Question

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?

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

Answer 1

The correct answer is c) 30 hours.

The half-life of sodium-24 is 15 hours. This means that after 15 hours, half of the initial amount of sodium-24 will remain, and the other half will have decayed.

If only one-eighth of the sodium-24 remains, it means that 7/8 of the initial amount has decayed.

Since each half-life is 15 hours, we can determine how many half-lives have passed by dividing 7/8 by 1/2:

(7/8)/(1/2) = (7/8) * (2/1) = 7/4

This means that 7/4 of a half-life has passed.

To find the time that has passed, we multiply the number of half-lives by the length of each half-life:
(7/4) * 15 hours = 105/4 hours = 26.25 hours ≈ 30 hours (rounded to the nearest hour)