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The radioactive isotope of carbon is ${{\text{C}}^{14}}$.
A. True
B. False

Last updated date: 13th Jun 2024
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Hint: For this problem, we have to study all the isotopes of carbon and their physical and chemical properties so that we can compare all the isotopes of carbon. And state whether the given statement is true or false.

Complete step by step answer:
- In the question, we have to explain whether the given is true or not about the radioactive property of the isotope of carbon.
- As we know that carbon has the atomic number of 6 with atomic mass of 12g. The element is placed in the periodic table in group 14 and period 2.
- Now, we will study about the isotopes of carbon in brief.
- 15 isotopes of the carbon are known till now which have atomic mass 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21 and 22.
- But among all these isotopes, carbon with atomic mass 12 and 13 are considered as the most stable form due to which they cannot undergo the radioactive decay.
- Whereas the isotope of carbon with atomic mass 8 has the least half of about $2\text{ }\times \text{ 1}{{\text{0}}^{-21}}$s.
- Now, we will study about ${{\text{C}}^{14}}$ which is found naturally in the environment in trace amounts. The isotope is known for its radioactive properties.
- It is formed when the addition of neutron in the nitrogen atom take place i.e.
  ${}^{14}\text{N + }{}^{1}\text{n }\to \text{ C}_{6}^{14}\text{ + }{{\text{H}}^{1}}$
- ${{\text{C}}^{14}}$ is considered as the unstable isotopes as it undergoes beta decay through which it yields nitrogen i.e.
$\text{C}_{6}^{14}\text{ }\to \text{ }_{7}^{14}\text{N + }{{\text{e}}^{-}}$
Therefore, the given statement is true.
So, the correct answer is “Option A”.

Note: The isotope of carbon with atomic mass 14 is used for determining the age of carbonaceous material. Also, the ${{\text{C}}^{14}}$ isotope of carbon is the most long - lived isotope which has a half-life of about 5730 years.