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## toadytica305 2 years ago No idea how to solve this.. The half-life of radium is 1690 years. If 10 grams is present now, how much will be present in 50 years?

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1. matricked

here first of all find the disintegrating constant

2. matricked

i am not sure abt the formula but it is somewhat like disintegrating constant =0.693/(hal-life time)

3. matricked

then use ln (amt present after t yrs/amt initially present) = -(disintegrating constant)* time

4. Kira_Yamato

5. toadytica305

@Kira_Yamato Can you explain how you did it?

6. dpaInc

radio active decay problems modelled by : $$\large y=Ce^{kt}$$ where C is your initial amount (10 grams), and k is your "disintegrating" constant as explained by @matricked. you'll need to find k so you'll need to solve the equation: $$\large 5=10e^{k \cdot 1690}$$ because the half-life is 1690 years, there will only be 5 grams left of the original 10 grams when 1690 years have elapsed. This is what @Kira Yamato did above. k=-(ln2)/1690. So the model for the half-life decay is: $$\large y=10e^{(-\frac{ln2}{1690}\cdot t)}$$ To answer your question, use a calculator to find y when t=50 years.

7. Akram-Alsabty

@dpaInc @toadytica305 @Kira_Yamato that's how you solve the problem. we do not need to stick a negative sign to K because when you solve K will be negative.

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