Calcium Reactor
Calcium Reactor
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Strontium-90, with a half-life of 28 years???? help!?
Strontium-90, with a half-life of 28 years, is a waste product from nuclear fission reactors. One of the reasons great care is taken in the storage and disposal of this substance stems from the fact that strontium-90 is, in some chemical respects, similar to ordinary calcium. Thus, strontium-90 in the biosphere, entering the food chain via plants or animals, would eventually be absorbed into our bones. That would be bad.
Compute the decay constant K for strontium-90.
How long must a given quantity of strontium-90 be stored before its radioactivity is reduced by a factor of 1000? (i.e. until only 1/1000 of the original quantity remains)
___________years
About how many times must the radioactivity be cut in half in order for it to be reduced by such a factor of 1000?
How long does it take for exactly that many half-lives to pass?
______years
The decay equation is
A(t) = A(0)e^(-kt)
where A(t) is the amount after t years, A(0) is the initial amount, k is the rate constant, and t is the time in years. Since the half life is 28 years, we have
A(t)/A(0) = 0.5 = e^(-28k)
ln(0.5) = -28k
-0.693147181 = -28k
k = 0.024755256
The time to get to 1/000 of the original amount is
A(t)/A(0) = 0.001 = e^(-0.024755256t)
ln(0.001) = -0.024755256t
t = -6.907755279/(-0.024755256) = 279.04196 years
The number of reductions is
0.5^n = 0.001
n = ln(0.001)/ln(0.5) = 9.965784285
The time for that many half lives to pass is 28(9.965784285) = 279.04196 years






















































































