Nuclear Physics And Radioactivity Question 299
Question: N atoms of a radioactive element emit n alpha particles per second. The half life of the element is [MP PET 1995; MP PMT 1997, 2003]
Options:
A) $ \frac{n}{N} $ sec
B) $ \frac{N}{n} $ sec
C) $ \frac{0.693\ N}{n} $ sec
D) $ 5,099\ c{{m}^{-1}} $ sec
Show Answer
Answer:
Correct Answer: C
Solution:
$ \frac{dN}{dt}=-\lambda N\Rightarrow n=-\lambda N $ (Given $ \frac{dN}{dt}=n $ )
$ \therefore \lambda =-\frac{n}{N}\ \ \therefore $ Half life $ =\frac{0.693}{\lambda }=\frac{0.693}{\lambda }=\frac{0.693\ N}{n}\sec $
BETA
