Question 946030
 Radium-221 has a half-life of 30 sec. How long will it take for 91% of a sample to decay? 
:
That leaves 9% remaining
:
The formula; A = Ao*2^(-t/h) where:
A = remaining amt after t time
Ao = initial amt (t=0)
t = time of decay
h = half-life of substance
In this problem let Ao = 1, then A = .09, given half-life of 30 sec
1*2^(-t/30) = .09
log(2^(-t/30) = log(.09)
log equiv of exponents
{{{-t/30}}}*log(2) = log(.09)
{{{-t/30}}} = {{{log((.09))/log((2))}}}
use the calc to find the logs
{{{-t/30}}} = -3.474
multiply both sides by -30
t = -30 * -3.474
t = +104.2 ~ 104 seconds