A sample of radon has an activity of 80,000 Bq. If the half-life of radon is 15 h, how long before the sample's activity is 5,000 Bq?
Half life = 15h
Activity
A(t)=A(0)*2^(-t/15)
Solve for t in
A(t)=5000=80000(2^(-t/15))
to get t=60 (hours)
To determine how long it takes for the activity of radon to decrease to 5,000 Bq, we can use the concept of half-life.
The half-life of radon is provided as 15 hours, which means that in 15 hours, the activity will decrease by half. In other words, after 15 hours, the activity will be reduced to 40,000 Bq (half of 80,000 Bq).
To find out how many half-lives it takes to reach 5,000 Bq, we can divide the initial activity (80,000 Bq) by the final activity (5,000 Bq) and take the logarithm base 2 of the quotient. The formula is:
Number of half-lives = log2 (Initial activity / Final activity)
In this case:
Number of half-lives = log2 (80,000 Bq / 5,000 Bq)
Now, let's perform the calculation:
Number of half-lives = log2 (16)
To solve this, we need to determine the power to which 2 must be raised to obtain 16:
2^x = 16
Since we know that 2^4 = 16, x = 4.
Therefore, the number of half-lives required is 4.
Now, to determine the time it takes for the radon sample's activity to reach 5,000 Bq, we can multiply the half-life (15 hours) by the number of half-lives (4):
Time = Half-life x Number of half-lives
= 15 h x 4
= 60 hours
So, it will take approximately 60 hours for the activity of the radon sample to decrease to 5,000 Bq.