Question

Carbon dating is best suited for determining the age of fossils if their age in years is of the order of
A. \[{10^3}\]
B. \[{10^4}\]
C. \[{10^5}\]
D. \[{10^6}\]

Answer 1

Hint: Carbon dating is a method used to determine the age of fossils or ancient objects by calculating the decaying \[_6{C^{14}}\] - the radioactive carbon which is absorbed as \[C{O_2}\] by the fossil when it was alive.

Complete step by step solution:
Carbon dating or radioactive dating is the method to find the age of the ancient object or fossil, by calculating the decay of radioactive carbon \[_6{C^{14}}\] in the fossils. It is also an important application of beta decay.

Every living organism absorbs carbon dioxide (\[C{O_2}\]) while it lives. The atmosphere has mostly\[_6{C^{12}}\], which is not radioactive and very less amount of radioactive carbon \[_6{C^{14}}\] (only \[1.3{\rm{x1}}{{\rm{0}}^{ - 12}}\% \]). The \[_6{C^{14}}\] in our atmosphere always decays but, cosmic rays from space constantly bombards the atoms in the atmosphere, which creates \[_6{C^{14}}\]and the ratio of it remains constant.

The half-life of \[_6{C^{14}}\] is 5730 years. Since, living organisms continuously absorb \[C{O_2}\] from the atmosphere, \[_6{C^{14}}\] also gets absorbed by them. But when they die, the absorption stops and \[_6{C^{14}}\] starts to decay. The ratio between \[_6{C^{14}}\] and \[_6{C^{12}}\] in the fossils decreases as time increases. Hence, carbon dating can be done on fossils by finding the difference in ratio of \[_6{C^{14}}\] and \[_6{C^{12}}\].
It is best for fossils of order of \[{10^4}\] years to be examined for carbon dating. For example, consider a fossil of 57,000 years, this can be calculated by carbon dating, we can write 57,000 as \[5.7{\rm{x1}}{{\rm{0}}^4}\] years which is of the order \[{10^4}\] years.

If the fossil is more than the order of \[{10^4}\]years older, then it is hard to calculate the age using carbon dating, since the age tracks destroy over time and it is hard to detect the tracks of the fossils.

Hence, the correct answer is option B.

Note: To find the age of a fossil using carbon dating, we need to find the rate of the decay using the formula \[R = {R_0}{e^{ - \lambda t}}\], where, \[{R_0}\] is the rate at t = 0, \[\lambda \] is the decay constant and t is the time taken for the decay.