Question

Radium-221 has a half-life of 30 s. how long (in seconds) will it take for 84% of a sample to decay? a) 45 seconds

b) 50 seconds
c) 55 seconds
d) 60 seconds

Answer 1

To determine how long it takes for 84% of Radium-221 to decay, one must understand the concept of half-lives. Given that none of the answer choices provided fall in the correct interval between 60 and 90 seconds, the question does not have a correct answer listed.

Step-by-step explanation:

The question asks how long it will take for 84% of a sample of Radium-221, with a half-life of 30 seconds, to decay. To find the time taken, we use the concept of half-lives which is how long it takes for half of a radioactive sample to decay. Since 84% decay means only 16% remains, we can establish that:
First half-life (50% remains) -> 30 seconds
Second half-life (25% remains) -> 60 seconds
Third half-life (12.5% remains) -> 90 seconds.

At 60 seconds, 25% of the sample would remain, and by 90 seconds only 12.5% of the sample would remain, which is less than the 16% that we need. Thus, the time for 84% to decay must be between 60 and 90 seconds, which means none of the provided options (45, 50, 55, 60 seconds) are correct.