Question

Question 139

A half-life is the amount of time that it takes for a radioactive substance to decay one-half of its original quantity.
Suppose radioactive decay causes 300 grams of a substance to decrease $300\times 2^{-3}$ grams after 3 half-lives. Evaluate $300\times 2^{-3}$ to determine how many grams of the substance is left.
Explain why the expression $300\times 2^{-n}$ can be used to find the amount of the substance that remains after n half-lives.

Answer 1

Since, 300 g of a substance decreases to $300\times 2^{-3}g$ after 3 half-lives.

Similarly, 300 g of a substance would decrease to $300\times 2^{-n}g$ after n half-lives.

So, we have to evaluate :
$300\times 2^{-3}$
$=300\times 2^{-3}$
$=\frac{300}{8}[\because 2^3=8]$
$=37.5g$