Physical constant

In science, the physical constant is the name given to the value of a physical magnitude that, given a system of units, remains invariable in physical processes over time. In contrast, a mathematical constant represents an unchanging value that is not directly involved in any physical process.

There are many physical constants; some of the best known are Planck's reduced constant ( {displaystyle hbar }), the gravitation constant (G{displaystyle G}), the speed of light (c{displaystyle c}), allowivity in the void (ε ε 0{displaystyle epsilon}), magnetic permeability in the vacuum (μ μ 0{displaystyle mu _{0}}) and the elementary load (e{displaystyle e}). All these, being so fundamental, are called universal constants.

On the other hand, since 1937 Paul Dirac and other scientists have speculated that the value of physical constants might decrease in proportion to the age of the Universe. To date, no experiment has indicated that this is the case, although it has been possible to calculate the maximum levels of this hypothetical variation of the constants. The maximum levels of annual variation are, in any case, very small, being 10^-5 for the fine structure and 10^-11 for the gravitation constant. The issue is still a matter of controversy today.

Some considerations

Dimensional and dimensionless constants

Physical constants can have dimensions such as, for example, the speed of light in the vacuum (which in the SI is expressed in meters per second), while others, such as the constant of fine structure (α α {displaystyle alpha }) that characterizes the interaction between electrons and photons, is dimensional.

Unless natural units are used, the value of constants that have dimensions will depend on the unit system used. By contrast, dimensionless constants are independent of the system of units used and are known as fundamental physical constants. The fine structure constant is probably the best known of these dimensionless constants. The ratios of the masses (or other properties) of the particles are also fundamental physical constants.

Physical constants and life in the Universe

In many of these constants a precise adjustment occurs that makes the existence of the human being in the cosmos compatible. If the value of certain of those constants were only slightly different from what they possess, the Universe would have to be radically different, making it impossible for life as we know it to emerge. The fact that the Universe is properly calibrated and adjusted to accommodate intelligent life has intrigued many and has also been the subject of scientific and philosophical debate. Perhaps one of the best answers that explains the adjustment of the constants is the one given by the anthropic principle. This affirms that since the human being is here, the Universe must be a universe capable of housing it and, therefore, it is not possible to wonder about the possibility that these values were different since, if so, there would be no one who could ask him.

Tables of physical constants

NOTE: Although many properties of materials and particles are constant, they are not shown in tables as they are specific to the respective materials or particles.

Table of universal constants

Amount	Symbol	Value	Relative error
Vacuum characteristic impedance	Z0=μ μ 0c{displaystyle Z_{0}=mu _{0}c,}	376,730 313 461... Ω	defined
Electrical vacuum permit	ε ε 0{displaystyle epsilon _{0},}	8,854 187 817... × 10-12 F·m-1	defined
Magnetic Permeability of Vacuum	μ μ 0{displaystyle mu _{0},}	4π × 10-7 N·A-2 = 1,2566 370 614... × 10-6 N·A-2	defined
Constant universal gravitation	G{displaystyle G,}	6,671 91(99) × 10-11 N·m2/kg2	1.5 × 10-6
Constant of Planck	h{displaystyle h,}	6,626 070 15 × 10- 34 J·s	defined
Reduced Constant of Planck	=h2π π {displaystyle hbar ={frac {h}{2pi }}}}	1,054 571 817 646 16 × 10- 34 J·s	Exactly
Speed of light in the vacuum	c=1μ μ 0ε ε 0{displaystyle c={frac {1}{sqrt {mu _{0}epsilon _{0}}}}{,}	299 792 458 m·s-1	defined

Table of electromagnetic constants

Amount	Symbol	Value1 (units SI)	Relative error
Bohr Magneton	μ μ B=e /2me{displaystyle mu _{B}=ehbar /2m_{e}}	9,27400949(80) × 10-24 J·T-1	8.6 × 10-8
Nuclear Magneton	μ μ N=e /2mp{displaystyle mu _{N}=ehbar /2m_{p}}}	5,050 783 43(43) × 10-27 J·T-1	8.6 × 10-8
Quantum resistance	R0=h/2e2{displaystyle R_{0}=h/2e^{2},}	12 906,403 729 652 3 Ω	Exactly
Constant von Klitzing	RK=h/e2{displaystyle R_{K}=h/e^{2},}	25 812.807 459 304 5 Ω	Exactly

Table of atomic and nuclear constants

Amount		Symbol	Value1 (units SI)	Relative error
Radio de Bohr		a0=α α /4π π R∞ ∞ {displaystyle a_{0}=alpha /4pi R_{infty },}	0.529 177 2108(18) × 10-10 m	3.3 × 10-9
Fermi coupling Constant		GF/( c)3{displaystyle G_{F}/(hbar c)^{3}	1,166 39(1) × 10-5 GeV-2	8.6 × 10-6
Consisting of fine structure		α α =μ μ 0e2c/(2h)=e2/(4π π ε ε 0 c){displaystyle alpha =mu _{0}e^{2}c/(2h)=e^{2}/(4pi epsilon _{0}hbar c),}	7,297 352 568(24) × 10-3	3.3 × 10-9
Hartree Energy		Eh=2R∞ ∞ hc{displaystyle E_{h}=2R_{infty }hc,}	4,359 744 17(75) × 10-18 J	1.7 × 10-7
Quantum of circulation		h/2me{displaystyle h/2m_{e},}	3,636 947 550(24) × 10-4 m2 s-1	6.7 × 10-9
Rydberg Constant		R∞ ∞ =α α 2mec/2h{displaystyle R_{infty }=alpha ^{2}m_{ec/2h,}	10 973 731.568 525(73) m-1	6,6 × 10-12
Effective Thomson Section		(8π π /3)re2{displaystyle (8pi /3)r_{e}^{2}}	0.665 245 873(13) × 10- 28 m2	2.0 × 10-8
Weinberg Angle		without2 θ θ W=1− − (mW/mZ)2{displaystyle sin ^{2}theta _{W}=1-(m_{W}/m_{Z})^{2},}	0.222 15(76)	3.4 × 10-3

Table of physical-chemical constants

Amount		Symbol	Value1 (units SI)	Relative error
Constant atomic mass		mu=1u{displaystyle m_{u}=1 u,}	1,660 538 86(28) × 10-27 kg	1.7 × 10-7
Number of Avogadro		NA,L{displaystyle N_{A},L,}	6,022 140 76 × 1023	defined
Boltzmann Constant		k=R/NA{displaystyle k=R/N_{A},}	1,380 649 × 10-23 J·K-1	defined
Constant Faraday		F=NAe{displaystyle F=N_{A}e,}	96 485,332 123 310 018 4 C·mol-1	Exactly
First radiation constant		c1=2π π hc2{displaystyle c_{1}=2pi hc^{2},}	3,741 771 852 191 76 × 10-16 W·m2	Exactly
	for spectral radiance	c1L{displaystyle c_{1L},}	1,191 042 82(20) × 10-16 W · m2 sr-1	1.7 × 10-7
Number of Loschmidt	a T{displaystyle T}=273.15 K and p{displaystyle p}=101.325 kPa	n0=NA/Vm{displaystyle n_{0}=N_{A}/V_{m},}	2,686 7773(47) × 1025 m-3	1.8 × 10-6
Universal consistency of ideal gases		R{displaystyle R,}	8.314 462 618 153 24 J·K-1·mol-1	Exactly
Constant molar of Planck		NAh{displaystyle N_{A}h,}	3,990 312 712 893 431 4 × 10-10 J · s · mol-1	Exactly
Molar volume of an ideal gas	a T{displaystyle T}=273.15 K and p{displaystyle p}= 100 kPa	Vm=RT/p{displaystyle V_{m}=RT/p,}	22,710 981(40) × 10-3 m3 · mol-1	1.7 × 10-6
	a T{displaystyle T}=273.15 K and p{displaystyle p}=101.325 kPa		22,413 996(39) × 10-3 m3 · mol-1	1.7 × 10-6
Sackur-Tetrode Constant	a T{displaystyle T}=1 K and p{displaystyle p}= 100 kPa	S0/R=52{displaystyle S_{0}/R={frac {5}{2}}}}} +ln [chuckles](2π π mukT/h2)3/2kT/p]{displaystyle +ln left[(2pi m_{u}kT/h^{2}}{3/2}kT/pright]}}	-1,151 7047(44)	3.8 x 10-6
	a T{displaystyle T}=1 K and p{displaystyle p}=101.325 kPa		-1.164 8677(44)	3.8 x 10-6
Second radiation constant		c2=hc/k{displaystyle c_{2}=hc/k,}	1,438 776 877 503 93 × 10-2 m·K	Exactly
Constant Stefan-Boltzmann		σ σ =(π π 2/60)k4/ 3c2{displaystyle sigma =(pi ^{2}/60)k^{4}/hbar ^{3}c^{2}}	5.670 374 419 184 43 × 10-8 W·m-2·K-4	Exactly
Constant of the Displacement Act of Wien		benergia=(hc/k)/{displaystyle b_{energia}=(hc/k)/,} 4,965 114 231...	2,897 7685(51) × 10-3 m · K	1.7 × 10-6
Conventional value of Josephson's constant2		KJ− − 90{displaystyle K_{J-90},}	483 597,9 × 109 Hz · V-1	defined