Physics Exercises/Fundamental Constants

Table of Constants

Fundamental constants from NIST Physics Lab

Name	Symbol	Value	Units	Relative Uncertainty
Speed of light (in vacuum)	$c$	$299792458$	$\mathrm{m}{\mathrm{s}}^{-1}$	(exact)
Magnetic constant	${\mu }_0$	$4\pi \times 10^{-7}\approx$	$\mathrm{N}{\mathrm{A}}^{-2}$	(exact)
Electric constant	${ϵ}_0$	$1/({\mu }_0{c}^2)\approx$	$\mathrm{F}{\mathrm{m}}^{-1}$	(exact)
Newtonian gravitational constant	$G$	$6.6742(10)\times 10^{-11}$	${\mathrm{m}}^3{\mathrm{k}\mathrm{g}}^{-1}{\mathrm{s}}^{-2}$	$1.5\times 10^{-4}$
Plank's constant	$h$	$6.6260693(11)\times 10^{-34}$	$\mathrm{J}\mathrm{s}$	$1.7\times 10^{-7}$
Elementary charge	$e$	$1.60217653(14)\times 10^{-19}$	$\mathrm{C}$	$8.5\times 10^{-8}$
Mass of the electron	$m_e$	$9.1093826(16)\times 10^{-31}$	$\mathrm{k}\mathrm{g}$	$1.7\times 10^{-7}$
Mass of the proton	$m_p$	$1.67262171(29)\times 10^{-27}$	$\mathrm{k}\mathrm{g}$	$1.7\times 10^{-7}$
Mass of a neutron	$m_n$
Fine structure constant	$\alpha =e^2/(2{ϵ}_{0}hc)$	$7.297352568(24)\times 10^{-3}$	dimentionless	$3.3\times 10^{-9}$
Molar gass constant	$R$	$8.314472(15)$	$\mathrm{J}{\mathrm{m}\mathrm{o}\mathrm{l}}^{-1}{\mathrm{K}}^{-1}$	$1.7\times 10^{-6}$
Boltzmann's constant	$k$	$1.3806505(24)$	$\mathrm{J}{\mathrm{K}}^{-1}$	$1.8\times 10^{-6}$
Avogadro's number	$N_A$	$6.0221415(10)\times 10^{23}$	${\mathrm{m}\mathrm{o}\mathrm{l}}^{-1}$	$1.7\times 10^{-7}$
Rydberg constant	$R_{\mathrm{\infty }}$	$10973731.568525(73)$	${\mathrm{m}}^{-1}$	$6.6\times 10^{-12}$
Atmosphere	$\mathrm{a}\mathrm{t}\mathrm{m}$	$101325$		(exact)
Electronvolt	$\mathrm{e}\mathrm{V}$	$1.60\times 10^{-19}$
Bohr radius	$a_0$	$5.292\times 10^{-11}$
Coulomb's constant	$k$	$\frac{1}{4\pi {ϵ}_0}\approx$
Faraday constant	$F$	$e\times N_A\approx$
Gravitational acceleration on Earth	$g$
Mass of the Earth
Mass of the Moon
Mean radius of the Earth
Mean radius of the Moon
Dirac's Constant	$\hslash$
Speed of sound in air at STP
Unified Atomic Mass Unit	$u$
Vacuum Permittivity	${ϵ}_0$

• 1 Atmosphere Pressure (1 atm) : 1.0 × 10⁵ N/m² = 1.0 × 10⁵ Pa
• 1 Electron Volt (1 eV) : 1.60 × 10⁻¹⁹ J
• Bohr radius (a₀)  : 5.292 × 10⁻¹¹ m
• Coulomb's Law Constant (k) : 1/(4 π ε₀) = 9.0 × 10⁹ N·m²/C²
• Faraday constant (F)  : 96,485 C·mol⁻¹
• Gravitational accelaration (g) : 9.80665 m·s^-2
• Mass of a neutron (m_n) : 1.67495 × 10⁻²⁷ kg
• Mass of Earth : 5.98 × 10²⁴ kg
• Mass of the Moon : 7.35 × 10²² kg
• Mean radius of Earth : 6.37 × 10⁶ m
• Mean radius of the Moon : 1.74 × 10⁶ m
• Dirac's Constant ($\hslash$) : $h/(2\pi )$ = 1.05457148 × 10⁻³⁴ J·s
• Speed of sound in air at STP : 3.31 × 10² m/s
• Unified Atomic Mass Unit (u) : 1.66 × 10⁻²⁷ kg
• Vacuum Permittivity (ε₀) : 8.85 × 10⁻¹² C²/(N·m²)

Item	Proton	Neutron	Electron
Mass	1	1	Negligible
Charge	+1	0	-1
Spin	$\frac{1}{2}$	$\frac{1}{2}$	$\frac{1}{2}$

See Also

Wiki-links

• Wikipedia Article

External Links

• NIST Physics Lab