Discussion
In case of radioisotopes the activity reduces to ........................ of initial value after 2 half lives.
Answer: C
After two half-lives the activity falls to 1/4 of the initial activity.
Each half-life halves the activity:
\[ \begin{aligned} A &= A_{0}\left(\tfrac{1}{2}\right)^{n} \\ &= A_{0}\left(\tfrac{1}{2}\right)^{2} = \tfrac{1}{4}A_{0} \end{aligned} \]
One half is the value after a single half-life. One third and one sixth come from treating the decay as linear or dividing by the number of half-lives, which is not how exponential decay works.
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