Page 56 - Radiochemistry and nuclear chemistry

Nuclear Mass and Stability 45

neutron orbital is transformed into a proton fitting into a vacant lower energy proton orbital;
see the example for A = 12 in Figure 3.2. These questions of nuclear forces and the energy
levels of nucleons are discussed more extensively in Chapter 1 1.

3.3. Mass defect

It was noted in Chapter 1 that the masses of nuclei (in u) are close to the mass number
A. Using the mass of carbon-12 as the basis (162C - 12 u), the hydrogen atom and the
neutron do not have exactly unit masses. We would expect that the mass M a of an atom
with mass number A would be given by the number of protons (L0 times the mass of the
hydrogen atom (MI.I) plus the number of neutrons (N) times the mass of the neutron (Mn),
i.e.

M a ~ ZM H + NM n (3.1)

For deuterium with one neutron and one proton in the nucleus, we would then anticipate
an atomic mass of

M H + M n = 1.007 825 + 1.008 665 = 2.016 490 u

When the mass of the deuterium atom is measured, it is found to be 2.014 102 u. The
difference between the measured and calculated mass values, which in the case of deuterium
equals -0.002 388 u, is called the mass defect (AMa):

AM A = M a -ZM H - N M n (3.2)

From the Einstein equation, E = mc 2, which is discussed further in Chapters 4 and 12,
one can calculate that one atomic mass unit is equivalent to 931.5 MeV, where MeV is a
million electron volts.

E= mc 2 = 931.5AM a (3.3)

The relationship of energy and mass would indicate that in the formation of deuterium by
the combination of a proton and neutron, the mass defect of 0.002 388 u would be observed
as the liberation of an equivalent amount of energy, i.e. 931.5 • 0.002 388 = 2.224 MeV.
Indeed, the emission of this amount of energy (in the form of 7-rays) is observed when a
proton captures a low energy neutron to form 2H. As a matter of fact, in this particular
ease, the energy liberated in the formation of deuterium has been used in the reverse
calculation to obtain the mass of the neutron since it is not possible to determine directly
the mass of the free neutron. With the definition (3.2) all stable nuclei are found to have
negative AM a values; thus the term "defect'.
In nuclide (or isotope) tables the neutral atomic mass is not always given, but instead the
mass excess (often, unfortunately, also called mass defect). We indicate this as ~,4 and
define it as the difference between the measured mass and the mass number of the particular
atom: