Section: 1 | CODATA Recommended Values of the Fundamental Physical Constants: 2018 |

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CODATA RECOMMENDED VALUES OF THE FUNDAMENTAL PHYSICAL CONSTANTS: 2018

Eite Tiesinga, Peter J. Mohr, David B. Newell, and Barry N. Taylor

This report gives the 2018 self-consistent set of values of the constants and conversion factors of physics and chemistry recommended by the Committee on Data for Science and Technology (CODATA). These values are based on a least-squares adjustment that take into account all data available up to December 31, 2018. They also reflect the major changes to the SI units made in 2019. See the International System of Units (SI) in this section for further details about these changes.

The tables below are extracted from reports (Refs. 1-4) prepared by the authors under the auspices of the CODATA Task Group on Fundamental Constants and the International Bureau of Weights and Measures (BIPM). The present members of the task group are:

D. B. Newell, National Institute of Standards and Technology, United States of America (Chair)
K. Pachucki, University of Warsaw, Poland (Co-Chair)
F. Cabiati, Istituto Nazionale di Ricerca Metrologica, Italy
K. Fujii, National Metrology Institute of Japan, Japan
S. G. Karshenboim, The Central Astronomical Observatory of the Russian Academy of Sciences at Pulkovo, Russia
H. Margolis, National Physical Laboratory, United Kingdom
E. de Mirandés, Bureau International des Poids et Mesures
P. J. Mohr, National Institute of Standards and Technology, United States of America
F. Nez, Laboratoire Kastler-Brossel, France
R. Pohl, QUANTUM, Johannes Gutenberg-Universitat, Germany
J. Qu, National Institute of Metrology, China
T. J. Quinn, Bureau International des Poids et Mesures (Emeritus)
A. Surzhykov, Physikalisch-Technische Bundesanstalt, Germany
B. N. Taylor, National Institute of Standards and Technology, United States of America (Emeritus)
E. Tiesinga, National Institute of Standards and Technology, United States of America
M. Wang, Institute of Modern Physics, China
B. M. Wood, National Research Council, Canada (Vice-Chair)

References

Mohr, P. J., Newell, D. B., and Taylor, B. N., J. Phys. Chem. Ref. Data 45, 043102, 2016. [https://doi.org/10.1063/1.4954402]
Mohr, P. J., Newell, D. B., and Taylor, B. N., Rev. Mod. Phys. 88, 035009, 2016. [https://doi.org/10.1103/RevModPhys.88.035009]
Available on the Web at <physics.nist.gov/constants>.
Newell, D. B., and Tiesinga, E., The International System of Units (SI), NIST Special Publication 330, 2019 Edition, National Institute of Standards and Technology, Gaithersburg, MD, 2019. [https://doi.org/10.6028/NIST.SP.330-2019]

The 2018 set of CODATA recommended values of the fundamental physical constants is based on the recently adopted definitions of the SI units as derived from a set of seven defining constants, as shown in Table 1.

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TABLE 1. The Seven Defining Constants of the SI and the Seven Corresponding Units They Define (Note: All constants are exact)

Defining constant	Symbol	Numerical value	Unit
hyperfine transition of cesium (¹¹³Cs)	Δν_Cs	9 192 631 770	Hz
speed of light in vacuum	c, c₀	299 792 458	m s^-1
Planck constant	h	6.626 070 15 × 10^-34	J s
elementary charge	e	1.602 176 634 × 10^-19	C
Boltzmann constant	k	1.380 649 × 10^-23	J K^-1
Avogadro constant	N_A	6.022 140 76 × 10²³	mol^-1
luminous efficacy	K_cd	683	lm W^-1

Table 2 is an abbreviated list of the CODATA recomended values of the fundamental constants of physics and chemistry, based on the 2018 adjustment and the recently adopted defining SI constants and units (Table 1). Uncertainties are given when appropriate. See References 3 and 4 for additional information.

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TABLE 2. Frequently Used Fundamental Constants of Physics and Chemistry Based on the 2018 CODATA Adjustment

Quantity	Symbol	Numerical value	Unit	Uncertainty
Continued on next page...
electron volt (e/C) J	eV	1.602 176 634 × 10^-19	J	exact
Josephson constant 2e/h	K_J	483 597.848 4... × 10⁹	Hz V^-1	exact
von Klitzing constant 2πh/e²	R_K	25 812 807 45...	Ω	exact
molar gas constant	R	8.314 462 618...	J mol^-1 K^-1	exact
Stefan-Boltzmann constant (π²/60)k⁴/ℏ³c²	σ	5.670 374 419... × 10^-8	W m^-2 K^-4	exact
(unified) atomic mass unit (1/12)m(¹²C)	u	1.660 539 066 60 × 10^-27	kg	0.000 000 000 50 × 10^-27
Newtonian constant of gravitation	G	6.674 30⁢ × 10^-11	m³ kg^-1 s^-2	0.000 15 × 10^-11
fine-structure constant e²/4πϵ₀ℏc	α	7.297 352 5693 × 10^-3		0.000 000 0011 × 10^-3
inverse fine-structure constant	α^-1	137.035 999 084⁢		0.000 000 021
Rydberg constant α²⁢m_e⁢c/2⁢h	R_∞	10 973 731.568 160	m^-1	0.000 021
vac. magnetic permeability 4παℏ/(e²c)	μ₀	1.256 637 062 12 × 10^-6	N A^-2	0.000 000 000 19 × 10^-6
electron mass	m_e	9.109 383 7015 × 10^-31	kg	0.000 000 0028 × 10^-31
proton mass	m_p	1.672 621 923 69 × 10^-27	kg	0.000 000 000 51 × 10^-27
proton-electron mass ratio	m_p/m_e	1836.152 673 43		0.000 000 11
reduced Compton wavelength ℏ/(m_ec)	C	3.861 592 6796 × 10^-13	m	0.000 000 0012 × 10^-13
Bohr radius ℏ/(αm_ec)	α₀	5.291 772 109 03 × 10^-11	m	0.000 000 000 80 × 10^-11
Bohr magneton eℏ/(2m_e)	μ_B	9.274 010 0783 × 10^-24	J T^-1	0.000 000 0028 × 10^-24
h/2⁢π	ℏ	1.054 571 817... × 10^-34	J s	exact
vac. electric permittivity 1/(μ₀⁢c²)	ϵ₀	8.854 187 8128 × 10^-12	F m^-1	0.000 000 0013 × 10^-12

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