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
30 hours
b
15 hours
c
45 hours
d
60 hours
c) 45 hours
To determine how much time has passed, you can use the concept of half-life and the fact that only one-eighth of the sodium-24 remains.
Since the half-life of sodium-24 is approximately 15 hours, it means that after every 15 hours, the amount of sodium-24 reduces by half.
In this case, if only one-eighth of the sodium-24 remains, it means that it has gone through three half-lives (because 2^3 = 8, representing the fraction that remains).
So, to find out the total time that has passed, you need to multiply the half-life (15 hours) by the number of half-lives (3).
15 hours x 3 = 45 hours
Therefore, about 45 hours have passed. Hence, the correct answer is option c) 45 hours.
To determine the amount of time that has passed, we can use the concept of half-life.
The half-life of sodium-24 is approximately 15 hours, which means that after each 15-hour period, the amount of sodium-24 remaining will be reduced by half.
If only one-eighth of the sodium-24 remains, it means that the remaining amount is eight times smaller than the original amount.
Since each half-life reduces the amount by half, we can calculate how many half-lives would be required to reduce the amount to one-eighth.
One-eighth is equal to (1/2)^3 because 2*2*2 = 8.
So, three half-lives have passed.
Since each half-life is 15 hours, the total amount of time that has passed is 15 hours * 3 = 45 hours.
Therefore, the answer is c) 45 hours.