Question

The half-life of plutonium-234 is 9 hours. If 80 milligrams is present now, how much will be present in 3 days?

A. 26.67 mg
B. 10 mg
C. 1.88 mg
D. 0.3125 mg

Answer 1

To find the amount of plutonium-234 remaining after 3 days, convert days to hours and calculate the number of half-lives that have passed. Using the formula for radioactive decay, the calculation shows that there will be 0.3125 mg of plutonium-234 remaining after 3 days. Option d.

Step-by-step explanation:

The student has asked about calculating the amount of a radioactive isotope remaining after a certain period, given its half-life. In this case, we need to determine how much plutonium-234, which has a half-life of 9 hours, will be left after 3 days. We use the formula N = N0(1/2)^(t/T), where N is the remaining amount, N0 is the initial amount, t is the elapsed time, and T is the half-life of the substance.

First, convert 3 days to hours: 3 days * 24 hours/day = 72 hours.
The number of half-lives in 72 hours is 72 hours / 9 hours/half-life = 8 half-lives.

Then, plug in the values to calculate the remaining amount:
N = 80 mg * (1/2)^8
N = 80 mg * (1/256)
N = 0.3125 mg

Hence, the answer is D. 0.3125 mg.