Question

Nuclear power plants produce a waste product of cesium-137, which has a half-life of 30 years. how long would it take for the cesium to decay to 1/8 of its original amount?

Answer 1

$m(final)=m(initial)*( \frac{1}{2} )^{ \frac{time}{half-life} m(final)= (1/8) *m(initial)$

$\frac{1}{8} m(initial)=m(initial)*( \frac{1}{2})^{ \frac{time}{halg-life} }$

$\frac{1}{8} = \left( \frac{1}{2} \right)^{\frac{time}{30} }$

$( \frac{1}{2})^{3}= (\frac{1}{2} )^{ \frac{time}{30}} \\ \\ 3= \frac{time}{30} \\ \\ time = 90 (years)$