Nuclear Physics And Radioactivity Question 80
Question: A radioactive sample of U238 decay to Pb through a process for which half life is 4.5 ´ 109 years. The ratio of number of nuclei of Pb to U238 after a time of 1.5 ´ 109 years (given 21/3 = 1.26) [Based on IIT-JEE (Mains) 2004]
Options:
A) 0.12
B) 0.26
C) 1.2
D) 0.37
Show Answer
Answer:
Correct Answer: B
Solution:
Here $ \frac{N}{N_{0}}={{( \frac{1}{2} )}^{n}}={{( \frac{1}{2} )}^{1/3}} $ where n = Number of half lives $ =\frac{1}{3} $
Þ $ \frac{N}{N_{0}}=\frac{1}{1.26} $
Þ $ \frac{N_{U}}{N_{Pb}+N_{U}}=\frac{1}{1.26} $
Þ $ N_{Pb}=0.26,N_{U} $
Þ $ \frac{N_{Pb}}{N_{U}}=0.26 $
BETA
