NEET Sample Paper NEET Sample Test Paper-51

  • question_answer 23) A radioactive element decays by\[\beta -emission\]. A detector records n beta particles in 2s and in next \[2s\] it records \[0.75n\] beta particle. Find mean life correct to nearest whole number-(Given \[\ell n\,2=0.6931,\text{ }\ell n\text{ }3\,\,=\,\,0986\])

    A) \[17s~\]                                    

    B) \[7\,s\]

    C) \[5\text{ }s\]                             

    D) \[15\text{ }s\]

    Correct Answer: B

    Solution :

    \[Let\text{ }{{N}_{0}}\text{ }=\text{ }initial\text{ }number\text{ }of\text{ }nuclei\] \[~n={{N}_{0}}-{{N}_{0}}{{e}^{-\lambda \,\times \,2}}\] \[\,1.75\,n={{N}_{0}}-{{N}_{0}}{{e}^{-4\lambda }}\] \[\frac{1}{1.75}=\frac{1-{{e}^{-2\lambda }}}{1-{{e}^{-4\lambda }}}\] \[1+{{e}^{-2\lambda }}\,\,=\,\,1.75\] \[{{e}^{2\lambda }}\,\,=\,\,\frac{1}{0.75}\,\,=\,\,1.33\] \[\,2\lambda =\ell n\,(1.33)\] \[\tau \,\,=\frac{1}{\lambda }\,\,=\,\,\frac{2}{\ell n(1.33)}\,\,=\,\,7s\]

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