Question

Radioactive isotope Berkelium-247 has a decay rate of 50.23% per thousand years. You have a sample of 155.4 mg. How much will be left 4500 years from now? (rounding to the nearest 10th of a mg)

a) 0.0 mg
b) 7.2 mg
c) 38.8 mg
d) 77.6 mg

Answer 1

After using the decay rate formula on the initial 155.4 mg of Berkelium-247, we have determined that roughly 38.8 mg of the isotope will be left after 4500 years, which corresponds to option c) 38.8 mg.

Step-by-step explanation:

To find out how much of the radioactive isotope Berkelium-247 will be left after 4500 years, we can use the decay rate given and apply it to the initial amount. The decay rate is 50.23% per thousand years. To find the fraction remaining after a certain number of periods, we use the formula:

remaining amount = initial amount × (1 - decay rate)^n

Where n is the number of thousand-year periods. Since we have 4.5 periods of 1000 years in 4500 years, we can plug the values into the formula:

remaining amount = 155.4 mg × (1 - 0.5023)^4.5

Calculating this we get:

remaining amount = 155.4 mg × (0.4977)^4.5

remaining amount ≈ 38.8 mg

Therefore, after 4500 years, there would be approximately 38.8 mg of Berkelium-247 left, rounding to the nearest tenth of a mg. The correct answer is option c) 38.8 mg.