Stability of isotopes

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Isotopes and nuclear stability

Isotopes are atoms of the same element that have the same atomic number (number of protons) but with different mass numbers due to different number of neutrons.

In an atom there exist attractive forces among the particles found in the nucleus; these forces operate either between the protons, neutrons or between protons and neutrons. Isotopes can be classified as either stable or unstable depending on whether these attractive forces are balanced or not. A nuclide is said to be stable if the attractive forces between the particles is balanced otherwise the nuclide is unstable. Some elements have all their isotopes being unstable while others have some of their isotopes being stable.

Stable isotopes have stable nuclei and do not undergo radioactive decay, they are said to be non-radioactive active. These isotopes do not emit radiations. If an isotope is unstable, then it undergoes radioactive decay and is therefore said to be radioactive, such isotopes are called radioisotopes. It has been validly argued that the instability of a nucleus is due to excess protons or neutrons in nucleus of an atom. A radioactive nuclide will try to attains stability by ejecting a proton,neutron or by releasing energy. The factors that determine the stability of a nucleus are;

• Neutrons (n) to protons (p) ratio 
• Sum of protons and neutrons
• Binding energy- the energy needed to overcome the attractive forces between the particles in the nucleus. Nucleus with higher binding energy is more stable.

Radioactive nuclides with lower n/p ratio  will decay by emitting a positron, alpha particle or by electron capture. Those with higher n/p ratios decay by beta emission. Nuclides with n/p ratio of  1 are stable. Unstable nuclide due to relatively higher protons than neutrons will decay by having its neutrons converted to protons and electrons;

${}_0{}^1\mathrm{n}$$\to$${}_1{}^1\mathrm{p}$ $+$${}_{-1}{}^0\mathrm{e}$

on the other hand, if the neutrons are more than protons, the nuclide decays by a proton being converted to a neutron and a positron, a posittron is a particle similar to an eletron but only differing in charge. A positron has a charge of +1.

${}_1{}^1\mathrm{p}$$\to$${}_0{}^1\mathrm{n}$ $+$${}_1{}^0\mathrm{e}$

The equation; ${}_1{}^1\mathrm{p}$$+$${}_{-1}{}^0\mathrm{e}$$\to {}_0{}^1\mathrm{n}$ describes eletron capture.

In a plot of neutrons vs protons, stable nuclei always fall in the band of stability also known as valle,belt or zone of stability.

The concept of margic numbers

Magic number is the atomic numbers of the most stable. Radioisotopes that have magic numbers of protons or neutrons are stable. Below are categories of magic numbers;

Magic numbers: 2, 8, 20, 28, 50, 82, 126

Isotopes with even number of protons and neutrons are generally stable, additionally, those isotope with atomic numbers $<20$ 

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