Atoms And Nuclei Question 364
Question: At radioactive equilibrium, the ratio between the atoms of two radioactive elements (X) and (Y) as found to be $ 3.2\times 10^{9}:1 $ respectively If half-life of the element is $ 1.6\times 10^{10} $ years, then half-life of the element W would be
Options:
A) $ 3.2\times 10^{9}years $
B) $ 5\times 10^{9}years $
C) $ 1.6\times 10^{10}years $
D) 5 years
Show Answer
Answer:
Correct Answer: D
Solution:
- $ X\xrightarrow{{\lambda _{1}}}Y\xrightarrow{{\lambda _{2}}}Z $
At radioactive equilibrium, $ ({\lambda _{X}})\times (N _{X})=({\lambda _{Y}})\times (N _{Y}) $
$ \frac{{\lambda _{X}}}{{\lambda _{Y}}}=\frac{N _{Y}}{N _{X}}\frac{{{({t _{1/2}})} _{Y}}}{{{({t _{1/2}})} _{X}}}=\frac{N _{Y}}{N _{X}} $ or $ \frac{{{({t _{1/2}})} _{Y}}}{1.6\times 10^{10}} $ $ =\frac{1}{3.2\times 10^{9}}{{({t _{1/2}})} _{Y}}=5years $
