Page 219 - Instant notes

Nuclear structure 205

17 35 34.9688528 75.77
17 37 36.9659026 24.23

binding energy must be supplied to separate a nucleus into its constituent nucleons.

Relative atomic mass

The relative atomic mass of an individual atom is the atomic mass relative to 1/12th the
mass of an atom of carbon-12. By definition a relative atomic mass has no units. Since a
natural sample of an element may contain a mixture of different isotopes, each having
different atomic masses, the relative atomic mass of an element is equal to the weighted
average of the naturally occurring isotopes. For example, chlorine has two naturally
occurring isotopes, and , with relative atomic masses of 34.96885 and
36.96590, respectively. (The relative atomic masses are not whole numbers because
atomic masses of protons and neutrons are not whole numbers and mass is converted to
binding energy.) In a natural sample of chlorine the and isotopes are present in
the proportions 75.77% and 24.23%, respectively, so the overall relative atomic mass for
natural chlorine is:
0.7577×34.96885+0.2423×36.96590=35.453

Therefore one mole (or Avogadro’s number) of a natural sample of chlorine atoms has a
mass of 35.453 g.

Nuclear stability

The binding energy, E b, of a nucleus provides an indication of the total stability of the
nucleus relative to the individual constituent nucleons. A more useful indicator of relative
nuclear stability is the binding energy per nucleon which is the value of the binding
energy of a particular nucleus divided by the total number of nucleons, A, in the nucleus.
The value of E b/A as a function of A is plotted in Fig. 1. After a sharp increase for the
lightest elements the binding energy per nucleon remains fairly constant at around 8 MeV
for A≥16 (elements heavier than O in the periodic table), which reflects the attainment of
maximum packing around each individual nucleon once a minimum number have come
together. The shallow maximum in E b/A for values of A≈56 (elements around Fe in the
periodic table) indicates that these isotopes have enhanced relative stability. Because of
this maximum, the fission (splitting) of a heavy nucleus into a pair of nuclei of
approximate mass 56 is a process that releases energy. Similarly, the fusion (joining) of
two of the lightest nuclei is also a process that releases energy.