Question

A human body requires the $0.01M$ activity of radioactive substance after $24h$. Half-life of radioactive substance is $6h$,Then injection of maximum activity of radioactive substance that can be injected is:
A.$0.08$
B.$0.04$
C.$0.16$
D.$0.32$

Answer 1

We first need to discover the quantity of half-life that will sit back from rotting. At that point utilizing the formula, we will get the part of substance remaining and by taking it away from one, we will get the necessary solution.
Formula used:
Division of a substance staying after $n$ half-lives $= \dfrac{1}{{{2^n}}}$

Complete step by step answer:
Half-life ( ${t_{1 / 2}}$) is the time needed for an amount to decrease to half of its underlying worth. The term is regularly utilized in atomic material science to portray how rapidly flimsy particles go through radioactive rot or how long stable molecules endure. The term is additionally utilized all the more by and large to describe any kind of remarkable or non-outstanding rot. For instance, the clinical sciences allude to the organic half-life of medications and different synthetic compounds in the human body.
We have been given the half-life of the radioactive substance, ${t_{\dfrac{1}{2}}} = 6$ minutes.
Furthermore, we need to discover the level of substance rotted following $24$ minutes.
Thusly, number of half-lives passed, $n = \dfrac{{24}}{6} = 4$
Remaining activity $= 0.01M$ after $24h$
$Remaining{\text{ }}activity = {\text{ }}Initial{\text{ }}activity{\text{ }} \times {\left( {\dfrac{1}{2}} \right)^n}$
Thus, $0.01 = {\text{ }}Initial{\text{ }}activity{\text{ }} \times {\left( {\dfrac{1}{2}} \right)^4}$
Initial activity $= 0.01 \times 16 = 0.16{\text{ }}M$
Thus, the right choice is ($C$).

Additional Information:
The term half-life most generally is utilized in atomic physical science to portray how long a steady iota endures. In natural terms it is likewise alluded to as an organic half-life, whose transformation, multiplying time is utilized to decide the time taken by a medication to spread.
Half-life is utilized for measures whose rots happen dramatically or around dramatically. There are measures in which the half-life changes and numerous frequently utilize the terms like first half-life, second half-life, etc. for such sorts of cycles.

Note:
Half-life has a probabilistic character and represents the time in which, on mean, about half of entities decays. Assume in the event that we have just a single molecule, at that point it isn't cared for after one half-life, one portion of the iota will rot. Thus, we can say that half-life simply depicts the rot of unmistakable elements