Question

The ratio of half-life times of two elements A and B is $\frac{T_A}{T_B}$. The ratio of respective decay constant $\frac{{\lambda }_A}{{\lambda }_B}$, is

• A. $T_B/T_A$
• B. $T_A/T_B$
• C. $\frac{T_A+T_B}{T_A}$
• D. $\frac{T_A-T_B}{T_A}$

Answer 1

The correct option is B $T_A/T_B$

$T_{1/2}=\frac{\ln 2}{\lambda }\therefore \lambda =\frac{\ln 2}{T_{1/2}}$
${\Rightarrow \lambda }_A=\frac{\ln 2}{T_A},{\Rightarrow \lambda }_B=\frac{\ln 2}{T_B}\Rightarrow \frac{{\lambda }_A}{{\lambda }_B}=\frac{T_A}{T_B}.$