NEET Solved Paper 2017 Question 45
Question: Radioactive material ‘A’ has decay constant $ ‘8\lambda ’ $ and material ‘B’ has decay constant $ ‘\lambda ‘. $ Initially they have same number of nuclei. After what time, the ratio of number of nuclei of material ‘B’ to that ‘A’ will be $ \frac{1}{e} $ ?
Options:
A) $ \frac{1}{9\lambda } $
B) $ \frac{1}{\lambda } $
C) $ \frac{1}{7\lambda } $
D) $ \frac{1}{8\lambda } $
Show Answer
Answer:
Correct Answer: C
Solution:
- No option is correct If we take $ \frac{N _{A}}{N _{B}}=\frac{1}{e} $ Then $ \frac{N _{A}}{N _{B}}=\frac{{e^{-8\lambda t}}}{{e^{-\lambda t}}} $ $ \frac{1}{e}={e^{-7\lambda t}} $ $ -1=-7\lambda t $
$ t=\frac{1}{7\lambda } $
