A radioactive isotope has a half-life of 20 days. If 100 g of the substance is taken, the weight of the isotope remaining after 40 days is

Options

A. 25 g
B. 2.5 g
C. 60 g
D. 40 g

Explanation

To solve the problem of how much of a radioactive isotope remains after 40 days, we can use the concept of half-lives. Here’s a step-by-step solution:

### Step 1: Understand the half-life
The half-life of a radioactive isotope is the time it takes for half of the substance to decay. In this case, the half-life is given as 20 days.

### Step 2: Determine the number of half-lives in 40 days
To find out how many half-lives fit into 40 days, we divide the total time by the half-life:
\[ \text{Number of half-lives} = \frac{\text{Total time}}{\text{Half-life}} = \frac{40 \text{ days}}{20 \text{ days}} = 2 \]

### Step 3: Calculate the remaining amount after each half-life
Starting with 100 grams of the substance:
- After the first half-life (20 days), the amount remaining is:
\[ \text{Remaining after 1 half-life} = \frac{100 \text{ g}}{2} = 50 \text{ g} \]

- After the second half-life (another 20 days, totaling 40 days), the amount remaining is:
\[ \text{Remaining after 2 half-lives} = \frac{50 \text{ g}}{2} = 25 \text{ g} \]

### Conclusion
After 40 days, the weight of the radioactive isotope remaining is **25 grams**.