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The half-life of a radioactive material is 100 s. Then after 5 min, in 8 gm material remaining active material is?
(A) 1 gm
(B) 4 gm
(C) 2 gm
(D) 1.5 gm

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Last updated date: 13th Jun 2024
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Answer
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Hint: To answer this question we should be implementing the formula of half-life. Once we find an answer we can use the formula which develops the relationship between the remaining amount and the original amount of the radioactive material. This formula will give us the required amount as an answer.

Complete step by step answer:
The time that is given in the question is 5 minutes. This can be written as t = 5 minutes or $t = 5 \times 60\operatorname{s} = 300s$.
So now we can write that the number of half-lives is n or we can say
$n = \dfrac{t}{{{t_{1/2}}}}$
Put the values in the above equation to get:
$\dfrac{{300}}{{100}} = 3$
Now we have to find the relationship between the remaining amount which is N and the initial amount which is \[{N_0}\].
The formula to find the relationship between N and \[{N_0}\]is given by:
\[N = {N_0}{\left( {\dfrac{1}{2}} \right)^n}\]
Solving the above relation, we get that:
\[N = \dfrac{{{N_0}}}{8},{N_0} = 8gm\]
So we can say that after 5 minutes the remaining amount or N will be 1 gm.

So, the correct answer is Option A.

Note: In this question we have come across the term half-life. For the better understanding we need to know the meaning of the term half-life. By half-life we mean the time that is required for any specific quantity to reduce to half of the initial value of itself. The half-life actually signifies how the atoms that form the quantity are unstable and they undergo a radioactive decay. From the value of the half-life we can find out the stability of the atoms forming a specific quantity.