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Radioactivity is a phenomenon where the nucleus of an unstable substance undergoes a series of decay. So to calculate the rate of decay. First, this term was introduced, which means that.
The decay constant of a radioactive nuclide is its probability of decay per unit time. Therefore, the number of parent nuclides P decreases with time t as dP/P dt = −λ. The energies used in binding protons and neutrons by the nuclear forces are 1,000,000 times stronger than those of the electronic and molecular forces. Therefore, decay probabilities and λ’s are insensitive not only to temperature and pressure but also to the strength of the bonds in which the radioactive element is held.
The decay constant, proportionality between the size of a population of radioactive atoms and the rate at which the population decreases because of radioactive decay. For a particular decay mechanism, The radioactive decay constant is usually represented by the symbol λ. The definition may be expressed by the equation.
P = λ Δt
Where P is the probability of a given unstable nucleus decaying in the time interval Δt, which must be much smaller than the half-life of the nuclide. If there are initially N nuclei in a sample, the average change in that number, ΔN, resulting from decays after time Δt is
ΔN = -λ N Δt
This is an equation involving the decay constant. The decay constant is mainly used to find the half-life of different elements.
Decay Rate:
The decay rate of a radioactive substance is characterized by the following constant quantities:
The half-life (t1/2) is the time taken for the activity of a given amount of a radioactive substance to decay to half of its initial value.
The mean lifetime (τ, “tau”) is the average lifetime of a radioactive particle before decay.
The decay constant (λ, “lambda”) is the inverse of the mean lifetime.
Although these are constants, they are associated with the statistically random behaviour of a group of atoms. Assumptions using these constants are less accurate for a small number of atoms. Notice that short half-lives go with large decay constants.
There are also time-variable quantities to consider:
- Total activity (A) is the number of decays per unit time of a radioactive sample.
- The number of particles (N) is the total number of particles in the sample.
- Specific Activity (SA) number of decays per unit time per amount of substance of the sample at the time set to zero (t = 0). “Amount of substance” can be the mass, volume, or moles of the initial sample.
Where is the decay constant used?
Since the decay rate is constant, one can use the radioactive decay law and the half-life formula to find the age of fossils, which is known as radioactive carbon dating. One of the forms of radioactive dating is radiocarbon dating. Carbon 14 (C-14) is produced in the upper atmosphere through the collision of cosmic rays with atmospheric N-14.
This radioactive carbon is incorporated in plants and respiration and eventually with animals that feed upon plants. The ratio of C-14 to C-12 is 1:1012 within plants as well as in the atmosphere. This ratio, however, increases upon the death of an animal or when a plant decays because there is no new income of carbon 14. By knowing the half-life of carbon-14 (which is 5730 years), one can calculate the rate of disintegration of the nuclei within the organism or substance and thereby determine its age. It is possible to use other radioactive elements in order to determine the age of nonliving substances as well.
Conclusion
We can conclude by saying that the decay constant is a very important parameter used to calculate the radioactivity of any material, and it gives more idea of the properties of the given radioactive material and also we can find the half-life of different materials. This helps determine the rate at which these materials degrade themselves to attain stability. This property is useful for research and experimenting purposes.
