The half life of a radioactive isotope of Iodine 131 is 8 days. Starting with 64 mg of the Iodine 131, the amount that disintegrates in 24 days is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 56 mg
In each half-life the amount of a radioactive sample left undecayed falls to half. The number of half-lives in 24 days is
\( \displaystyle n = \frac{t}{T_{1/2}} = \frac{24\,\mathrm{days}}{8\,\mathrm{days}} = 3 \)
\( \displaystyle N = \frac{N_0}{2^{n}} = \frac{64\,\mathrm{mg}}{2^{3}} = 8\,\mathrm{mg} \)
This is the amount left. The amount that has disintegrated is the rest.
\( 64 - 8 = 56\,\mathrm{mg} \)