SOLUTION: Radium-221 has a half-life of 30 sec. How long will it take for 91% of a sample to decay? (Round your answer to the nearest whole number.)

Question 946030: Radium-221 has a half-life of 30 sec. How long will it take for 91% of a sample to decay? (Round your answer to the nearest whole number.)

Found 2 solutions by ankor@dixie-net.com, josgarithmetic:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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
*log(2) = log(.09)
=
use the calc to find the logs
= -3.474
multiply both sides by -30
t = -30 * -3.474
t = +104.2 ~ 104 seconds
Answer by josgarithmetic(39623) (Show Source): You can put this solution on YOUR website!
Material has half life of t seconds. How long will it take for s percent of Material sample to decay?

Question is to find how much time until quantity present changes from I to .

First find k, and then use k to find time to let s percent of sample to decay.

, you know t=30 seconds and want the value...

.

Model Revised: .
Starting with I=1, t is what when ?
(Your value given for s is 91).
-

t=-ln(1-s/100)/(-0.0231)
-
Easier to avoid sign mistakes if directly using the actual values.

, seconds.
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