Answer to Question #112969 in Chemistry for harry

Question

An isotope of caesium (caesium-137) has a half-life of 30 years. If 1.0 g of caesium-137 disintegrates over a period of 90 years, how many g of caesium- 137 would remain?

Answer 1

First, let's find out which amount of isotope is left after 90 years. Let M be the initial amount, then amount left after n years, given that half-life is T, is

m=M*2^(-n/T)=M*2^(-90/30)=M*2^-3=M/8

Therefore, the amount of disintegrated isotope is M-m=M-M/8=7M/8.

Now one can find the ratio of amount that left to amount that disintegrated:

m/(M-m)=(M/8)/(7M/8)=1/7

That is, the amount of left isotope is 1/7 of the amount disintegrated.

Answer: 1/7 of a gram.