JEE Main & Advanced Chemistry Surface & Nuclear Chemistry / भूतल और नाभिकीय रसायन Nuclear Stability

Nuclides can be grouped on the basis of nuclear stability,  i.e. stable and unstable nucleus. The most acceptable theory about the atomic nuclear stability is based upon the fact that the observed atomic mass of all known isotopes (except hydrogen) is always less from the sum of the weights of protons and neutrons present in it. Electron (b- particle) from a radioactive nucleus may be regarded as derived from a neutron in the following way,

\[Neutron\to Proton+Electron\]

Similarly, photons are produced from internal stresses within the nucleus.

The stability of nucleus may be discussed in terms of any one of the following,

(1) Nuclear Binding Energy and Mass defect : It is observed that atomic mass of all nuclei (except hydrogen) is different from the sum of masses of protons and neutrons. The difference is termed mass defect.

Mass defect = Total mass of nucleons – obs. atomic mass

The mass defect is converted into energy. This energy is called the binding energy. This is the energy required to break the nucleus into is constituents (p and n).

Binding energy = Mass defect \[\times 931MeV\]

The stability of the nucleus is explained on the value of binding energy per nucleon and not on the basis of total binding energy . Binding energy per nucleon is maximum (8.7 MeV) in the case of iron (56). The value of binding energy per nucleon can be increased either by fusion of lighter nuclei or fission of heavier nuclei.

Value of binding energy predicts the relative stability of the different isotopes of an element. If the value of binding energy is negative, the product nucleus or nuclei will be less stable than the reactant nucleus. Thus the relative stability of the different isotopes of an element can be predicted by the values of binding energy for each successive addition of one neutron to the nucleus.

\[_{2}H{{e}^{3}}+{{\,}_{0}}{{n}^{1}}{{\xrightarrow{{}}}_{2\,}}H{{e}^{4}}+20.5MeV\]

 \[_{2}H{{e}^{4}}+{{\,}_{0}}{{n}^{1}}\xrightarrow{{}}{{\,}_{2}}H{{e}^{5}}-0.8MeV\]

Therefore, \[_{2}H{{e}^{4}}\] is more stable than \[_{2}H{{e}^{3}}\] and \[_{2}H{{e}^{5}}\].

(2) Packing fraction : The difference of actual isotopic mass and the mass number in terms of packing fraction is defined as,

\[\text{Packing fraction}=\frac{\text{Actual isotopicmass}-\text{Mass number}}{\text{Mass number}}\times {{10}^{4}}\]

The value of packing fraction depends upon the manner of packing of the nucleons with in the nucleus. Its value can be negative, positive or even zero. A negative packing fraction generally indicates stability of the nucleus.

In general, lower the packing fraction, greater is the binding energy per nucleon and hence greater is the stability. The relatively low packing fraction of He, C and O implies their exceptional stability, packing fraction is least for Fe  (negative) and highest for H  (+78).

 (3) Magic number : Nucleus of atom, like extra-nuclear electrons, also has definite energy levels (shells).

Nuclei with 2, 8, 20, 28, 50, 82 or 126 protons or neutrons have been found to be particularly stable with a large number of isotopes. These numbers, commonly known as Magic numbers are defined as the number of nucleons required for completion of the energy levels of the nucleus. Nucleons are arranged in shells as two protons or two neutrons (with paired spins) just like electrons arranged in the extra-nuclear part. Thus the following nuclei \[_{2}H{{e}^{4}},{{\,}_{8}}{{O}^{16}}{{,}_{20}}C{{a}^{40}}\] and \[_{82}P{{b}^{208}}\] containing protons 2, 8, 20 and 82 respectively (all magic numbers) and neutrons 2, 8, 20 and 126 respectively (all magic numbers) are the most stable.

       Magic numbers for protons :   2, 8, 20, 28, 50, 82,114

       Magic numbers for neutrons : 2, 8, 20, 28, 50, 126, 184, 196

When both the number of protons and number of neutrons are magic numbers, the nucleus is very stable. That is why most of the radioactive disintegration series terminate into stable isotope of lead (magic number for proton = 82, magic number for neutron = 126).  Nuclei with nucleons just above the magic numbers are less stable and hence these may emit some particles to attain magic numbers.

(4) Neutron-proton ratio or causes of radioactivity    It has been found that the stability of nucleus depends upon the neutron to proton ratio (n/p). If we plot the number of neutrons against number of protons for nuclei of various elements, it has been observed that most of the stable (non-radioactive) nuclei lie in a belt shown by shaded region in figure this is called stability belt or stability zone. The nuclei whose n/p ratio does not lie in the belt are unstable and undergo spontaneous radioactive disintegration.  

It has been observed that,    

(i) \[n/p\] ratio for stable nuclei lies quite close to unity for elements with low atomic numbers (20 or less) but it is more than one for nuclei having higher atomic numbers. Nuclei having \[n/p\]ratio either very high or low undergo nuclear transformation.

(ii) When \[n/p\]ratio is higher than required for stability, the nuclei have the tendency to emit \[\beta -\]rays i.e., a neutron is converted into a proton.

(iii) When \[n/p\]ratio is  lower than required for stability, the nuclei increase the ratio, either by emitting \[\alpha -\]particle or by emitting a position or by K-electron capture.