A) 60 sec
B) 80 sec
C) 20 sec
D) 40 sec
Correct Answer: D
Solution :
[d] \[{{A}_{1}}\] \[{{A}_{1}}\] Half life \[{{t}_{{\scriptstyle{}^{1}/{}_{2}}}}=20\,Sec\] \[{{t}_{{\scriptstyle{}^{1}/{}_{2}}}}=40\,Sec\,\] \[Initial\,{{N}_{0}}=40g\] \[{{N}_{0}}=160g\] \[final\,{{N}_{1}}\] \[{{N}_{1}}\] \[{{N}_{1}}={{N}_{{{0}_{1}}}}{{\left[ \frac{1}{2} \right]}^{{\scriptstyle{}^{T}/{}_{20}}}}similarly\,{{N}_{2}}={{N}_{{{0}_{2}}}}{{\left[ \frac{1}{2} \right]}^{{\scriptstyle{}^{T}/{}_{40}}}}\] \[{{N}_{1}}={{N}_{2}}\] \[{{N}_{{{0}_{1}}}}{{\left( \frac{1}{2} \right)}^{{\scriptstyle{}^{T}/{}_{20}}}}={{N}_{{{0}_{2}}}}{{\left( \frac{1}{2} \right)}^{{\scriptstyle{}^{T}/{}_{40}}}}\] \[40{{\left( \frac{1}{2} \right)}^{{\scriptstyle{}^{T}/{}_{20}}}}=160{{\left( \frac{1}{2} \right)}^{{\scriptstyle{}^{T}/{}_{40}}}}\] \[\frac{1}{4}={{\left( \frac{1}{2} \right)}^{\frac{T}{10}-\frac{T}{20}}}\] \[{{\left( \frac{1}{2} \right)}^{2}}={{\left( \frac{1}{2} \right)}^{\frac{T}{2}}}\] \[T=40\sec \]You need to login to perform this action.
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