Page 24 - Radiochemistry and nuclear chemistry

Nuclei, Isotopes and Isotope Separation 13

In nuclear science it has been found convenient to use the atomic masses rather than
nuclear masses. The number of electrons are always balanced in a nuclear reaction, and the
changes in the binding energy of the electrons in different atoms are insignificant within the
degree of accuracy used in the mass calculations. Therefore the difference in atomic masses
of reactants and products in a nuclear reaction gives the difference in the masses of the
nuclei involved. In the next chapter, where the equivalence between mass and energy is
discussexl, it is shown that all nuclear reactions are accompanied by changes in nuclear
masses.
The mass of the nucleus can be approximated by subtracting the sum of the masses of the
electrons from the atomic mass. The mass of an electron is 0.000549 u. In kilograms, this
mass is 9.1094 x 10 -31. Since the neutral carbon atom has 6 electrons, the approximate
mass of the nucleus is 1.992 648 x 10-26-6 x (9.1094 x 10 -31) = 1.992 101 • 10-26 kg.
This calculation has not included the difference in the mass of the 6 extra electrons
attributable to the binding energy of these electrons. However, this binding energy has a
mass equivalence which is smaller than the least significant figure in the calculation.
The mass of a neutron is 1.008 665 u while that of the hydrogen atom is 1.007 825 u.
Since both neutrons and protons have almost unit atomic masses, the atomic mass of a
nuclide should be close to the number of nucleons, i.e. the mass number. However, when
the table of elements in the periodic system (Appendix I) is studied it becomes obvious that
many elements have masses which are far removed from integral values. Chlorine, for
example, has an atomic mass value of 35.453 u, while copper has one of 63.54 u. These
values of the atomic masses can be explained by the effect of the relative abundances of the
isotopes of the dements contributing to produce the observed net mass.
If an element consists of n I atoms of isotope 1, n 2 atoms of isotope 2, etc., the atomic
fraction x 1 for isotope 1 is defined as:

x I = nl/(n 1 + n 2 + ...) = nll~,n i (2.2)

The isotopic ratio is the ratio between the atomic fractions (or abundances) of the isotopes.
For isotopes 1 and 2, the isotopic ratio is

~1 = XllX2 = nl/n2; ~2 = x2lXl = n21nl (2.3)

The atomic mass of an element (or atomic weight) M is defined as the average of the
isotopic masses, i.e. M i is weighted by the atomic fraction x i of its isotope:

M= x 1M 1 + x 2 M 2 + ... = Ex iM i (2.4)

As an example, natural chlorine consists of two isotopes of which one has an abundance
of 75.77 % and an atomic mass of 34.9689 u and the second has an abundance of 24.23 %
and a mass of 36.9659 u. The resultant average atomic mass for the element is 35.453. The
atomic mass of copper of 63.546 can be attributed to the presence of an isotope in 69.17 %
abundance with a mass of 62.9296 u and of a second isotope of 30.83 % abundance and
64.9278 u. Atomic masses and abundances of some isotopes are given in Table 2.1.