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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:
Relative atomic mass (symbol: A r; sometimes abbreviated RAM or r.a.m.), also known by the deprecated synonym atomic weight, is a dimensionless physical quantity defined as the ratio of the average mass of atoms of a chemical element in a given sample to the atomic mass constant.
The unified atomic mass unit (symbol: u) is equivalent to the dalton. One dalton is approximately the mass of one a single proton or neutron. [2] The unified atomic mass unit has a value of 1.660 538 921 (73) × 10 −27 kg. [3] The amu without the "unified" prefix is an obsolete unit based on oxygen, which was replaced in 1961.
In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantities (such as length, mass, time, and electric current) and units of measurement (such as metres and grams) and tracking these dimensions as calculations or comparisons are performed.
Given two bodies, one with mass m 1 and the other with mass m 2, the equivalent one-body problem, with the position of one body with respect to the other as the unknown, is that of a single body of mass [1] [2] = = + = +, where the force on this mass is given by the force between the two bodies.
Atomic mass is often measured in dalton (Da) or unified atomic mass unit (u). One dalton is equal to 1 ⁄ 12 the mass of a carbon-12 atom in its natural state. Thus, the numeric value of the atomic mass when expressed in daltons has nearly the same value as the mass number.
The molar mass constant, usually denoted by M u, is a physical constant defined as one twelfth of the molar mass of carbon-12: M u = M(12 C)/12. [1] The molar mass of an element or compound is its relative atomic mass (atomic weight) or relative molecular mass (molecular weight or formula weight) multiplied by the molar mass constant.
the statistical confidence interval or tolerance interval of the initial measurement; the number of significant figures of the measurement; the intended use of the measurement, including the engineering tolerances; historical definitions of the units and their derivatives used in old measurements; e.g., international foot vs. US survey foot.