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 30 hours c 60 hours d 45 hours
The correct answer is d) 45 hours.
In one half-life of sodium-24, one-half of the original amount remains. Therefore, if one-eighth of the sodium-24 remains, we can determine how many half-lives have passed.
One-eighth is equal to (1/2)^3. This means that three half-lives have passed since one-eighth of the original amount remains.
Since each half-life is approximately 15 hours, we can multiply the number of half-lives (3) by the duration of each half-life (15 hours) to determine the total time that has passed.
3 x 15 = 45 hours
Therefore, about 45 hours have passed.
To determine the amount of time that has passed when only one-eighth of a substance remains, we need to calculate how many half-lives have occurred.
Since the half-life of sodium-24 is approximately 15 hours, we divide the time passed by the half-life to determine the number of half-lives:
Time passed / Half-life = Number of half-lives
In this case, we are given that only one-eighth (1/8) of the sodium-24 remains. Therefore, the fraction remaining is 1/8.
To find the number of half-lives, we can use the following formula:
(1/2)^(number of half-lives) = fraction remaining
Substituting the given values, we have:
(1/2)^(number of half-lives) = 1/8
To simplify the equation, we can rewrite the fraction on the right side as a power of 2:
(1/2)^(number of half-lives) = 2^(-3)
Since the bases are the same, we can equate the exponents:
number of half-lives = -3
Therefore, the number of half-lives that has occurred is -3.
However, it is not possible to have a negative number of half-lives, so we can assume that the question is asking for the time it takes for one eighth to decay, not for the remaining quantity to be one-eighth.
Thus, the amount of time that has passed when only one-eighth of the sodium-24 remains is 3 half-lives of 15 hours each, which is equal to 45 hours.
Therefore, the correct answer is d) 45 hours.
To determine the amount of time that has passed, we can use the concept of half-life.
The half-life period is the amount of time it takes for half of the radioactive substance to decay. In this case, the half-life of sodium-24 is given as approximately 15 hours.
Since one-eighth of the sodium-24 remains, we can interpret this as three half-lives.
To calculate the time that has passed for three half-lives, we multiply the half-life of sodium-24 (15 hours) by the number of half-lives (3).
15 hours (half-life) * 3 (half-lives) = 45 hours
Therefore, the correct answer is d) 45 hours.