On this page, we discuss the stability of nuclides in terms of their masses. The discussion applies to both stable and unstable nuclides.
In order to discuss the instability of nuclides, we look at their masses. There are several ways to look at their masses. Masses of nuclides can be compared to either their components (hydrogen atoms and neutrons) or some other standard such as 12C.
The following are some of the ways we look at the masses of nuclides.
|Binding energy (MeV)|
of some nuclides
Thus, binding energy is zero for hydrogen, as it is one of the standard. All other nuclides have positive BE. the binding energy for D, He and 238U are calculated below:
BE = (2*1.007825 + 2*1.008665 - 4.002603) 931.481 MeV = 28.30 MeV
BE = (92*1.007825 + 146*1.008665 - 238.0289) 931.481 MeV = 1822.06 MeV
These examples and the binding energy given in the Table support a general statement. The more nucleons packed into a nucleus, the more energy is released, and thus the higher the binding energy. Therefore binding energy is not a good indicator of nuclide stability.
|Average binding energy, BEave|
(MeV) of some nuclides
On the other hand, heavier nuclides than 58 also have lower average binding energies. When nuclides such as 235U and 239Pu split into two pieces (fission) of lighter nuclides, fission energy is also released.
The binding energies of both light and heavy nuclides are lower than nuclides with mass number around 58-60, as shown in a plot of the binding energy as a function of mass number.
Fission and fusion energy comes from the difference in binding energy of nuclides of different masses. The above plot is taken from Nuclear Binding Energy.
|Comparison of Masses for Some Nuclides|
|Nuclide||Mass, amu||Mass excess|
The mass excesses of some nuclides are compared with the negative average binding energy (-BEave), and binding energy (-BE) in the table here.
Since hydrogen and neutron are used as the standard for binding energy, and 12C is the standard for mass excess, binding energy cannot be converted directly to mass excess. However, the two are related. Nuclides with low mass excesses also have low binding energy.
Mass excess can be used to evaluate the energy of decay. The mass excesses of 40Sc21 and 40Ca20 are -20.527 and -34.847 MeV respectively. Thus the energy of the decay process
Of course, 1.02 MeV (2 times the rest mass of an electron) has to be spent in producing the positron-electron pair in positron decay, but not in electron capture. This example illustrates the fact that the mass excess not only vary as mass number A changes, it also vary as the atomic number Z changes for isobars.
|Mass excess of isobars|
with mass number 123
Since Te52 and Te52 have the lowest mass excesses, these are stable isobars among them.
For unstable nuclides, handbooks usually give mass excesses rather than their masses.