Nuclear Physics And Radioactivity Question 434
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:
[d] $ 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 $
BETA
