A sample of Radon-222 has a half-life of 3.82 days. After 11.46 days, there is 5 grams of Radon-222 remaining. How much Radon-222 was in the original sample? 30 grams

2 grams

15 grams

40 grams

40

Explanation:

The formula for radioactive decay is as follows:

Q = Q0 x (e^-rt), in which Q is the remaining mass after decay, Q0 is the original sample mass, r is the constant of decay, and t is the time given to decay.

We first start by finding the constant of decay which is r = ln2/t(1/2), natural log of 2 divided by the half life. (Note that you can similarly find the half life if given the constant in t(1/2) = ln2/r)

1) ln2/3.82
2) r = 0.181452141

Now that we have all our givens necessary, we can apply into the formula:

1) 5 = Q0 x (e^(-0.181452141x11.46))
2) 5 = Q0 x (e^(-2.079441536))
3) 5 = Q0 x 0.125
4) Q0 = 5/0.125
5) Q0 = 40

Hope this helps, brainliest would be appreciated :)

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