Question

$1$ grams of a sample ${}^{42}K$ remained unchanged after $62$ hours. What was the original mass of the sample ${}^{42}K$, if the half life is $12.4$ hours?

• A. $64grams$
• B. $32grams$
• C. $16grams$
• D. $8grams$
• E. $4grams$

Answer 1

The correct option is B $32grams$

Let $W$ g be the original mass of $K-42$ sample.
Number of half life periods $=\frac{62}{12.4}=5$
Amount of $K-42$ remaining after 5 half life periods $=\frac{W}{2^5}=1$
$W=1\times 2^5=32g$
Hence, $32$ g of $K-42$ were present initially.