Question

The half life ${C^{14}}$is 5730 years. What fraction of ${C^{14}}$will remain unchanged after 5 half lives?
(A) $\dfrac{1}{{16}}$
(B) $\dfrac{1}{8}$
(C) $\dfrac{1}{{64}}$
(D) $\dfrac{1}{{32}}$

Answer 1

Hint: To solve this question we should have the knowledge about the formula of calculating the half lives. In the formula we will come across the requirement for the number of years. This value is already present in the question. Once we put the value we will get the required answer for this question.

Complete step by step answer:
We should know that the fraction that is decayed after n half lives is ${\dfrac{1}{2}^n}$.
Here n is the number of years. As per this question the value of n is 5. So now we have to put the value of n in the above expression to get:
${\left( {\dfrac{1}{2}} \right)^5} = \dfrac{1}{{32}}$
So we can say that the $\dfrac{1}{{32}}$ fraction of ${C^{14}}$ will remain unchanged after 5 half lives.

Hence the correct answer is option D.

Note: In this question we have come across the term half life. For a better understanding we should be knowing the meaning of this term. So by half life we the amount of time that is taken by the atoms of a given amount of a radioactive substance to disintegrate. We should also know that half life is also known as biological half life. This is known as so because half life also signifies the amount of time that is taken for an activity of a substance in the body to lose half of the initial effectiveness.
The radioactive compound that is mentioned in this question is carbon-14 which is a radioactive isotope of carbon. The isotope has an atomic nucleus which contains 6 protons and 8 neutrons.