# half life solving initial quantity

• Mar 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
• Mar 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 $\displaystyle I(t) = I_0e^{rt}$

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

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

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

once you have $\displaystyle r$. plug in $\displaystyle I(t) = 1.5$, $\displaystyle t = 1000$, and $\displaystyle r =$ whatever. and solve for $\displaystyle I_0$
• Mar 23rd 2008, 06:25 PM
theman
thanks, but i still dun know how to solve for the rate of the decay...
• Mar 23rd 2008, 06:40 PM
topsquark
Quote:

Originally Posted by Jhevon
now, $\displaystyle \mbox{half-life} = \frac {\ln 2}r$

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

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
• Mar 23rd 2008, 06:55 PM
theman
lol, sorry, im kinda stupid, but i just solved it thanks!
• Mar 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.
• Mar 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.

$\displaystyle I = I_0 e^{rt}$

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

-Dan
• Mar 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