Mass excess

From Wikipedia, the free encyclopedia

The introduction to this article provides insufficient context for those unfamiliar with the subject.
Please help improve the article with a good introductory style.

The mass excess of a nuclide is the difference between its actual mass and its mass number. ^[1] It is not the same as binding energy, although the concepts are related.^[2]It is a useful quantity when deciding whether a radioactive decay will occur and, if it does, how much energy will be released. Radioactive decay processes will only occur if the mass excess of the products is less than the mass excess of the parent nuclide.

The difference between the actual mass and the mass number arises from the mass-energy equivalence E=mc². When two nucleons come together, the potential energy between them due to the strong nuclear force is converted to mass. Qualitatively, if a nuclide has a high mass excess, this indicates that the nucleus is tightly bound.

[edit] Example

Consider the nuclear fission of ²³⁶U into ⁹²Kr ¹⁴¹Ba and three neutrons.

²³⁶U → ⁹²Kr + ¹⁴¹Ba + 3 n

The mass number of ²³⁶U is 236 u (atomic mass units), but the actual mass is $236.045563$ u, so the mass excess is $+ 0.045563$ u. Calculated in the same manner, the mass excess for ⁹²Kr, ¹⁴¹Ba, and a neutron are $- 0.073843$ u, $- 0.085588$ u and $0.0086648$ u, respectively. The mass excess of the reactant is $+ 0.045563$ u, and the mass excess of the products is $- 0.073843 + ( - 0.085588) + 3 * (0.0086648) = - 0.1334366$ The difference between reactants and products is $0.045563 - ( - 0.133436) = 0.1789996$ u, which shows that the mass excess of the products is less than that of the reactants, and so the decay can occur.