Sodium-24 has a half-life of approximately 15 hours. If only one-eighth of the sodium-24 remains, about how much time has passed?

Question

a
60 hours
b
15 hours
c
45 hours
d
30 hours

Answer 1

To determine how much time has passed when only one-eighth of sodium-24 remains, we can use the concept of half-life.

If the half-life is 15 hours, we can find out how many half-lives have passed to get from the original amount to one-eighth of it.

1. After 1 half-life (15 hours), the amount remaining is: \( \frac{1}{2} \)

2. After 2 half-lives (30 hours), the amount remaining is: \( \frac{1}{4} \)

3. After 3 half-lives (45 hours), the amount remaining is: \( \frac{1}{8} \)

Thus, it takes 3 half-lives to go from the original amount to one-eighth of it.

3 half-lives = 3 × 15 hours = 45 hours.

Therefore, the time that has passed is approximately 45 hours.

The answer is: c) 45 hours.