Nuclear Physics And Radioactivity Question 71
Question: A and B are two radioactive substances whose half lives are 1 and 2 years respectively. Initially 10 gm of A and 1 gm of B is taken. The time (approximate) after which they will have same quantity remaining is [UPSEAT 2003]
Options:
A) 6.62 years
B) 5 years
C) 3.2 years
D) 7 years
Show Answer
Answer:
Correct Answer: A
Solution:
$ N=N_{0}{{( \frac{1}{2} )}^{t/{T_{1/2}}}}\Rightarrow N_{A}=10{{( \frac{1}{2} )}^{t/1}} $ and $ N_{B}=1{{( \frac{1}{2} )}^{t/2}} $ Given $ N_{A}=N_{B}\Rightarrow 10{{( \frac{1}{2} )}^{t}}={{( \frac{1}{2} )}^{t/2}} $
$ \Rightarrow 10={{( \frac{1}{2} )}^{-t/2}}\Rightarrow 10={{2}^{t/2}}. $ Taking log both the sides. $ {\log_{10}}10=\frac{t}{2}{\log_{10}}2\Rightarrow 1=\frac{t}{2}\times 0.3010 $
$ \Rightarrow t=6.62 $ years.
BETA
