Question

A radioactive substance has a half-life of 1 year. The fraction of this material, that would remain after 5 years will
A. \[\frac{1}{{32}}\]
B. \[\frac{1}{5}\]
C. \[\frac{1}{2}\]
D. \[\frac{4}{5}\]

Answer 1

Hint: Half-life is the time required for half of the original value of a certain quantity of a radioactive element to decay. It is indicated by \[{T_{1/2}}\] ​. In this question, we need to find the fraction of a radioactive substance that remains after 5 years. So, the below-mentioned formula is used to find a fraction of a radioactive substance.

Formula used:
\[\frac{N}{{{N_0}}} = {(\frac{1}{2})^n}\]
where n is the Number of lives, T is the Total time, and \[{T_{1/2}}\]is half-life.



Complete answer:
Given,
Total time T=5
Half-life \[{T_{1/2}}\]=1
n=?
Number of Lives \[n = \frac{T}{{{T_{1/2}}}}\]
\[n = \frac{5}{1}\]
Hence, n=5
We know that,
\[\frac{N}{{{N_0}}} = {(\frac{1}{2})^n}\]
=\[{(\frac{1}{2})^5}\]
=\[\frac{1}{{32}}\]
Hence in 5 years the \[{(\frac{1}{{32}})^{th}}\] substance will remain.
Therefore the correct answer is Option A.



Note: Students should know the formula of the number of lives. They should be aware of the total time and half time in the given question. If they changed both, they would get the wrong answer.