# Help

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• Nov 9th 2009, 01:28 PM
NFG123
Help
So after I received help earlier today with two problems, I've been flying through my homework. This is until I reached this problem. I don't even know what this applies to, yet alone know how to figure this out. Could someone lay out an equation or something please.

The half-life of radium is 1690 years. If 60 grams are present now, how much will be present in 2450 years? When solving, round the decay constant,r, to 5 decimal places.
• Nov 9th 2009, 02:10 PM
Jameson
Quote:

Originally Posted by NFG123
So after I received help earlier today with two problems, I've been flying through my homework. This is until I reached this problem. I don't even know what this applies to, yet alone know how to figure this out. Could someone lay out an equation or something please.

The half-life of radium is 1690 years. If 60 grams are present now, how much will be present in 2450 years? When solving, round the decay constant,r, to 5 decimal places.

You don't need to apologize for asking help or say it's your last time. This site wants to help you if you are using it correctly, which you seem to be :)

What does half life mean? It means after the half life has passed, one half of the substance is gone. Mathematically this means $\displaystyle A(t)=A_0 \left( \frac{1}{2} \right) ^{\frac{t}{h}}$. Now where did this come from? Look at (t/h), where t is time and h is the half life. When t=h that means that the the time has reached the half life and this fraction will also be 1. If the fraction is 1, then you get $\displaystyle A(t)=A_0 \left( \frac{1}{2} \right) ^1$, which is just one half of the starting amount. This makes sense because that's what the half life definition is.

So plug in the half life time your problem gives you in that equation for h and you can now know the amount left at any time t.