The half-life of a certain radioisotope is 8 days. How much (mass) of a 80 mg sample will remain after 24 days?

10 mg of the sample will be remaining after 24 days.

Explanation:

Half life time of any radioactive element is defined as the time required to decay half of the initial concentration of radioactive element. Thus, if here is given that the half life time of a certain radioisotope is 8 days. Then, this means in 8 days, the concentration will be halved. So as here the concentration is given as 80 mg, then after 8 days, it will be reduced to 80/2 = 40 mg.

Then again after 8 days, it will be reduced to 40/2 = 20 mg. So now, totally 16 days are over. After this, if again 8 days are spent, then the reduced concentration will be 20/2=10 mg.

So, 1st 8 days, the concentration reduced from 80 mg to 40 mg (80/2).

Then, in the second 8 days interval which is total 16 days, the concentration of 40 mg will reduce to 20 mg (40/2).

Then again 8 days will add up to total of 24 days and the concentration will be reduced from 20 mg to 10 mg (20/2).

Thus, 10 mg of the sample will be remaining after 24 days.