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)

3.125 g

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.