Question

At any instant the ratio of the amount of two radioactive elements is $2:1$.If their half-lives respectively are $12$ hours and $16$ hours, then after two days, the ratio of the substances is

• A. $1:1$
• B. $1:2$
• C. $3:1$
• D. $4:1$

Answer 1

Answer: (A)

$1:1$

Let amount of first element $=2x$

Let amount of second element $=x$
Formula:-

Amount left after x half lives $=(\frac{1}{2}{)}^x\times$ original amount
Amount left of 1st after 4 half lives $=(\frac{1}{2}{)}^4\times 2x=\frac{x}{8}$

Amount left of 2nd after 3 half lives $=(\frac{1}{2}{)}^3\times x=\frac{x}{8}$
Ratio of substances left $=\frac{x}{8}:\frac{x}{8}=1:1$