Radium has a half-life of 1620 years and decays into radon, which has a half-life of 3.82 days. A 10-gm source of radium is sealed, and the radon produced is pumped off every 24 hours. How many mill curies of radon are pumped off each time?
To find the number of mill curies of radon pumped off each time, we need to calculate the decay of radon over a 24-hour period.
First, let's find how much radium decays into radon over 1620 years:
Since the half-life of radium is 1620 years, we can use the following formula to calculate the remaining amount of radium after a certain number of half-lives:
Remaining Radium = Initial Radium * (1/2)^(Time / Half-life)
In this case, the initial amount of radium is 10 grams, and the time is 1620 years. Plugging in these values, we have:
Remaining Radium = 10 * (1/2)^(1620 / 1620)
= 10 * (1/2)^1
= 10 * 0.5
= 5 grams
So after 1620 years, 5 grams of radium remain.
Now, to find the amount of radon produced from the remaining 5 grams of radium in a 24-hour period:
We can use the same formula as before, considering the half-life of radon. The initial amount of radium is now 5 grams, and the time is 24 hours (which is equivalent to 1 day):
Remaining Radium = 5 * (1/2)^(1 / 3.82)
≈ 5 * (1/2)^0.26178
≈ 5 * 0.8908
≈ 4.454 grams
So, in a 24-hour period, approximately 4.454 grams of radium decay into radon.
Finally, to convert this amount from grams to mill curies, we need to use the conversion factor:
1 gram = 37,000 mill curies
Therefore, the amount of radon pumped off each time is:
4.454 grams * 37,000 mill curies/gram ≈ 164,618 mill curies
So, approximately 164,618 mill curies of radon are pumped off each time.