Question

We have $230g$ of substances with a half-life of $0.75years.$ How much will remain after $3$ years?

Answer 1

We first need to find out the number of half-lives that will pass in the given time of decaying. Then using the formula, we will get the fraction of substance remaining and on subtracting it from one; we will get the required solution. The formula we will use will be fraction of a substance remaining after $n$ half-lives $=\dfrac{1}{{{2}^{n}}}$

Complete answer:
Each time a period of time goes by that is equal to the half-life; there will be only $\dfrac{1}{2}$ of the previous amount of material remaining. In this case, three years represents $\dfrac{3}{0.75}=4$ half-lives.
The term half-life most commonly is used in nuclear physics to describe how long a stable atom survives. In biological terms it is also referred as biological half-life, whose conversion, doubling time is used to determine the time taken by a drug to spread.
Half-life is used for processes whose decays occur exponentially or approximately exponentially. There are processes in which the half-life changes and many often use the terms like first half-life, second half-life and so on for such types of processes. So, the amount that remains has been halved four times:
$\dfrac{1}{2}\times \dfrac{1}{2}\times \dfrac{1}{2}\times \dfrac{1}{2}={{\left( \dfrac{1}{2} \right)}^{4}}=\dfrac{1}{16}$
Thus we have, there is $\dfrac{1}{16}$ of the original amount, which is; $230\times \dfrac{1}{16}=14.375g$

Note:
Half-life has a probabilistic nature and denotes the time in which, on average, about half of entities decays. Suppose if we have only one atom, then it is not like after one half-life, one half of the atom will decay. So, we can say that half-life just describes the decay of distinct entities.