Radioactivity decay law explained

Radioactivity is a phenomenon through which an amount of energy is produced from the spontaneous reactions of less stable nuclei. They have characteristics such as the liberation of excess amounts of energy and spontaneous, in nature, first-order reactions. Radioactive decay law states that the number of nuclei of any radioactive matter undergoing the decaying process per unit time is directly proportional to the total number of nuclei in the sample material.

Radioactivity 

Definition: The process of radioactivity was discovered by A.H. Becquerel in 1896. 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.

Every radioactive species is characterised by its half-life because radioactive reactions come under the first-order reactions. In the process of radioactive decay, an excess amount of energy is produced, generally ten lakhs times more than the amount of energy produced during an exothermic reaction. This process is not affected by any parameters such as temperature and pressure, as it is a nuclear reaction instead of an electronic phenomenon. 

However, this can also be slightly altered by increasing the pressures on some radionuclides. The chemical symbol of the element shows a radioactive (unstable element).

Measurement unit 

The SI unit of radioactivity is Curie, named after Marie Curie, and it is defined as the 37 billion integration per second (dis/sec), i.e., 3.700 × 1010 disintegrations per second. Recently, a new unit is also used to measure the radioactive reaction is the Becquerel (1bq=1dis/sec).

Subunits of Curie are Pico Curie, microCurie, nano Curie and milli Curie, and its larger units are Kilo Curie and Mega Curie. Generally, PicoCurie to nano Curie is used for measuring the very low levels of energy work. In usual energy work, like nuclear activation analysis studies and radiotracer, microCurie are used. Radioactive related reactions are very harmful to the environment and living beings hence special precautions must be taken to avoid any mishappening.

The causes for the radioactivity are as follows;

●  Natural causes,

●  Atomic bomb explosion, and

●  Fusion- and fission-related reactions from atomic reactor operations.

Types of radioactive decay

There are three types of radioactive decays in nature:

• Alpha decay (α-decay)- in this helium nucleus is emitted out.

• Beta-decay (β-decay)- in this process, electrons and positrons are emitted out.

• Gamma decay (γ-decay)- in this photon is emitted out.

Let’s learn more about the decay laws of radioactivity, 

Laws of Radioactive Decay of Elements

According to this law, the number of nuclei of any radioactive matter that undergoes the decaying process per unit time is directly proportional to the total number of nuclei in the sample material.

In other words, this law states that the rate of decaying of the nucleus of any radioactive material is independent of time.

Thus,

N represents the total number of nuclei and ΔN represents the number of nuclei undergoing the decaying process at a time Δt

Then,

ΔN/ Δt ∝ N

Or, ΔN/ Δt = λN … (1), in this λ is a decay/disintegration constant.

Change in the number of nuclei in the sample is,

dN = – ΔN at a time Δt.

Hence, change of decaying per unit time of N is,  

dN/dt = – λN

Or, dN/N = – λ dt

After integrating both sides,

We get, N – ln N0 = – λ (t – t0), where N0 represents the number of radioactive nuclei in the sample at a time t0

N represents the number of radioactive nuclei at a consequent time t.

And by putting, t0=0

Or, N(t) = N0e– λt 

The Law of Radioactive decay is represented by an equation.

The fundamental laws of radioactive decay depend upon the decay, which shows the conversion of the parent nucleus to a daughter nucleus is presented in the statistical process. The disintegration of a radioactive element is an essential property that remains constant at any time.

Decay rate refers to the disintegration of a number of radioactive elements per unit time,

A = dN / dt = N (1)

Through integration and boundary conditions on both sides in the beginning

t = 0 and N = N0

we get,

 ln(N/N0) = t

and exponential decay exponent,  

N = N0e-t ,from this equation, 

We get, 

A = A0e-t, in which A represents the age of the material)

Conclusion

Radioactivity is a spontaneous process in which an amount of energy is released from the less stable nuclei. The process of radioactivity was discovered by A.H. Becquerel in 1896. The process of radioactive decay is critical for many human activities, from medicinal to electrical production purposes and in astronomy. Radioactive decay law states that the number of nuclei of any radioactive matter undergoing the decaying process per unit time is directly proportional to the total number of nuclei in the sample material.