Answered

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The half-life of Radium-226 is 1590 years. If a sample contains 400 mg, how many mg will remain after 1000
years?

Sagot :

foreveryoung11

Answer:

258.65 mg will be remain after 1000 years

Step-by-step 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.

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