Question

The half-life for the radioactive decay of calcium $-17$ is $4.5$ days. How many half-lives have elapsed after $18$ days?

Answer 1

Hint : We know that the radioactivity refers to the phenomenon in which the substance decays by emission of radiation. Half-life is defined as the time taken by the material in which the number of undecayed atoms becomes half. A material containing unstable nuclei is considered radioactive.

Complete Step By Step Answer:
Half-life is the time for half the radioactive nuclei in any sample to undergo radioactive decay. For example, after two half-lives, there will be one fourth the original material remains, after three half-lives one eight the original material remains, and so on. Half-life is a convenient way to assess the rapidity of decay.
We can solve this problem by using the radioactive decay equation. According to the question, the half-life of the radioactive nucleus is $4.5$ days.
Four half-lives have elapsed and the radioactivity left is $\dfrac{1}{16}th$ of the initial value. Thus we have $4$ many half-lives have elapsed after $18$ days for half-life for the radioactive decay of calcium $-17$ .

Note :
Most of the candidates will take the ratio of the decay the same as in the question. In the question, the ratio indicates the amount of decayed substance. But, in the equation of radioactive decay, we required the amount that is remaining after the decay. So as per the question, we have to find the remaining nuclei after the decay from the ratio of decayed nuclei. Since it is a ratio, we can simply find the difference between the initial amount and decayed amount.