The SI System
Overview
This section covers the SI, or International Systems of Units. Within the SI units the relationship between quantity value \(A\), numerical value \(\left\{ A \right\}\), and the unit \(\left[ A \right]\) in SI is
\[A = \left\{ A \right\}\left[ A \right]\]SI chooses seven constants as fundamental, in having their value fixed, when expressed in the corresponding SI units. Thus the current definition is (SI Brochure, 20919. pg. 127)
The International System of Units, the SI, is the system of units in which
- the unperturbed ground state hyperfine transition frequency of the caesium 133 atom, \(\Delta\nu_\text{Cs}\), is \(9\ 192\ 631\ 770\ \text{Hz}\),
- the speed of light in vacuum, \(c\), is \(299\ 792\ 458\ \text{m/s}\),
- the Planck constant, \(h\), is \(6.626\ 070\ 15 \times 10^{−34}\ \text{J}\ \text{s}\),
- the elementary charge, \(e\), is \(1.602\ 176\ 634 \times 10^{−19}\ \text{C}\),
- the Boltzmann constant, \(k\), is \(1.380\ 649 \times 10^{−23}\ \text{J/K}\),
- the Avogadro constant, \(N_A\), is \(6.022\ 140\ 76 \times 1023\ \text{mol}^{−1}\),
- the luminous efficacy of monochromatic radiation of frequency \(540 \times 1012\ \text{Hz}\), \(K_\text{cd}\), is \(683\ \text{lm}/\text{W}\),
where the hertz, joule, coulomb, lumen, and watt, with unit symbols \(\text{Hz}\), \(\text{J}\), \(\text{C}\), \(\text{lm}\), and \(\text{W}\), respectively, are related to the units second, metre, kilogram, ampere, kelvin, mole, and candela, with unit symbols \(\text{s}\), \(\text{m}\), \(\text{kg}\), \(\text{A}\), \(\text{K}\), \(\text{mol}\), and \(\text{cd}\), respectively, according to \(\text{Hz} = \text{s}^{–1}\), \(\text{J} = \text{kg}\ \text{m}^2\ \text{s}^{–2}\), \(\text{C} = \text{A}\ \text{s}\), \(\text{lm} = \text{cd}\ \text{m}^2\ \text{m}^{–2} = \text{cd}\ \text{sr}\), and \(\text{W} = \text{kg}\ \text{m}^2\ \text{s}^{–3}\).
References
- SI Brochure: The International System of Units (SI) (2019). Bureau International des Poids et Mesures. Ninth Edition. [online].