Radioactivity

1. Most of the naturally occurring elements are stable. However, some of the isotopes of heavy elements such as thallium, bismuth, radium and uranium are unstable isotopes.
2. These unstable elements undergo stages of disintegration and emit radiations till a more stable nucleus is reached. Such elements are called radioactive isotopes.
3. Thus the radioactivity can be defined as a process of continuous and spontaneous (i.e. naturally without any external help) disintegration of radioactivity isotopes.
4. The radioactivity is accompanied by emission of alpha (α), beta (β), gamma (γ) radiations from the atomic nucleus.
5. It should be noted that the natural phenomenon of emitting radioactive waves (α, β and γ rays) by the unstable elements is called radioactivity and after the number of stages of successive disintegration, a stable isotope is formed.
6. Radioactivity is important since it provides the source of energy for small power devices and a source of radiation for use in medicines industry and research.

 Rate of Radioactive Decay and Half Cycle :

• The rate of radio-radiations from unit mass of unstable isotope is fixed till the stable isotope is formed. The time during which radioactive isotope becomes stable is called decay period of isotope.
• The rate of decay is the function of very large number of radioactive nuclei of an isotope present at that instant. Note that the radioactive decay does not depend on temperature, pressure, physical or chemical state of the matter except the very large number of radioactive nuclei present at a particular instant.
• If N is the number of radioactive nuclei of any one species at any time t, the decay rate is directly proportional to N, i.e.

-dN/dt = λ . N

Where, λ is called decay constant

∴ -dN/N = λ . dt

• The radioactive nature of different isotopes is measured by a time known as half life time (t/2). The rate of decay (-dN/dt) is also called as activity (A). Therefore,

A = -dN/dt = λ.N_o e^– λt

• The half life time of a particular isotope is defined as the time required for the number of active nuclei to decay to half of its number. Thus,

N/No = ½ = e ^{– λ} . t_1/2 ,
where t_1/2 is half life time

∴ t_1/2 = In(2)/λ
= 0.6931/ λ

• Therefore, the half life time is inversely proportional to decay constant 2. Figure shows the radioactive decay rates as a function of half life.

The half life times of few radioactive isotopes are listed below :