Nuclear Physics And Radioactivity Question 384
Question: Activity of radioactive element decreased to one third of original activity $ R_{0} $ in 9 years. After further 9 years, its activity will be [DCE 2002]
Options:
A) $ R_{0} $
B) $ \frac{2}{3}R_{0} $
C) $ R_{0}/9 $
D) $ R_{0}/6 $
Show Answer
Answer:
Correct Answer: C
Solution:
Activity $ R=R_{0}{{e}^{-\lambda t}} $ $ \frac{R_{0}}{3}=R_{0}{{e}^{-\lambda \times 9}}\Rightarrow {{e}^{-9\lambda }}=\frac{1}{3} $ …(i) After further 9 years $ {R}’=R,{{e}^{-\lambda t}}=\frac{R_{0}}{3}\times {{e}^{-\lambda \times 9}} $ …(ii) From equation (i) and (ii) $ {R}’=\frac{R_{0}}{9} $ .
BETA
