Mass excess

Themass excessof anuclideis the difference between its actual mass and itsmass numberindaltons.It is one of the predominant methods for tabulating nuclear mass. The mass of anatomic nucleusis 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 constituentprotonsandneutrons.Thus, the mass excess is an expression of thenuclear binding energy,relative to the binding energy pernucleonofcarbon-12(which defines the dalton). If the mass excess is negative, the nucleus has more binding energy than¹²C, and vice versa. If a nucleus has a large excess of mass compared to a nearby nuclear species, it canradioactively decay,releasing energy.

Energy scale of nuclear reactions

The¹²C 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 reactionkinematicsor decay. Only a small fraction of the total energy that is associated with an atomic nucleus bymass–energy equivalence,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 theelectronvolt,which derives fromacceleratortechnology. The combination of this practical point with the theoretical relationE=mc²makes the unit megaelectronvolt over the speed of light squared (MeV/c²) a convenient form in which to express nuclear mass. However, the numerical values of nuclear masses in MeV/c²are quite large (even the proton mass is ~938.27 MeV/c²), while mass excesses range in the tens of MeV/c².This makes tabulated mass excess less cumbersome for use in calculations. The 1/c²factor 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/c²without altering the numerical value.

Example

Consider thenuclear fissionof²³⁶U into⁹²Kr,¹⁴¹Ba, and three neutrons.

²³⁶U →⁹²Kr +¹⁴¹Ba + 3 n

Themass numberof the reactant,²³⁶U, is 236. Because the actual mass is236.045563Da,its mass excess is +0.045563Da.Calculated in the same manner, the respective mass excesses for the products,⁹²Kr,¹⁴¹Ba, and three neutrons, are−0.073843Da,−0.085588Daand3 ×0.008665Da= +0.025994Da,respectively, for a total mass excess of−0.133437Da.The difference between the mass excess of the reactants and that of the products is0.179000Da,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 using1 Da=931.494MeV/c²,andE=mc²,yielding166.737 MeV.

References

• Krane, K. S (1987).Introductory Nuclear Physics.John Wiley & Sons.ISBN0-471-80553-X.
• Tipler, P. A; Llewellyn, R. A. (2004).Modern Physics.W. H. Freeman and Company.ISBN0-7167-4345-0.

External links

• Audi, G.; Kondev, F. G.; Wang, M.; Huang, W. J.; Naimi, S. (2017)."The NUBASE2016 evaluation of nuclear properties"(PDF).Chinese Physics C.41(3): 030001.Bibcode:2017ChPhC..41c0001A.doi:10.1088/1674-1137/41/3/030001.