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

90 years

Step-by-step explanation:

it takes three halves of one to get to 1/8.

So 30 times 3 = 90

Answer 2

`m(final)=m(initial)*( (1)/(2) )^{ (time)/(half-life) m(final)= (1/8) *m(initial)`


`(1)/(8) m(initial)=m(initial)*( (1)/(2))^{ (time)/(halg-life) }`


`(1)/(8) = \left( (1)/(2) \right)^{(time)/(30) }`


`( (1)/(2))^(3)= ((1)/(2) )^{ (time)/(30)} \\ \\ 3= (time)/(30) \\ \\ time = 90 (years)`