Nuclear Physics And Radioactivity Question 66
Question: For a substance the average life for a-emission is 1620 years and for b emission is 405 years. After how much time the 1/4 of the material remains after a and b emission [RPET 1999]
Options:
A) 1500 years
B) 300 years
C) 449 years
D) 810 years
Show Answer
Answer:
Correct Answer: C
Solution:
$ {\lambda_{\alpha }}=\frac{1}{1620} $ per year and $ {\lambda_{\beta }}=\frac{1}{405} $ per year and it is given that the fraction of the remained activity $ \frac{A}{A_{0}}=\frac{1}{4} $ Total decay constant $ \lambda ={\lambda_{\alpha }}+{\lambda_{\beta }}=\frac{1}{1620}+\frac{1}{405}=\frac{1}{324}per,year $ We know that $ A=A_{0}{{e}^{-\lambda t}} $
Þ $ t=\frac{1}{\lambda }{\log_{e}}\frac{A_{0}}{A} $
Þ $ t=\frac{1}{\lambda }{\log_{e}}4=\frac{2}{\lambda }{\log_{e}}2 $ =324 ´ 2 ´ 0.693 = 449 years.
BETA
