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

$\displaystyle A_i = 10$

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

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

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

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

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

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

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

now make $\displaystyle t=1000$

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

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

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

7. Originally Posted by pickslides
or is it

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