half life solving initial quantity

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March 23rd 2008, 06:12 PM
theman

half life solving initial quantity

half life: 1620, initial quantity:x, amount after 1000 years:1.5 g

I need to solve for the initial quantity with the info given, thx for the help
March 23rd 2008, 06:16 PM
Jhevon

Quote:

Originally Posted by theman

half life: 1620, initial quantity:x, amount after 1000 years:1.5 g

I need to solve for the initial quantity with the info given, thx for the help

we use the equation $I(t) = I_0e^{rt}$

where $r$ is the rate of decay, $I(t)$ is the amount at time $t$ , $I_0$ is the intial amount (what we are searching for).

now, $\mbox{half-life} = \frac {\ln 2}r$

you know the half-life, so you can find $r$ .

once you have $r$ . plug in $I(t) = 1.5$ , $t = 1000$ , and $r =$ whatever. and solve for $I_0$
March 23rd 2008, 06:25 PM
theman

thanks, but i still dun know how to solve for the rate of the decay...
March 23rd 2008, 06:40 PM
topsquark

Quote:

Originally Posted by Jhevon

now, $\mbox{half-life} = \frac {\ln 2}r$

you know the half-life, so you can find $r$ .

Quote:

Originally Posted by theman

thanks, but i still dun know how to solve for the rate of the decay...

You can't solve that equation for r??

-Dan
March 23rd 2008, 06:55 PM
theman

lol, sorry, im kinda stupid, but i just solved it thanks!
March 23rd 2008, 06:56 PM
theman

um, sorry, but one more thing. With the same info and the initial quantity i got was 2.3 g. How would u solve it for 10,000 years.
March 23rd 2008, 06:59 PM
topsquark

Quote:

Originally Posted by theman

um, sorry, but one more thing. With the same info and the initial quantity i got was 2.3 g. How would u solve it for 10,000 years.

$I = I_0 e^{rt}$

You have $I_0$ and r. Just plug in t = 10000 years.

-Dan
March 23rd 2008, 07:10 PM
mr fantastic

Quote:

Originally Posted by theman

half life: 1620, initial quantity:x, amount after 1000 years:1.5 g

I need to solve for the initial quantity with the info given, thx for the help

(Swear) double posts (Headbang) .