Radioactivity is a phenomenon through which energy is produced from the spontaneous reactions of less stable nuclei. They have the characteristics such as the liberation of excess energy and spontaneous, in nature, first-order reactions. The investigation and study of radioactive decay is not dependent upon the environmental conditions. The disintegration rate is directly proportional to the number of atoms and activity for any radioactive element. It is measured about atoms per unit time. Radioactive processes are very harmful and bring hazardous effects to the environment and living beings. This article will help you in understanding the decay rate.

Radioactivity

It is a phenomenon in which stable atomic nuclei are formed by a spontaneous disintegration of least or less stable atomic nuclei.

Features of radioactivity reactions

• Release of a tremendous amount of energy (exoergic),
• Random in nature (follows spontaneity),
• A kind of first-order process, and
• Utilisation of a small amount of mass for producing energy.

Kinds of radioactive decay

• Alpha emission
• Beta emission
• Positron emission
• Electron capture
• Gamma emission

Decay rates

As there is a loss of unstable particles that are very small in size and the amount of energy released is very high in nature compared to size, it is difficult to trace radioactive decay. 

 In other words, the investigation and study of radioactive decay do not depend upon environmental conditions. The disintegration rate is directly proportional to the number of atoms and activity for any radioactive element. It is measured with regard to atoms per unit time.

 Let ‘A’ be the rate of disintegration and ‘N’ as the number of radioactive atoms,

Then, the interrelationship is represented by the given equation below,

 A∝N

 In mathematical terms,

 A = λN, in which, A is the total activity and is the number of disintegration per unit time, N is the total number of particles, and λ is the decay constant.

Chemical Kinetics & Rate of Decaying

With regard to chemical kinetics, the reactions under the radioactive decay are first-order reactions, and the reaction is directly interlinked with the concentration of one reactant. However, it does not depend on any other factor. 

Also, a type of exponential decay function that implies that the more the number of atoms, the faster the process. As per the mathematical calculations, the relationship between quantity and time for any radioactive reaction is represented below,

 dN/dt = −λN

 dN(t)/dt = −λN

 By integrating both sides of the equation,

 lnN(t) = −λt + C

 where C  represents the constant of integration.

N(t)  is the amplitude of  N  after the lapse of time t.

λ  is the decay rate constant, and its unit is  time-1.

The Decay rate for half-life

In the process of radioactivity, the duration of time required by atomic nuclei of any radioactive isotope to decay by its one-half amount from its initial stage is called the half-life.

In other words, the half-life for a radioactive isotope is defined as the time taken to decay the one-half portion of the radioactive isotope.

The given equation represents the quantitative interlinkage between the number nuclei at time zero N0 and the number N after an interval of time t,

N = N0e−λt,

where e=2.71828 is shown as the base of the natural logarithm, and

λ represents the decay constant for the nuclei.

According to the equation, the value of λ is higher if the half-life span is shorter.

The equation below shows the relationship between decay constant (λ) and half-life (t),

λ = ln (2)/t1/2 ≈ 0.693/t1/2

Furthermore, for understanding this relationship,

Let t =  t1/2 and put this in the equation

N = N0e−λt,

And, we will get,

N = N0e−λt = N0e−0.693 = 0.500N0

By dividing this with two, we will get the integral numbers of half-lives again and again. For instance, if we divide N by 2 ten times after ten half-lives. 

Conclusion

Radioactivity processes are sudden and energy liberated processes in nature. The duration of time required by atomic nuclei of any radioactive isotope to decay by its one-half amount from its initial stage is called the half-life. It is a very useful method to assess the rate of the decay process. The half-life concept is also applicable to other subatomic particles related to particle physics. The investigation and study of radioactive decay do not depend upon environmental conditions. The disintegration rate is directly proportional to the number of atoms and activity for any radioactive element. It is measured with regard to atoms per unit time. Radioactive processes are very harmful and bring hazardous effects to the environment and living beings.