Question 1005726: Radium-221 has a half life of 30 seconds, how long will it take for 72% of a sample to decay?
Please help me !! Found 2 solutions by fractalier, rothauserc:Answer by fractalier(6550) (Show Source):
You can put this solution on YOUR website! We use the formula
A(t) = Ao * (1/2)^(t/30)
.28Ao = Ao * (1/2)^(t/30)
.28 = (1/2)^(t/30)
Now take ln and get
ln .28 = (-t/30)ln 2
t = -30 * ln(.28) / ln 2 = 55.1 seconds
You can put this solution on YOUR website! A = Ao * (1/2)^t/h, where Ao is initial amount, h is decay rate in hours, t is time
.28*Ao = Ao * (1/2)^(t/h)
.28 = (1/2)^(t/0.008333333)
note h = 30/3600 = 0.008333333
use definition of logarithm
t/0.008333333 = log base (1/2) (0.28)
t = 1.8365 * 0.008333333 * 3600
t = 55.09 seconds
