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When charged particles move in electric and magnetic fields the following two laws apply: Lorentz force law: = (+),; Newton's second law of motion: = =; where F is the force applied to the ion, m is the mass of the particle, a is the acceleration, Q is the electric charge, E is the electric field, and v × B is the cross product of the ion's velocity and the magnetic flux density.
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 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.
Furthermore, spectroscopic measurements can be made both with regular hydrogen (consisting of a proton and an electron) or muonic hydrogen (an exotic atom consisting of a proton and a negative muon). An inconsistency between proton charge radius measurements made using different techniques [ 12 ] was known as the proton radius puzzle , but more ...
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.
This new value was intermediate between the two earlier definitions, but closer to the one used by chemists (who would be affected the most by the change). [12] [13] The new unit was named the "unified atomic mass unit" and given a new symbol "u", to replace the old "amu" that had been used for the oxygen-based unit. [17]
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.
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.