The mass excess of a

nuclide A nuclide (or nucleide, from atomic nucleus, nucleus, also known as nuclear species) is a class of atoms characterized by their number of protons, ''Z'', their number of neutrons, ''N'', and their nuclear energy state. The word ''nuclide'' was co ...

is the difference between its actual mass and its

mass number The mass number (symbol ''A'', from the German word ''Atomgewicht'' tomic weight, also called atomic mass number or nucleon number, is the total number of protons and neutrons (together known as nucleons) in an atomic nucleus. It is approxima ...

in daltons. It is one of the predominant methods for tabulating nuclear mass. The mass of an

atomic nucleus The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford based on the 1909 Geiger–Marsden gold foil experiment. After the discovery of the neutron ...

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

proton A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mass ...

s and

neutron The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the atomic nucleus, nuclei of atoms. Since protons and ...

s. Thus, the mass excess is an expression of the

nuclear binding energy Nuclear binding energy in experimental physics is the minimum energy that is required to disassemble the nucleus of an atom into its constituent protons and neutrons, known collectively as nucleons. The binding energy for stable nuclei is alway ...

, relative to the binding energy per

nucleon In physics and chemistry, a nucleon is either a proton or a neutron, considered in its role as a component of an atomic nucleus. The number of nucleons in a nucleus defines the atom's mass number (nucleon number). Until the 1960s, nucleons were ...

carbon-12 Carbon-12 (12C) is the most abundant of the two stable isotopes of carbon ( carbon-13 being the other), amounting to 98.93% of element carbon on Earth; its abundance is due to the triple-alpha process by which it is created in stars. Carbon- ...

(which defines the dalton). If the mass excess is negative, the nucleus has more binding energy than ¹²C, and vice versa. If a nucleus has a large excess of mass compared to a nearby nuclear species, it can radioactively decay, releasing energy.

Energy scale of nuclear reactions

The ¹²C standard provides a convenient unit (the dalton) in which to express nuclear mass for defining the mass excess. However, its usefulness arises in the calculation of nuclear reaction

kinematics Kinematics is a subfield of physics, developed in classical mechanics, that describes the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering the forces that cause them to move. Kinematics, as a fiel ...

or decay. Only a small fraction of the total energy that is associated with an atomic nucleus by

mass–energy equivalence In physics, mass–energy equivalence is the relationship between mass and energy in a system's rest frame, where the two quantities differ only by a multiplicative constant and the units of measurement. The principle is described by the physicis ...

, on the order of 0.01% to 0.1% of the total mass, may be absorbed or liberated as radiation. By working in terms of the mass excess, much of the mass changes which arise from the transfer or release of nucleons is effectively removed, highlighting the net energy difference. Nuclear reaction kinematics are customarily performed in units involving the

electronvolt In physics, an electronvolt (symbol eV, also written electron-volt and electron volt) is the measure of an amount of kinetic energy gained by a single electron accelerating from rest through an electric potential difference of one volt in vacu ...

, which derives from accelerator technology. The combination of this practical point with the theoretical relation makes the unit megaelectronvolt over the speed of light squared (MeV/''c''²) a convenient form in which to express nuclear mass. However, the numerical values of nuclear masses in MeV/''c''² are quite large (even the proton mass is ~938.27 MeV/c²), while mass excesses range in the tens of MeV/''c''². This makes tabulated mass excess less cumbersome for use in calculations. The 1/''c''² factor is typically omitted when quoting mass excess values in MeV, since the interest is more often energy and not mass; if one wanted units of mass, one would simply change the units from MeV to MeV/''c''² without altering the numerical value.

Example

Consider the

nuclear fission Nuclear fission is a reaction in which the nucleus of an atom splits into two or more smaller nuclei. The fission process often produces gamma photons, and releases a very large amount of energy even by the energetic standards of radio ...

of ²³⁶U into ⁹²Kr, ¹⁴¹Ba, and three neutrons. :²³⁶U → ⁹²Kr + ¹⁴¹Ba + 3 n The

of the reactant, ²³⁶U, is 236. Because the actual mass is , its mass excess is +. Calculated in the same manner, the respective mass excesses for the products, ⁹²Kr, ¹⁴¹Ba, and three neutrons, are , and , respectively, for a total mass excess of . The difference between the mass excess of the reactants and that of the products is , which shows that the mass excess of the products is less than that of the reactants, and so the fission can occur – a calculation which could have also been done with only the masses of the reactants. The mass excess can be converted into energy using = , and , yielding .

References

* *

External links

*{{NUBASE2016 Nuclear physics Nuclear chemistry