Question

Suppose you have a rock that contained 1 microgram of a radioactive isotope at the time when it solidified. How much of this isotope remains if five half-lives have passed since it formed?

a) 0.03125 micrograms
b) 0.0625 micrograms
c) 0.125 micrograms
d) 0.25 micrograms

Answer 1

After five half-lives have passed, the amount of radioactive isotope remaining from the initial 1 microgram is 0.03125 micrograms. The calculation is based on repeatedly halving the initial amount five times.

Step-by-step explanation:

To calculate the amount of a radioactive isotope remaining after a certain number of half-lives, you can use the formula: amount remaining = initial amount × (½)number of half-lives.

Since the initial amount of isotope was 1 microgram and five half-lives have passed, we apply the formula as follows: 1 microgram × (½)5 = 1 microgram × (½ × ½ × ½ × ½ × ½) = 1 microgram × 1/32 = 0.03125 micrograms. Therefore, the correct answer is a) 0.03125 micrograms.