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Hartree defined units based on three physical constants: [1]: 91 Both in order to eliminate various universal constants from the equations and also to avoid high powers of 10 in numerical work, it is convenient to express quantities in terms of units, which may be called 'atomic units', defined as follows:
The atomic units have been chosen to use several constants relating to the electron: the electron mass, the elementary charge, the Coulomb constant and the reduced Planck constant. The unit of energy in this system is the total energy of the electron in the Bohr atom and called the Hartree energy. The unit of length is the Bohr radius.
While the values of the physical constants are independent of the system of units in use, each uncertainty as stated reflects our lack of knowledge of the corresponding value as expressed in SI units, and is strongly dependent on how those units are defined. For example, the atomic mass constant is exactly known when expressed using the dalton ...
Because a dalton, a unit commonly used to measure atomic mass, is exactly 1/12 of the mass of a carbon-12 atom, this definition of the mole entailed that the mass of one mole of a compound or element in grams was numerically equal to the average mass of one molecule or atom of the substance in daltons, and that the number of daltons in a gram ...
A -finite measure on a measurable space (,) is called atomic or purely atomic if every measurable set of positive measure contains an atom. This is equivalent to say that there is a countable partition of X {\displaystyle X} formed by atoms up to a null set. [ 3 ]
This is the definition declared in the modern International System of Units in 1960. [13] The definition of the joule as J = kg⋅m 2 ⋅s −2 has remained unchanged since 1946, but the joule as a derived unit has inherited changes in the definitions of the second (in 1960 and 1967), the metre (in 1983) and the kilogram . [14]
The SI system after 1983, but before the 2019 revision: Dependence of base unit definitions on other base units (for example, the metre is defined as the distance travelled by light in a specific fraction of a second), with the constants of nature and artefacts used to define them (such as the mass of the IPK for the kilogram).
In physics, natural unit systems are measurement systems for which selected physical constants have been set to 1 through nondimensionalization of physical units.For example, the speed of light c may be set to 1, and it may then be omitted, equating mass and energy directly E = m rather than using c as a conversion factor in the typical mass–energy equivalence equation E = mc 2.