Stability of Nuclei with
Respect to Neutron-proton Ratio
The nuclear stability is related to the neutron-proton
ratio. For different
elements, if the number of neutrons is plotted against the number of protons,
it is found that the elements with the stable nuclei lie within a region, known
as zone of stability or stability belt.
It is
important of note that
For element with atomic number
below 20, the n/p ratio is 1.as the atomic number increase, there is much
increase in the number of neutrons as compared to the number of protons. Due to
this, n/p goes on increasing and becomes 1.5 at the upper end of the belt.
When n/p ratio is more than
1.52, the element is radioactive and spontaneous disintegrate. Such elements
lie outside the zone of the stability.
Case-1
Consider
when n/p ratio is too high:
In such a case, the isotope
falls above the zone of stability. Such an isotope is unstable and tends to
come within the stability zone by the emission of β-ray. The
emission of β-particle increases the number of
proton by one unit. Due to this, n/p falls and comes to the stability belt.
For example, in 614C,
the n/p ratio is 8/6 or 1.3 and is unstable. Thus, it is found to disintegrate
so as to have n/p equal to one. 614Cž714N+-10e, For 714N,
the n/p value is 1.
Case-2
Consider
when n/p ratio is too low.
We know that there are no
naturally occurring elements with n/p less than one. Such examples with n/p less
than are one found in some artificial nuclides. In such cases, nucleus would
lie below the zone of stability. Such unstable nuclei tend to come within the
zone of stability by losing a positron.
611Cž511B++10e (In 511B, n/p=6/5=1.2)
Stability
on the basis of packing fraction
It has been
found that leaving some higher isotopes, majority of isotopic masses are less
than whole numbers, (For example, exact atomic mass of O is 15.99,that of Ag is
107.87 and so on). Aston explained these deviations in terms of mass defect and
binding energy. Thus, according to him, “Formation of nucleus protons and
neutrons is accompanied by mass defect with the release of energy called
binding energy”.
Binding
Energy
The difference between the actual
mass of an isotope of an element and the sum of the masses of proton, neutrons
and electrons present in it is called mass defect.
The mass defect is responsible
for binding the nucleons in the nucleus.
It can be converted into energy
by applying Einstein’s equation (E=mc2)
It is
called binding energy. Greater the value of binding energy per nucleon, greater
is the stability of nuclide.
The energy
equivalence of 1amu is calculated as below:
1amu=1.66×10-27 kg.
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