Nuclear Physics And Radioactivity Question 105
Question: The radioactivity of sample is $ R_{1} $ at a time $ T_{1} $ and $ R_{2} $ at a time $ T_{2} $ . If the half-life of the specimen is T, the number of atoms that have disintegrated in the time ( $ T_{2}-T_{1} $ ) is proportional to
Options:
A) $ R_{1}T_{1}-R_{2}T_{2} $
B) $ R_{1}-R_{2} $
C) $ \frac{(R_{1}-R_{2})}{4} $
D) $ (R_{1}-R_{2}) $
Show Answer
Answer:
Correct Answer: D
Solution:
$ T_{1}=N_{1}\lambda ,R_{2}=N_{2}\lambda $ Also $ T=\frac{{\log_{e}}2}{\lambda } $ or $ \lambda =\frac{{\log_{e}}2}{T} $
$ \therefore R_{1}-R_{2}=(N_{1}-N_{2})\lambda $ $ =(N_{1}-N_{2})\frac{{\log_{e}}2}{T} $
$ \therefore (N_{1}-N_{2})=\frac{(R_{1}-R_{2})T}{{\log_{e}}2} $ i.e. $ (N_{1}-N_{2})\propto (R_{1}-R_{2})T $
BETA
