User:Unitfreak

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The following table compares a number of modern unit systems:

Quantity / Symbol	Planck	Stoney	Schrödinger	Atomic	Electronic	Neoclassical [1]	SI Metric
Speed of Light $c \,$	$1 \,$	$1 \,$	$\frac{1}{\alpha} \$	$\frac{1}{\alpha} \$	$1 \,$	$10^8 \$	$299 792 458 \$
Planck's constant $h \,$	$2\pi \,$	$\frac{2\pi}{\alpha} \$	$2\pi \,$	$2\pi \,$	$\frac{2\pi}{\alpha} \$	$10^{-33} \$	$\frac{4 \times 10^{-18}}{(25812.807) (483597.9)^2} \$
Dirac's constant $\hbar=\frac{h}{2 \pi}$	$1 \,$	$\frac{1}{\alpha} \$	$1 \,$	$1 \,$	$\frac{1}{\alpha} \$	$\frac{10^{-33}}{2 \pi} \$	$\frac{2 \times 10^{-18}}{\pi (25812.807) (483597.9)^2} \$
elementary charge $e \,$	$\sqrt{\alpha} \,$	$1 \,$	$1 \,$	$1 \,$	$1 \,$	$10^{-18}\$	$\frac{2 \times 10^{-9}}{(25812.807) (483597.9)} \$
Josephson constant $K_J =\frac{2e}{h} \,$	$\frac{\sqrt{\alpha}}{\pi} \,$	$\frac{\alpha}{\pi} \,$	$\frac{1}{\pi} \,$	$\frac{1}{\pi} \,$	$\frac{\alpha}{\pi} \,$	$2 \times 10^{15} \$	$483597.9 \times 10^9 \,$
von Klitzing constant $R_K =\frac{h}{e^2} \,$	$\frac{2\pi}{\alpha} \,$	$\frac{2\pi}{\alpha} \,$	$2\pi \,$	$2\pi \,$	$\frac{2\pi}{\alpha} \,$	$1000 \$	$25812.807 \,$
Vacuum Impediance $Z_0 = 2 \alpha R_K \,$	$4 \pi \,$	$4 \pi \,$	$4 \pi \alpha \,$	$4 \pi \alpha \,$	$4 \pi \,$	$2000 \alpha \$	$2 \alpha (25812.807) \,$
electric constant $\epsilon_0 = \frac{1}{Z_0 c} \,$	$\frac{1}{4 \pi} \,$	$\frac{1}{4 \pi} \,$	$\frac{1}{4 \pi} \,$	$\frac{1}{4 \pi} \,$	$\frac{1}{4 \pi} \,$	$\frac{10^{-11}}{2 \alpha} \$	$\frac{1}{2 \alpha (25812.807) (299792458)} \$
magnetic constant $\mu_0 = \frac{Z_0}{c} \,$	$4 \pi \,$	$4 \pi \,$	$4 \pi \alpha^2 \,$	$4 \pi \alpha^2 \,$	$4 \pi \,$	$2 \alpha \times 10^{-5} \$	$\frac{2 \alpha (25812.807)}{299792458} \$
gravitational constant $G \,$	$1 \,$	$1 \,$	$1 \,$	$- \,$	$- \,$	$- \,$	$- \,$
electron mass $m_e \,$	$- \,$	$- \,$	$- \,$	$1 \,$	$1 \,$	$\frac{10^{-34}}{\alpha^2} \$	$- \,$
Compton Wavelength $\lambda_C = \frac{h}{m_e c} \,$	$- \,$	$- \,$	$- \,$	$2 \pi \alpha \,$	$\frac{2 \pi}{\alpha} \,$	$\alpha^2 10^{-7} \,$	$- \,$
Bohr Radius $a_0 = \frac{\lambda_C}{2 \pi \alpha} \,$	$- \,$	$- \,$	$- \,$	$1 \,$	$\frac{1}{\alpha^2} \,$	$\frac{\alpha 10^{-7}}{2 \pi} \,$	$- \,$
Rydberg constant $R_\infin = \frac{\alpha^2}{2 \lambda_C} \,$	$- \,$	$- \,$	$- \,$	$\frac{\alpha}{4 \pi} \,$	$\frac{\alpha^3}{4 \pi} \,$	$\frac{10^7}{2} \,$	$- \,$
Hartree energy $E_h = \alpha^2 m_e c^2 \$	$- \,$	$- \,$	$- \,$	$1 \,$	$\alpha^2 \,$	$10^{-18} \$	$- \,$
caesium hyperfine transition frequency	$- \,$	$- \,$	$- \,$	$- \,$	$- \,$	$- \,$	$9\ 192\ 631\ 770 \,$

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