SOLUTION: The half life of a certain radioactive materials is 3 hours. How many kilograms of this material will be left after 48 hours if there are initially 10 kilograms?

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Question 1122713: The half life of a certain radioactive materials is 3 hours. How many kilograms of this material will be left after 48 hours if there are initially 10 kilograms?
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
P=Po*e^(-kt); P/Po=1/2
1/2=e^(-3k)
ln both sides
-0.693=-3k
k=0.231
Let t=48
P=10*e^(-0231*48); that will be e^(-11.088)
P=1.529 x 10^(-4) kg

Check
48 hours is 16 half lives
2^(-16)=1.5 x 10^(-5) same as above fraction of the original amount.

Answer by ikleyn(52800) (Show Source):
You can put this solution on YOUR website!
.

In such problems, using exponents like is the way to create unnecessary difficulties for yourself. Simply use the fact that the 48 hours are 16 times half-life. It will give you remaining mass (in kilograms) of the original material.

Also, to better understand the Physics (which most school students simply do not know),
keep in your mind, that actually the total mass of a sample (the bulk mass) changes INSIGNIFICANTLY at the radioactive decay.

Simply one chemical element is transforming to another chemical element / (or to its isotope). Again, the total mass of the original sample material changes insignificantly. Otherwise, it would be a nuclear explosion.