Question

The ratio of half-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

Answer: (A)

$T_B/T_A$

The ratio of half-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 $\frac{T_B}{T_A}$.
The relationship between the half life period and the decay constant is

$T_A=\frac{0.693}{{\lambda }_A}$ ......$\left(1\right)$

$T_B=\frac{0.693}{{\lambda }_B}$ ......$\left(2\right)$, we get
Divide equation $\left(2\right)$ with equation $\left(1\right)$,

$\frac{T_B}{T_A}=\frac{{\lambda }_A}{{\lambda }_B}$