Nuclear Physics And Radioactivity Question 58
Question: The half life of radioactive Radon is 3.8 days. The time at the end of which $ 1/20^{th} $ of the Radon sample will remain undecayed is (Given $ {\log_{10}}e=0.4343 $ ) [IIT 1981]
Options:
A) 3.8 days
B) 16.5 days
C) 33 days
D) 76 days
Show Answer
Answer:
Correct Answer: B
Solution:
By the formula $ N=N_{0}{{e}^{-\lambda t}} $ Given $ \frac{N}{N_{0}}=\frac{1}{20} $ and $ \lambda =\frac{0.6931}{3.8} $
Þ $ 20={{e}^{\frac{0.6931\times t}{3.8}}} $ Taking log of both sides or log 20 $ =\frac{0.6931\times t}{3.8}{\log_{10}}e $ or 1.3010 $ =\frac{0.6931\times t\times 0.4343}{3.8} $
Þ $ t=16.5 $ days.
BETA
