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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 ...
Defining equation SI units Dimension Number of atoms N = Number of atoms remaining at time t. N 0 = Initial number of atoms at time t = 0 N D = Number of atoms decayed at time t = + dimensionless dimensionless Decay rate, activity of a radioisotope: A = Bq = Hz = s −1 [T] −1: Decay constant: λ
The stable nucleus has approximately a constant density and therefore the nuclear radius R can be approximated by the following formula, R = r 0 A 1 / 3 {\displaystyle R=r_{0}A^{1/3}\,} where A = Atomic mass number (the number of protons Z , plus the number of neutrons N ) and r 0 = 1.25 fm = 1.25 × 10 −15 m.
The components of an atom and of a nucleus have varying densities. The proton is not a fundamental particle, being composed of quark–gluon matter. Its size is approximately 10 −15 meters and its density 10 18 kg/m 3. The descriptive term nuclear density is also applied to situations where similarly high densities occur, such as within ...
The problem of defining a radius for the atomic nucleus has some similarity to that of defining a radius for the entire atom; neither has well defined boundaries.However, basic liquid drop models of the nucleus imagine a fairly uniform density of nucleons, theoretically giving a more recognizable surface to a nucleus than an atom, the latter being composed of highly diffuse electron clouds ...
The Bohr radius ( ) is a physical constant, approximately equal to the most probable distance between the nucleus and the electron in a hydrogen atom in its ground state. It is named after Niels Bohr, due to its role in the Bohr model of an atom. Its value is 5.291 772 105 44 (82) × 10 −11 m. [1] [2]
The concept of atomic radius was preceded in the 19th century by the concept of atomic volume, a relative measure of how much space would on average an atom occupy in a given solid or liquid material. [3] By the end of the century this term was also used in an absolute sense, as a molar volume divided by Avogadro constant. [4]
Once this mass difference, called the mass defect or mass deficiency, is known, Einstein's mass–energy equivalence formula E = mc 2 can be used to compute the binding energy of any nucleus. Early nuclear physicists used to refer to computing this value as a "packing fraction" calculation.