Nuclear Physics And Radioactivity Question 59
Question: If 10% of a radioactive material decays in 5 days, then the amount of original material left after 20 days is approximately [MNR 1987]
Options:
A) 60%
B) 65%
C) 70%
D) 75%
Show Answer
Answer:
Correct Answer: B
Solution:
$ N=N_{0}{{e}^{-\lambda t}} $
$ \therefore \ 0.9N_{0}=N_{0}{{e}^{-\lambda \times 5}}\Rightarrow 5\lambda ={\log_{e}}\frac{1}{0.9} $ …… (i) and $ xN_{0}=N_{0}{{e}^{-\lambda \times 20}}\Rightarrow 20\lambda ={\log_{e}}( \frac{1}{x} ) $ …… (ii) Dividing (i) by (ii), we get $ \frac{1}{4}=\frac{{\log_{e}}(1/0.9)}{{\log_{e}}(1/x)}=\frac{{\log_{10}}(1/0.9)}{{\log_{10}}(1/x)}=\frac{{\log_{10}}0.9}{{\log_{10}}x} $
$ \Rightarrow {\log_{10}}x=4{\log_{10}}0.9\Rightarrow x=0.658=65.8% $
BETA
