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In physics, reduced mass is a measure of the effective inertial mass of a system with two or more particles when the particles are interacting with each other. Reduced mass allows the two-body problem to be solved as if it were a one-body problem. Note, however, that the mass determining the gravitational force is not reduced.
where = / (+) is the reduced mass of the electron–proton system (with being the mass of proton). The use of reduced mass is a generalization of the two-body problem from classical physics beyond the case in which the approximation that the mass of the orbiting body is negligible compared to the mass of the body being orbited.
The mass of an atomic nucleus is less than the sum of the individual masses of the free constituent protons and neutrons. The difference in mass can be calculated by the Einstein equation, E = mc 2, where E is the nuclear binding energy, c is the speed of light, and m is the difference in mass. This 'missing mass' is known as the mass defect ...
In nuclear physics, the semi-empirical mass formula (SEMF) (sometimes also called the Weizsäcker formula, Bethe–Weizsäcker formula, or Bethe–Weizsäcker mass formula to distinguish it from the Bethe–Weizsäcker process) is used to approximate the mass of an atomic nucleus from its number of protons and neutrons.
Q values are also featured in particle physics. For example, Sargent's rule states that weak reaction rates are proportional to Q 5. The Q value is the kinetic energy released in the decay at rest. For neutron decay, some mass disappears as neutrons convert to a proton, electron and antineutrino: [2]
The mass excess of a nuclide is the difference between its actual mass and its mass number in daltons.It is one of the predominant methods for tabulating nuclear mass. The mass of an atomic nucleus is well approximated (less than 0.1% difference for most nuclides) by its mass number, which indicates that most of the mass of a nucleus arises from mass of its constituent protons and neutrons.
If one of the two initial protons is stationary, we find that the impinging proton must be given at least of energy, that is, 5.63 GeV. On the other hand, if both protons are accelerated one towards the other (in a collider ) with equal energies, then each needs to be given only m p c 2 {\displaystyle m_{p}c^{2}} of energy.
All quantities are in Gaussian units except energy and temperature which are in electronvolts.For the sake of simplicity, a single ionic species is assumed. The ion mass is expressed in units of the proton mass, = / and the ion charge in units of the elementary charge, = / (in the case of a fully ionized atom, equals to the respective atomic number).