The half-life of radon-222 is 4 days: What fraction of radioactive radon-222 remain after 16 days? would 01/8 1/32 01/4 01/16
The Correct Answer and Explanation is:
To find the fraction of radioactive radon-222 that remains after 16 days, we need to use the concept of half-life. The half-life of radon-222 is given as 4 days, meaning that every 4 days, the amount of radon-222 is reduced by half.
Step 1: Determine the number of half-lives that have passed
To calculate how many half-lives have passed in 16 days, divide the total time (16 days) by the half-life (4 days): Number of half-lives=164=4\text{Number of half-lives} = \frac{16}{4} = 4Number of half-lives=416=4
So, 4 half-lives have passed.
Step 2: Calculate the remaining fraction
After each half-life, the amount of the substance is halved. Therefore, after 4 half-lives, the remaining fraction of radon-222 is: Remaining fraction=(12)4=116\text{Remaining fraction} = \left( \frac{1}{2} \right)^4 = \frac{1}{16}Remaining fraction=(21)4=161
Thus, the fraction of radioactive radon-222 remaining after 16 days is 1/16.
Explanation:
- Each half-life reduces the amount of radioactive substance by half.
- After 1 half-life (4 days), half of the original amount remains: 1/2.
- After 2 half-lives (8 days), half of that remains: 1/4.
- After 3 half-lives (12 days), half of that remains: 1/8.
- After 4 half-lives (16 days), half of that remains: 1/16.
Thus, after 16 days, the remaining fraction is 1/16.
Answer: 1/16.
