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In metrology, the Planck constant is used, together with other constants, to define the kilogram, the SI unit of mass. [4] The SI units are defined in such a way that, when the Planck constant is expressed in SI units, it has the exact value h {\displaystyle h} = 6.626 070 15 × 10 −34 J⋅Hz −1 .
The Planck units are based on the quantum of action, now usually known as the Planck constant, which appeared in the Wien approximation for black-body radiation. Planck underlined the universality of the new unit system, writing: [ 5 ]
The constants listed here are known values of physical constants expressed in SI units; that is, physical quantities that are generally believed to be universal in nature and thus are independent of the unit system in which they are measured. Many of these are redundant, in the sense that they obey a known relationship with other physical ...
Planck considered only the units based on the universal constants G, h, c, and k B to arrive at natural units for length, time, mass, and temperature, but no electromagnetic units. [7] The Planck system of units is now understood to use the reduced Planck constant, ħ, in place of the Planck constant, h. [8]
A set of base units in the atomic system as in one proposal are the electron rest mass, the magnitude of the electronic charge, the Planck constant, and the permittivity. [6] [9] In the atomic units system, each of these takes the value 1; the corresponding values in the International System of Units [10]: 132 are given in the table.
For example, Planck units, constructed from c, G, ħ, and k B give conveniently sized measurement units for use in studies of quantum gravity, and atomic units, constructed from ħ, m e, e and 4πε 0 give convenient units in atomic physics. The choice of constants used leads to widely varying quantities.
The kilogram is defined by setting the Planck constant h exactly to 6.626 070 15 × 10 −34 J⋅s (J = kg⋅m 2 ⋅s −2), given the definitions of the metre and the second. [1] kg: SI: Physics: Basic: ampere: A: I: electric current: The flow of exactly 1 / 1.602 176 634 × 10 −19 times the elementary charge e per second.
It is defined by taking the fixed numerical value of the Planck constant h to be 6.626 070 15 × 10 −34 when expressed in the unit J s, which is equal to kg m 2 s −1, where the metre and the second are defined in terms of c and ∆ν Cs." [1] The mass of one litre of water at the temperature of melting ice. A litre is one thousandth of a ...