The amount of radioactive substance left after 75 hrs, when 100g of it is taken initially, will be: (half life of radioactive substance is 15 hrs)
Answer & explanation
Correct answer: option 4
The correct answer is Option 4. 3.125 g.
We are given:
Initial amount of radioactive substance = 100 g
Half-life = 15 hours
Time elapsed = 75 hours
The number of half-lives that have passed can be calculated as:
\(\text{Number of half-lives} = \frac{\text{Time elapsed}}{\text{Half-life}} = \frac{75 \text{ hrs}}{15 \text{ hrs}} = 5\)
The amount of substance left after \(n\) half-lives is given by:
\(\text{Remaining amount} = \text{Initial amount} \times \left( \frac{1}{2} \right)^n\)
Where \(n\) is the number of half-lives.
In this case:
\(\text{Remaining amount} = 100 \times \left( \frac{1}{2} \right)^5\)
\(\text{Remaining amount} = 100 \times \frac{1}{32} \)
\(\text{Remaining amount} = 3.125 \text{ g}\)
The amount of radioactive substance left after 75 hours will be 3.125 g.