A) 2 yr
B) 4 yr
C) 5 yr
D) 6 yr
Correct Answer: B
Solution :
Given, \[N=\frac{{{N}_{0}}}{32}\] Now, we know that \[\frac{N}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{n}}\] \[\frac{1}{32}\,\,=\,\,{{\left( \frac{1}{2} \right)}^{n}}\] \[{{\left( \frac{1}{2} \right)}^{5}}\,\,=\,\,{{\left( \frac{1}{2} \right)}^{n}}\] \[\Rightarrow \] \[n= 5\] So, there are 5 half life in 20 year. \[\therefore \,\,Half life of element = \frac{20}{5} =\,\,4 years.\]
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