SOLUTION: A 200 g sample of radioactive polonium-210 has half-life of 138 days. a) Determine the mass that remains after 5 years. b)How long does it take for this 200 g sample to decay

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Question 938336: A 200 g sample of radioactive polonium-210 has half-life of 138 days.
a) Determine the mass that remains after 5 years.
b)How long does it take for this 200 g sample to decay to 25 g?
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
p=I%2Ae%5E%28-kt%29
t, time in days
p, amount after time t
k, decay constant
I, initial amount

ln%28p%29=ln%28I%29%2Bln%28e%5E%28-kt%29%29
-kt%2Aln%28e%29%2Bln%28I%29=ln%28p%29
-kt=ln%28p%29-ln%28I%29
highlight_green%28kt=ln%28I%29-ln%28p%29%29-----You can use this form of the equation both to find k using the half-life information, and then to find t using the part (b) material quantities data.

k=%281%2F138%29ln%282%2F1%29, using time units of DAYS.
highlight%28k=0.00502%29

Be careful in part (a). Convert 5 years into how many days, and use the time in number of days, because that is what k was based on.
5%2A365.25=t in days.

(a)
p=200%2Ae%5E%28-%280.00502%29%285%2A365.25%29%29