Question

A nuclear waste site. cesium-137 is a particularly dangerous by-product of nuclear reactors. it has a half-life of 30 years. it can be readily absorbed into the food chain and is one of the materials that would be stored in the proposed waste site at yucca mountain (see the article opening this section). suppose we place 3000 grams of cesium-137 in a nuclear waste site.how much cesium-137 will be present after 60 years, or two half-lives?

Answer 1

The mass decay rate is of the form
$m(t) = m_{0} e^{-kt}$
where
m₀ = 3000 g,the initial mass
k = the decay constant
t = time, years.

Because the half-life is 30 years, therefore
$e^{-30k} = \frac{1}{2} \\\ -30k = ln(0.5) \\ k = \frac{ln(0.5)}{-30} =0.0231$

After 60 years, the mass remaining is
$m = 3000 e^{-0.0231*60} = 750 \, g$

Answer: 750 g