Nuclear Chemistry Question 30

Question: A first order nuclear reaction is half completed in 45 minutes. How long does it need 99.9% of the reaction to be completed

[KCET 2001]

Options:

A) 5 hours

B) 7.5 hours

C) 10 hours

D) 20 hours

Show Answer

Answer:

Correct Answer: B

Solution:

$ k=\frac{0.693}{0.75hr}=\frac{2\text{.303}}{t}\log \frac{a}{a-0.999a} $

$ =\frac{2.303}{t}\log 10^{3}=7.5hrs $ .