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?

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

@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.