SOLUTION: Suppose you begin with 2.8 mg of a pure radioactive substance and 3.6 h later determine that 0.35 mg remain. What is the half-life of the substance?

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Question 428542: Suppose you begin with 2.8 mg of a pure radioactive substance and 3.6 h later determine that 0.35 mg remain. What is the half-life of the substance?
Answer by Gogonati(855) About Me  (Show Source):
You can put this solution on YOUR website!
Solution:As we know the radioactive decay is given by: M%28t%29=Mo%2Ae%5E%28-k%2At%29

where M is th actual mass of the substance, Mo is the mass after t= 3.6 h,
and k is decay coefficient. Substitute our values:
0.35=2.8%2Ae%5E-3.6k, Take ln for both sides.
ln%280.35%29=-3.6k%2Aln%28e%29
k=-0.212 Now that, we know the coefficient of half-life, can compute the half-life.
0.35=2.8%2Ae%5E%28-0.212%2At%29, Take ln for both sides.
ln%280.35%29=-0.212t%2Alne
t=4.8 h.