Atoms And Nuclei Question 380
Question: The half-life of radioactive Radon is 3.8 days. The time at the end of which $ \frac{1}{20} $ th of the radon sample will remain undecayed is $ ( \text{given lo}{{g}_{e}}=0.4343 ) $
Options:
A) 3.8 days
B) 16.5 days
C) 33 days
D) 76 days.
Show Answer
Answer:
Correct Answer: B
Solution:
- $ {t_{1/2}}=3.8 $ day
$ \therefore \lambda =\frac{0.693}{{t_{1/2}}}=\frac{0.693}{3.8}=0.182 $
If the initial number of atom is $ a=A_{0} $ then after time t the number of atoms is $ a/20=A $ .
We have to find t. $ t=\frac{2.303}{\lambda }\log \frac{A_{0}}{A}=\frac{2.303}{0.182}\log \frac{a}{a/20} $ $ =\frac{2.303}{0.182}\log 20=16.46 $ days
