Atoms And Nuclei Question 399
Question: A radioactive isotope has a half-life of 200 years. How long will it take the activity to reduce to 1% of its original value?
Options:
A) 330 years
B) 460 years
C) 660 years
D) 920 years
Show Answer
Answer:
Correct Answer: C
Solution:
- $ N=N_{0}{{( \frac{1}{2} )}^{n}} $ so, for 1% decay $ \frac{1}{100}N_{0}=N_{0}{{( \frac{1}{2} )}^{n}}\Rightarrow \frac{1}{100}={{( \frac{1}{2} )}^{n}} $
$ \Rightarrow n=\frac{2}{\log 2}\Rightarrow \frac{t}{T}=\frac{2}{\log 2}\Rightarrow t=6.6T $ $ =6.6\times 100=660 $ years If $ \alpha $ and B are emitted simultaneously.
