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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 ...
If the nucleus is assumed to be spherically symmetric, an approximate relationship between nuclear radius and mass number arises above A=40 from the formula R=R o A 1/3 with R o = 1.2 ± 0.2 fm. [6] R is the predicted spherical nuclear radius, A is the mass number, and R o is a constant determined by experimental data.
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 ...
Critical radius is the minimum particle size from which an aggregate is thermodynamically stable. In other words, it is the lowest radius formed by atoms or molecules clustering together (in a gas, liquid or solid matrix) before a new phase inclusion (a bubble, a droplet or a solid particle) is viable and begins to grow.
Quantity (common name/s) (Common) symbol/s 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
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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]