Question

A radioactive nucleus A has a single decay mode with half life ${\tau }_A$. Another radioactive nucleus B has two decay modes 1 and 2. If decay mode 2 were absent, the half life of B would have been${\tau }_A/2$. If decay mode 1 were absent, the half life of B would have been 3${\tau }_A$. If the actual half life of B is ${\tau }_B$, then the ratio ${\tau }_A/{\tau }_B$ is :

• A. $3/7$
• B. $7/2$
• C. $7/3$
• D. $1$

Answer 1

Answer: (C)

$7/3$

${\tau }_b=\frac{ln2}{{\lambda }_B}$

${\lambda }_B={\lambda }_1+{\lambda }_2$

$\frac{ln2}{{\tau }_b}=\frac{2ln2}{{\tau }_A}+\frac{ln2}{3{\tau }_A}$

$\frac{{\tau }_B}{{\tau }_A}=\frac{3}{7}$