If only one-eighth of the sodium-24 remains, roughly how many hours have elapsed, given its half-life is approximately 15 hours?(1 point)

Question

Responses

45 hours
45 hours

15 hours
15 hours

30 hours
30 hours

60 hours
60 hours

Answer 1

To determine how many hours have elapsed for only one-eighth of sodium-24 to remain, we can use the concept of half-lives.

The half-life of sodium-24 is approximately 15 hours.

To go from the original amount to one-eighth of it, we need to undergo three half-lives, because:

• After the first half-life (15 hours), half of the original amount remains (1/2).
• After the second half-life (30 hours), half of that remaining amount is left (1/4).
• After the third half-life (45 hours), half of that remaining amount is left (1/8).

So, it takes 3 half-lives (3 x 15 hours) to reach one-eighth of the original amount.

Thus, the total time that has elapsed is:

3 half-lives × 15 hours = 45 hours.

The correct answer is:

45 hours.