Question

$3$ rutherfords of a radio active isotope of half-life equal to $3$ days was received after $12$ days. Initial isotope packed was

• A. $48rutherfords$
• B. $12rutherfords$
• C. $25rutherfords$
• D. $36rutherfords$

Answer 1

The correct option is A $48rutherfords$

$1rutherford$ $={10}^{6}dps$

Half life $=3days$
After $12days$, $4$ half-lives have passed,
Fraction of activity left $=(\frac{1}{2}{)}^4=\frac{1}{16}$

Let the original amount of activity be x.
$\frac{1}{16}\times x=3rutherfords\Rightarrow x=48rutherfords$