Atoms And Nuclei Question 382
Question: A radioactive nucleus can decay by two different processes. The half-life for the first process is $ t_{1} $ and that for the second process is $ t_{2} $ . If effective half-life is t, then
Options:
A) $ t=t_{1}+t_{2} $
B) $ \frac{1}{t}=\frac{1}{t_{1}}+\frac{1}{t_{2}} $
C) $ t=\frac{2t_{1}t_{2}}{t_{1}+t_{2}} $
D) $ t=\frac{t_{1}+t_{2}}{2} $
Show Answer
Answer:
Correct Answer: B
Solution:
- $ \frac{dN}{dt}=-N,({\lambda_{1}}+{\lambda_{2}})=-N\lambda $
$ \Rightarrow ,\lambda ={\lambda_{1}}+{\lambda_{2}} $ so $ \frac{1}{t}=\frac{1}{t_{1}}+\frac{1}{t_{2}},[ as,\lambda =\frac{0.693}{t} ] $
