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One of the interesting applications of radioactive decay is the technique of radioactive dating.Radioactive dating allows the estimation of the age of any object which was alive once, using the natural radioactivity of 6C14. It also allows the estimation of the age of geological samples using the decay of long lived nuclides.

All radioactive decays follow first order kinetics. Therefore, the half-life of a radioactive element is independent of the amount of sample. With the help of half-life values of a suitable radioisotope of an element, which is present in a rock, or in an artifact, the age of the rock and the artifact can be determined. This is called radioactive dating.

The principle of radioactive decay is applied in the technique of radioactive dating, a process widely used by scientist to determine the age of materials and artifacts.
"Radioactive dating is defined as the method of determining the age of biological or geological samples by using the radioactive technique."
There are many radioactive isotopes by which we can determine the age of a given object but the two most commonly used methods are :
2. Uranium dating

Radioactive isotopes can be used to help understand chemical and biological processes in plants and other living beings. This is true for the following two reasons.
1. Radioisotopes are chemically identical with other isotopes of the same element and will be substituted in chemical reactions.
2. Radioactive forms of the element can be easily detected by $\alpha$ and $\beta$ radiations emitted by them.

Therefore the characteristic property of the radioisotope, namely its radioactivity can act as a tag or label, which permits the fate of the element or its compound containing this element to be traced through a series of chemical or physical changes.

Some of the application of tracer techniques are discussed below.

1. Agriculture- To see how plants utilize a given fertilizer a solution of phosphate containing radioactive 32P is injected into the root system of a plant. Since 32P behaves identically to that of 31P a more common and non-radioactive form of the element, it is used by the plant in the same way. A GM counter is then used to detect the movement of the radioactive 32P throughout the plant.
2. Medicine- In medicine specific isotopes are used to observe the condition of specific organs. For example, a small amount of 133I is injected into the patient and kidneys are scanned with a radiation counter in the case of blocked kidney.
3. Industry - Radioisotopes are commonly used in industry for checking blocked water pipes, detecting leakage in oil pipes etc. If there is leakage at a particular place, the radiation detector will show activity at that particular place.

Radioactive dating is used in determining the age of a dead tree or for that matter any dead organic matter. The isotope used is carbon

$14(^{14}c_6)$.Carbon-14 has a half-life of 5730 years.

Carbon-14 is present in atmosphere as a result of cosmic - ray is produced by the collision of a neutron with a nitrogen-14 nucleus.

Carbon-14 is unstable and decays by beta emissions to nitrogen. Because of the constant production of carbon-14 and its radioactive decay, a small fractional abundance of carbon-14 is maintained in the atmosphere.

• Living plants, which use carbon dioxide from the atmosphere, also maintain a constant amount of carbon-14.
• However, once a plant is dead, the ratio of carbon-14 to carbon-12 starts decreasing by radioactive emission.
• Therefore, by meaning the radioactivity of carbon-14 in a wood, the age of the (approximate) can be determined.

Below you could see problem

### Solved Example

Question: A sample of wood from the core of an ancient pine tree shows a carbon-14 content that is 53% of the atmospheric carbon-14. What is the approximate age of the tree?
Solution:

It is assumed that level of carbon-14 in the atmosphere is constant. Since radioactive decay follows 1st order kinetics, the ratio carbon-14 in the wood and the carbon-14 in the atmosphere is given by

$\frac{[\ ^{14}c_{wood}]}{[{14}c]_{atmosphere}}$=$e^{-k_1t}$

or ,In$\frac{[\ ^{14}c_{wood}]}{[{14}c]_{atmosphere}}$=$-k_1t$=$\frac{-0.693}{t\frac{1}{2}}t$

or, ln[0.55]=$\frac{-0.693}{5730 Years}\times t$

t=$\frac{0.5978\times 5730}{0.693}$Years

=4943 Years

The age of the tree is 4943 years.

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