Atoms And Nuclei Question 411
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
Options:
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}} $
Show Answer
Answer:
Correct Answer: A
Solution:
- $ {T_{1/2}}=\frac{In2}{\lambda }\therefore \lambda =\frac{In2}{{T_{1/2}}} $
$ \Rightarrow {\lambda_{A}}=\frac{In2}{T_{A}},{\lambda_{B}}=\frac{In2}{T_{B}}\Rightarrow \frac{{\lambda_{A}}}{{\lambda_{B}}}=\frac{T_{B}}{T_{A}}. $
