Answer:
258.65 mg will be remain after 1000 years
Explanation:
This problem can be solved several ways, I prefer the natural log approach for reasons I won’t go into here:
Activity final = Activity initial e^-kt, where
k = the decay constant, = ln2/half life = 0.693/1590, = 0.000436/year
t = the decay time, in the same time base as k
The problem can be worked in units of activity, mass, or number of atoms.
400 x e^-0.000436 x 1000 = 400 x e^-.436 = 258.65 mg
you can check this by estimating. There is about 2/3 of a half life, so there should be more than 200 mg, which would be the value at one half life.