Radioactivity-Half-life

Radioactivity is a phenomenon through which an amount of energy is produced from the spontaneous reactions of less stable nuclei. Half-life is a very important and useful feature of any radioactive decay. The half-life for a radioactive isotope is defined as the time taken to decay the one-half portion of the radioactive isotope. 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, it is related to particle physics. Through this article, the concept of a half-life will be clear.

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Definitions & understanding

Radioactivity: 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.

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

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

For instance, Cobalt-60, a radioactive isotope used in the radiotherapy procedure, has a half-life of 5.26 years. Hence, after the half-life, the sample amount will decrease to its half amount of the initial stage.

Half-life is a very important and useful feature of any radioactive decay. It is constant for any specific radioactive isotope; it does not depend upon any other conditions and is independent of the amount of isotope at the beginning stage. The value of radioactive isotope does not depend upon the moment chosen; also, the duration of time taken will always be the same. For any radioactive nuclei, the range of duration of a half-life is from a second to billions of years.

 In the world, there are three natural nuclei of unstable isotopes that have half-lives more than a billion years and they are Potassium-40, uranium-238, and thorium-232. There is a direct relationship between the time taken and radioactivity of any element, i.e., the radioactivity will be lesser in case of a longer duration of half-life. For example, for any isotope that has a half-life of a million, then their radioactivity will be less than a million times.

Significance

Half-life plays important role in the area of radioactive isotope; these are mentioned below;

1. It helps in identifying the exact dates of artifacts (in calculating the age of any substance).

2. It helps in the calculation of time for storing any radioactive waste until they become safe.

3. It also supports the doctors in analysing and use of safe radioactive tracers.

4. It is a very useful method to assess the rate of the decay process.

However, it is different from the mean life of any radioactive nucleus.

Range

The range of half-life is varied for different radioactive isotopes,

Shorter duration is 10-23 seconds for unstable nucleus and they have very weak nuclear forces, and more than 1016 years for the least unstable nucleus and they have far better nuclear forces within them. 

The strength of the forces in any radioactive isotope depends upon the combination of neutrons and protons. In many cases of unstable nuclei of atoms, the half-life is represented as a specific property. The rate of the process is slower in the case of gamma decay and faster in alpha and beta decay. The range of half-life in beta decay is higher from the 100th of a second and, in alpha decay, higher from 1 million of a second. However, in the case of gamma decay, it is very difficult to measure the half-life duration due to a shorter duration (between 10-14 seconds).

The half-life concept is also applicable to other subatomic particles, it is related to particle physics.

Exponential equation

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 span of half-life is shorter.

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

λ = ln (2) t1/2 ≈ 0.693 t 1/2

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 = 0.500 N0

By dividing this with 2 again and again, we will get the integral numbers of half-lives. For instance, after ten half-lives, if we divide N by 2 ten times. This will reduce the N by 1024 times.

This exponential relationship can be used at any arbitrary time.

Conclusion

Hence, radioactivity processes are very 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, it is related to particle physics.