SOLUTION: The half-life of radium is 1600 years. If 1000g are initially present, how much will remain after 3200 years? How long will it take to decay to 50g?

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Question 954560: The half-life of radium is 1600 years. If 1000g are initially present, how much will remain after 3200 years? How long will it take to decay to 50g?
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
The first question is easily answered with no fancy calculations. 3200 years is TWO half-lives. 250 grams remain. Continuing in half-lives, you can come near the number of years to reach 50 grams, but a computation using the decay model might be better.

y=I%2Ae%5E%28-kt%29
ln%28y%29=ln%28I%29-kt
-kt=ln%28y%29-ln%28I%29
k=%28ln%28I%29-ln%28y%29%29%2Ft
k=ln%282%29%2F1600
k=4.33%2A10%5E%28-4%29

The decay formula will give t=ln%28I%2Fy%29%2Fk

highlight%28t%5B50g%5D=ln%281000%2F50%29%2F%280.000433%29%29
compute that, for years.

6900 years