Half life math prob?

Question

the half life of radium is 1690 years. if 10 grams are present now how much will be present in 50 years??

please help!

Answer 1

This should be in physics, but no matter.


The general equation for any half-life problem is:

N(t) = (n_o) exp(-kt),
where n_o is the amount we started with and k is a parameter we need to find first.

So first we need to find k.
We use the half-life information. THis tells us that we'll have half the amount that we started with after 1690 years. That is,
N(1690) = 1/2 * n_o.

Plug this in:
1/2 n_o = n_o exp(-k*1690)

0.5 = exp(-1690k)
ln(0.5) = -1690k

k = -ln(0.5)/1690, whatever that is.

So have k now. Now just sub in your n_o, and 50 years:

N(50) = 10*exp(-k*50) where you sub in the k that you found. And voila, there's your answer. Hope this helps.

Answer 2

half life or t1/2 is the time taken for a compound to degrade by 50 %. ie it takes 1 gram of radium 1690 years to become 500 mg of radium. so 50 years is 2.9 % of the half life....plot it on an exponential curve and viola!. pretty much 9.8 grams i reckon....
in the greater scheme of things 50 years means bupkiss to radium.

Answer 3

This requires the use of the decay curves or logarithms. will get back to you tomorrow.