p=101.325 kPa 22.413 996(39) × 10-3 m3 ·mol-1 1.7 × 10-6
Sackur-Tetrode constant at T=1 K and p=100 kPa S_0 / R = \frac{5}{2}
+ \ln\left[ (2\pi m_u k T / h^2)^{3/2} k T / p \right]		 -1.151 7047(44) 3.8 × 10-6
at T=1 K and p=101.325 kPa -1.164 8677(44) 3.8 × 10-6
second radiation constant c_2 = h c / k \, 1.438 7752(25) × 10-2 m·K 1.7 × 10-6
Stefan-Boltzmann constant \sigma = (\pi^2 / 60) k^4 / \hbar^3 c^2 5.670 400(40) × 10-8 W·m-2·K-4 7.0 × 10-6
Wien displacement law constant b = (h c / k) / \, 4.965 114 231... 2.897 7685(51) × 10-3 m · K 1.7 × 10-6

Table of adopted values

Quantity Symbol Value (SI units) Relative Standard Uncertainty
conventional value of Josephson constant2 K_{J-90} \, 483 597.9 × 109 Hz · V-1 defined
conventional value of von Klitzing constant3 R_{K-90} \, 25 812.807 Ω defined
molar mass constant M_u = M(\,^{12}\mbox{C}) / 12 1 × 10-3 kg · mol-1 defined
of carbon-12 M(\,^{12}\mbox{C}) = N_A m(\,^{12}\mbox{C}) 12 × 10-3 kg · mol−1 defined
standard acceleration of gravity (gee, free fall on Earth) g_n \,\! 9.806 65 m·s-2 defined
standard atmosphere \mbox{atm} \, 101 325 Pa defined

Notes

1The values are given in the so-called concise form; the number in brackets is the standard uncertainty, which is the value multiplied by the relative standard uncertainty.
2This is the value adopted internationally for realizing representations of the volt using the Josephson effect.
3This is the value adopted internationally for realizing representations of the ohm using the quantum Hall effect.

See also

Further reading

References

  • CODATA Recommendations - 2002 CODATA Internationally recommended values of the Fundamental Physical Constants