radioactive decay?

Question

hello. is there a standard form for a radioactive decay MATH problem?

for example, 226Ra has half life of 1620 yrs. what percent will remain after 100yrs?

thanks for your help

Answer 1

One half-life equation used is
P= Po (0.5^ (t/k)), where
P= amount remaining
Po= initial amount
t= time
k= half-life

So for your question, Po= 100%, t=100, k=1620
P= 100 (0.5^ (100/1620))
P= 95.812% or ~96% remaining after 100 years

Answer 2

time %remaining formula
1620 50 1/2^1
3240 25 1/2^2
It appears the fraction remaining is 1/2 to the power of the number of half-lives elapsed. So the amount remaining after 100 years would be 1/2^(5/81) -- about 95.811557818859294019905303317824%, according to my calculator.

Answer 3

under normal conditions radioactive material decays at a constant rate,so divide the half life by 16.2 that will give you the amount of decay for 100 years then then subtract the answer from 1620 thats whats left after 100 years.

Answer 4

divide the time which has passed by the half life. this will give you the number of half lives which have passed.

divide the original amount of the substance by 2 to the half life. IE three half lives divide by 2^3 = 8 IE 1/8Th of the original amount is left.

100/1620 = .0617. I have no easy way of figuring 2 to the .0617 power.