# Thread: Half life question

1. ## Half life question

Got this problem in our homework set. I cannot get the answer that is in the back of the book (6.48?)

Trying to find the amount of 226Ra after 1000 years. The half life is 1,599 and the initial amount is 10g.

Our book says the formula is Af=(Ai)e^-r/t

2. $A_f=A_ie^{\frac{-r}{t}}$

$A_i = 10$

$A_f=10\times e^{\frac{-r}{t}}$

use $(t,A_f) \rightarrow (5,1599)$

$5=10\times e^{\frac{-r}{1599}}$

$\frac{1}{2}= e^{\frac{-r}{1599}}$

$\frac{-r}{1599} = ln(\frac{1}{2})$

$r = -1599\times ln(\frac{1}{2})$

$A_f=10\times e^{\frac{1599\times ln(\frac{1}{2})}{t}}$

now make $t=1000$

3. $10\times\left (\frac{1}{2}\right )^\frac{1000}{1599}=6.48$

4. Ah, so I should be using A*.5^t/r ?

5. Yep

6. Originally Posted by pinnacle2009

Our book says the formula is Af=(Ai)e^-r/t
or is it

$
A_f=A_ie^{\frac{-t}{r}}
$

7. Originally Posted by pickslides
or is it

$
A_f=A_ie^{\frac{-t}{r}}
$
More than likely. After looking here, I believe my calculator is my problem. I was getting syntax errors and just an answer of zero on most of all the half life problems.