SOLUTION: a 50 mg sample of radioactive substance decays to 34 mg after 30 days. a. what is the half life of the sample b. how long will it takd for there to be 2 mg of the sample left

Question 250401: a 50 mg sample of radioactive substance decays to 34 mg after 30 days.
a. what is the half life of the sample
b. how long will it takd for there to be 2 mg of the sample left
Answer by Greenfinch(383) (Show Source): You can put this solution on YOUR website!
Half life equation
Amount left = Start amount x(e^-(time x constant)) which,in this case is
34 = 50 x e^(30k) or 34/50 = e^-(30k)
0.68 = e^-(30k)
ln(0.68)/30 = -k
so k = - 0.01285546.
For 1 half-life ln(0.5)= -0.01285546t
so t = 53.9 days
To go from 50 mg to 2 mg is ln(50/2) half-lives = 3.218875825
So that is 3.21887 x 53.9 days = 173.5 days
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