# Decay rates

• Jun 3rd 2008, 09:33 AM
Prod!gy
Decay rates
I'm having second thoughts on the answers I came up with...

Einsteinium-235 decays at a rate of 3.406% per day.

a. find the annual decay rate in exact form:
100(.96594)^365

b. Compute an approximation of your solution in part a accurate to two decimal places:
(This is where I was thrown off, as my equation truncated to two decimal places comes out to be 0.00, and I'm sure that's not the intention.)
3.21 x 10^-4

c. Find the half-life of Einsteinium-235 in exact form:
100(.96594)^t=50
log(96.594^t)=log(50)
t x log(96.594)=log(50)
t=(log(50))/(log(96.594))

d. Compute an approximation of your solution in part c accurate to two decimal places
0.85
(But I know that's obviously wrong. (Headbang))

Any help appreciated.
• Jun 3rd 2008, 09:39 AM
galactus
Half-life can easily be gotten from the formula

$\displaystyle k=\frac{-1}{T}ln(2)$

$\displaystyle k=ln(.96594)$

You know k, enter it in and solve for T.
• Jun 3rd 2008, 09:49 AM
Prod!gy