The half-life of radon-222 is 3.82 days. If a sample of gas contains 4.38ug of radon-222, how much will remain in the sample after 15.2 days?
k = 0.693/t1/2
Substitute k into the following:
ln(No/N) = kt
No = 4.38 ug.
N = solve for this.
k from above.
t = 15.2 days.
To find how much radon-222 will remain in the sample after 15.2 days, we need to use the concept of half-life. The half-life of radon-222 is 3.82 days, meaning that every 3.82 days, the amount of radon-222 in the sample will be reduced by half.
To solve this problem, we can divide the time elapsed (15.2 days) by the half-life (3.82 days) to determine how many half-lives have passed. This will allow us to calculate the amount of radon-222 remaining.
15.2 days ÷ 3.82 days = 3.98 half-lives
Now, we can use the half-life equation to determine the remaining amount of radon-222:
Remaining amount = Initial amount × (1/2)^(number of half-lives)
In this case, the initial amount of radon-222 is 4.38 μg. Plugging in the values:
Remaining amount = 4.38 μg × (1/2)^(3.98)
To calculate this, we can use a scientific calculator or perform the calculation step by step.
(1/2)^3.98 ≈ 0.094
Remaining amount ≈ 4.38 μg * 0.094
Remaining amount ≈ 0.41172 μg
Therefore, after 15.2 days, approximately 0.41172 μg of radon-222 will remain in the sample.