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Svet_ta [14]
4 years ago
10

The half life of Mercury-203, which is used in certain medical procedures, is approximately 47 days. If a shipment of 400 mg is

made to a medical company, how much Mercury-203 will be left after two weeks?
Approximately 388 mg.


Approximately 325 mg.


Approximately 39 mg.


Approximately 3.37 mg.
Mathematics
1 answer:
saw5 [17]4 years ago
3 0

The half-life is 47 days, which means that for any starting amount a_0 of Hg-203, we're left with \dfrac{a_0}2 after this amount of time.

\dfrac{a_0}2=a_2e^{47k}\implies\dfrac12=e^{47k}\implies-\dfrac{\ln2}{47}=k

So, the amount of Hg-203 a(d) left after d days is given by

a(d)=a_0e^{-(\ln2)/47\,d}

2 weeks = 14 days, so if we start with 400 mg, after two weeks we end up with

a(14)=400e^{-(\ln2)/47\cdot14}\approx325.38 mg

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