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:

56 mg

The correct answer is Option (4) → 56 mg

The radioactive isotope decay -

$N= N_0 \left( \frac{1}{2} \right)^{\frac{t}{T_{\frac{1}{2}}}}$

where:

$N_0$ = Initial amount of isotope = 64 mg

N = Remaining amount after time t = 24 days

$T_{\frac{1}{2}}$ = Half-life of isotope = 8 days

$N=64\left(\frac{1}{2}\right)^{\frac{24}{8}}$

$=64×\frac{1}{8}=8mg$

∴ Disintegrated amount = $N_0-N$

$=(64-8)mg=56mg$