SOLUTION: A sample of bismuth-210 decayed to 33% of its original mass after 8 days. (a)Find the half-life of this element. (b)Find the mass remaining after 12 days

Question 258067: A sample of bismuth-210 decayed to 33% of its original mass after 8 days.
(a)Find the half-life of this element.
(b)Find the mass remaining after 12 days
Found 2 solutions by richwmiller, drk:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
This is a math website. Please provide appropriate physics and/or chemistry formulas.
Answer by drk(1908) (Show Source): You can put this solution on YOUR website!
The decay function we need is
(i)
where A = final amount or percent of original, P = original portion, t = 1/2 life time, d = days.
From the given information, we get
(ii)
solving for t we get
(iii)
(iv)
(v)
which is t ~ 12.7596966
so we can rewrite (i) as
(vi)
The half life is ~ 12.76 days
--
If d = 12, we have the mass as
(vii)
(viii)
(ix)
after 12 days, we have 52.22% left
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