Question

The half-life of sodium-24 is 15 hours. How much of 100 grams sodium-24 would be left after 30 hours?

Answer 1

Hint: Half-life means when the concentration of the reactant taken at the starting of the reaction becomes half. To solve the question, first, divide the given time with the half-time of the compound, this will give the value that will tell us how many times the reaction will take place.

Complete answer: Half-life means when the concentration of the reactant taken at the starting of the reaction becomes half. The given compound in the question sodium-24 and the given half-life of this is 15 hours, this means that after 15 hours then the concentration of sodium-24 becomes half.
To solve the question, first, divide the given time with the half-time of the compound, this will give the value that will tell us how many times the reaction will take place. The given time is 30 hours, and the half-life is 15 hours.
$\dfrac{30}{15}=2$
There will be two reactions in 30 hours.
The mass of sodium-24 taken at the starting of the reaction is 100 grams, so when the first reaction takes place, then after 15 hours the mass will be 50 grams.
Now, the second reaction will take place, and again after 15 hours, the mass will become half. So, the mass is 50 grams, and after 15 hours it will be 25 grams.
Therefore, after 30 hours, 25 grams of sodium-24 will be left.

Note: If you were asked to find the mass at 45 hours, then you have to divide again the mass with 2, so after 45 hours, 12.5 grams of sodium will be left.