Question

Answer.com after three half-lives, what fraction of a radioactive sample has decayed?

Answer 1

After 1 half-life, 1/2 the sample has decayed. After 2 half-lives 3/4 of the matter has decayed. So after, 3 half-lives about 11/12 would have decayed.

Answer 2

Answer: Thus the fraction decayed is $\frac{7a_o}{8}$

Explanation: Radioactive decay follow first order kinetics.

Now, to calculate the amount decayed after n half lives, we use the formula:

$a=\frac{a_o}{2^n}$

where,

a = amount of reactant left after n-half lives

$a_o$ = Initial amount of the reactant

n = number of half lives  = 3

Putting values in above equation, we get:

$a=\frac{a_0}{2^3}$

$a=\frac{a_0}{8}$

The fraction decayed after 3 half lives will be $\frac{1}{8}$ of the initial amount.

Thus the fraction decayed is $a_0-\frac{a_0}{8}=\frac{7a_o}{8}$