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NEET Sample Paper NEET Sample Test Paper-56

  • question_answer
    A mixture consists of two radioactive materials \[{{A}_{1}}\] and \[{{A}_{2}}\] with half-lives of 20 sec and 10 sec, respectively. Initially, the mixture has 40g of \[{{A}_{1}}\]and 160g of\[{{A}_{2}}\]. The amount of the two in the mixture will become equal after:

    A) 60 sec                          

    B) 80 sec   

    C) 20 sec              

    D) 40 sec

    Correct Answer: D

    Solution :

    [d] \[{{A}_{1}}\]                            \[{{A}_{1}}\] Half life \[{{t}_{{\scriptstyle{}^{1}/{}_{2}}}}=20\,Sec\]            \[{{t}_{{\scriptstyle{}^{1}/{}_{2}}}}=40\,Sec\,\] \[Initial\,{{N}_{0}}=40g\]                      \[{{N}_{0}}=160g\] \[final\,{{N}_{1}}\]                                \[{{N}_{1}}\] \[{{N}_{1}}={{N}_{{{0}_{1}}}}{{\left[ \frac{1}{2} \right]}^{{\scriptstyle{}^{T}/{}_{20}}}}similarly\,{{N}_{2}}={{N}_{{{0}_{2}}}}{{\left[ \frac{1}{2} \right]}^{{\scriptstyle{}^{T}/{}_{40}}}}\]             \[{{N}_{1}}={{N}_{2}}\] \[{{N}_{{{0}_{1}}}}{{\left( \frac{1}{2} \right)}^{{\scriptstyle{}^{T}/{}_{20}}}}={{N}_{{{0}_{2}}}}{{\left( \frac{1}{2} \right)}^{{\scriptstyle{}^{T}/{}_{40}}}}\] \[40{{\left( \frac{1}{2} \right)}^{{\scriptstyle{}^{T}/{}_{20}}}}=160{{\left( \frac{1}{2} \right)}^{{\scriptstyle{}^{T}/{}_{40}}}}\] \[\frac{1}{4}={{\left( \frac{1}{2} \right)}^{\frac{T}{10}-\frac{T}{20}}}\]             \[{{\left( \frac{1}{2} \right)}^{2}}={{\left( \frac{1}{2} \right)}^{\frac{T}{2}}}\]             \[T=40\sec \]


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