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

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> 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      Log On


   

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) About Me  (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) About Me  (Show Source):
You can put this solution on YOUR website!
The decay function we need is
(i) A+=+P%281%2F2%29%5E%28d%2Ft%29
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) .33P+=+P+%281%2F2%29%5E%288%2Ft%29
solving for t we get
(iii) .33+=+%281%2F2%29%5E%288%2Ft%29
(iv) Log%28.33%29+=+%288%2Ft%29%2Alog%281%2F2%29
(v) +t+=+8%2Alog%28.5%29%2Flog%28.33%29
which is t ~ 12.7596966
so we can rewrite (i) as
(vi) A+=+P%281%2F2%29%5E%28d%2F12.7596966%29
The half life is ~ 12.76 days
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If d = 12, we have the mass as
(vii) A+=+P%281%2F2%29%5E%2812%2F12.7596966%29
(viii) A+=+P%281%2F2%29%5E%28.9378153%29
(ix) A+=+.5222P
after 12 days, we have 52.22% left