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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.
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). The other physical quantities used are the Boltzmann constant ( k B {\displaystyle k_{\text{B}}} ), speed of light ( c {\displaystyle c} ), and the ...
The effective mass is used in transport calculations, such as transport of electrons under the influence of fields or carrier gradients, but it also is used to calculate the carrier density and density of states in semiconductors. These masses are related but, as explained in the previous sections, are not the same because the weightings of ...
Its mass is slightly less than the mass of a neutron and approximately 1836 times the mass of an electron (the proton-to-electron mass ratio). Protons and neutrons, each with a mass of approximately one atomic mass unit, are jointly referred to as nucleons (particles present in atomic nuclei). One or more protons are present in the nucleus of ...
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 corresponding mass formula is defined purely in terms of the numbers of protons and neutrons it contains. The original Weizsäcker formula defines five terms: Volume energy , when an assembly of nucleons of the same size is packed together into the smallest volume, each interior nucleon has a certain number of other nucleons in contact with it.
We can calculate the minimum energy that the moving proton must have in order to create a pion. Transforming into the ZMF (Zero Momentum Frame or Center of Mass Frame) and assuming the outgoing particles have no KE (kinetic energy) when viewed in the ZMF, the conservation of energy equation is:
The rms charge radius is a measure of the size of an atomic nucleus, particularly the proton distribution. The proton radius is about one femtometre = 10 −15 metre. It can be measured by the scattering of electrons by the nucleus. Relative changes in the mean squared nuclear charge distribution can be precisely measured with atomic spectroscopy.