Question
Indium-117 has a half-life of 43 minutes. If you start with 500 grams of indium-117, how much time will it take to have 31.25 grams of indium-117 left in the sample?
A. 172 minutes
B. 86 minutes
C. 215 minutes
D. 129 minutes
A. 172 minutes
B. 86 minutes
C. 215 minutes
D. 129 minutes
Answers
GPT 3.5
The amount of indium-117 remaining in the sample can be modeled by the equation:
A(t) = A(0) * (1/2)^(t/h)
where A(t) is the amount remaining after time t, A(0) is the initial amount, t is the time elapsed, and h is the half-life.
Using this equation, we can plug in the values:
31.25 = 500 * (1/2)^(t/43)
Dividing both sides by 500:
0.0625 = (1/2)^(t/43)
Taking the logarithm of both sides:
log(0.0625) = log[(1/2)^(t/43)]
Using the logarithm property:
log(0.0625) = (t/43) * log(1/2)
Dividing both sides by log(1/2):
(t/43) = log(0.0625) / log(1/2)
Simplifying:
t = 43 * log(0.0625) / log(1/2)
Using a logarithm calculator, we find:
t ≈ 129.174
Therefore, it will take approximately 129 minutes to have 31.25 grams of indium-117 left in the sample.
The correct answer is D. 129 minutes.
A(t) = A(0) * (1/2)^(t/h)
where A(t) is the amount remaining after time t, A(0) is the initial amount, t is the time elapsed, and h is the half-life.
Using this equation, we can plug in the values:
31.25 = 500 * (1/2)^(t/43)
Dividing both sides by 500:
0.0625 = (1/2)^(t/43)
Taking the logarithm of both sides:
log(0.0625) = log[(1/2)^(t/43)]
Using the logarithm property:
log(0.0625) = (t/43) * log(1/2)
Dividing both sides by log(1/2):
(t/43) = log(0.0625) / log(1/2)
Simplifying:
t = 43 * log(0.0625) / log(1/2)
Using a logarithm calculator, we find:
t ≈ 129.174
Therefore, it will take approximately 129 minutes to have 31.25 grams of indium-117 left in the sample.
The correct answer is D. 129 minutes.