Decay Rate: Formula and Algorithm

Radioactive decay is the disintegration of the radioactive particles that leads to the formation of new types of particles from the parent radionuclide. Depending on ionisation type, there are three types of radioactive decay, alpha, beta and gamma decay and the half-lives of each of the types of decay differ in the values.

The decay rate varies for each of the types of decay because of the emission of different types of particles.

Radioactive decay-A detailed explanation

As the name says radioactive, radioactive decay is splitting up a radioactive element into some new ionised particles. 

The other common terms used for radioactive decay are radioactive disintegration, nuclear decay, radioactivity or nuclear disintegration as per the terms of nuclear physics.

Radioactive decay is a highly spontaneous process that occurs because of ionisations emitted during the process. Radioactive decay, a highly spontaneous process in nature, has remained unaffected from any physical entities such as pressure, temperature or chemical form. The exception to this is a few special cases in which these conditions might affect them directly or indirectly.

This non-dependency on all these physical conditions helps the scientists to analyse the radioactive element’s decay rate and the half-lives of that different type of radioactive decay without having to analyse the physical conditions of the radioactive elements. 

Elements in the periodic table that are prone to radioactivity due to their chemical composition and properties are known as radionuclides.

All the radioactive elements possess nucleons that consist of protons and neutrons. All the two particles of the nucleus, neutrons and protons, have two types of forces governing them. Those forces are electromagnetic because neutrons and protons are charged particles, with protons having a positive charge and a nuclear force that keeps these nucleons bound to the nucleus. 

In the process of radioactive disintegration, it is observed that it occurs when the nucleus is unstable. The unstable nucleus loses its energy and emits ionising particles and radiations, namely alpha, beta and gamma radiations. The element that possesses an unstable nucleus is called a radioactive element. The radioactive element typically breaks into 2 parts: 

One part of the Radioactive element is known as ‘Parent nuclide ‘. The other part breaks into ‘Daughter nuclide’, a transformed atom that is different from the parent radionuclide due to the bombardment. 

The daughter nuclide is also known as a decay product. This is because the atoms that are present in the parent nuclide goes on decaying and keeps changing into a new decay product. When the decay product reaches a stable stage where their radioactivity ceases, they stop decaying. 

In the majority of the radioactive elements, the radioactive decay happens only once, and after the first decay product is obtained, they become stable and are no longer found to be radioactive. 

Those radioactive elements that decay in more than a single step are known as ‘Radionuclides’ in nuclear physics. The chain of the series of decay products that are created to reach this stable state is known as the decay chain.

The series of each decay product is unique. All the decay products that are found to be within the decay chain are observed to be radioactive. It was noticed that the final product in the decay chain is only not radioactive and was stable. 

Some decay products in the decay chain are differently composed chemical elements. 

Every radionuclide element has a particular decaying rate that is known as the ‘Half-life of the particular element.’ 

The half-life of the radioactive element in an easy language is basically just the time that is needed for one half of the radioactive sample to undergo the process of decaying. The half-life of radioactive elements varies from millions of years to milliseconds. 

Types of Radioactive Decay 

The radioactive disintegration or the decaying of the radioactive elements results in the formation of different types of ionised particles known as alpha, beta and gamma particles.

The major types of radioactive decay that occur in nature are alpha, beta and gamma decay. 

The strong nuclear forces and the electromagnetic forces present between the nucleons govern the alpha and the gamma decay, while the beta decay is majorly governed by weak nuclear forces. 

Decay Rate:

The law of radioactive decay is based on the assumption that it is a purely statistical process.

Mathematically the expression is:

dN= λdt

where N= Number of radioactive nuclei

dN/dT= decrease in the no of radioactive nuclei per unit time

λ= probability of decay per nucleus per unit time

The radioactive disintegration or the decay rate is defined as the rate of disintegrations that occur per unit of time.

The decay rate formula can be expressed mathematically as:

A= -dN/dt= λ N

The decay rate algorithm can be expressed as: 

y = a( 1-r)t

here y= final amount of the radioactive element left

a= initial amount of the radioactive element

r= rate of decay

t= time taken for the decay

Conclusion

The decay rate and the decay constant in radioactivity depends upon how much of the radioactive particle has disintegrated within the stipulated time.