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NEET AIPMT SOLVED PAPER 2003

  • question_answer
                    A sample of radioactive element has a mass of 10 g at an instant t = 0. The approximate mass of this element in the sample after two mean lives is:                    

    A)                                                                                            3.70 g  

    B)                 6.30 g   

    C)                 1.35 g  

    D)                 2.50 g

    Correct Answer: C

    Solution :

                           Mean life                 \[\tau =\frac{1}{\lambda },\,\lambda \] beings decay constant.                 Also time given                 \[t=2\tau =2\times \frac{1}{\lambda }=\frac{2}{\lambda }\]                 Thus, mass remained after time t is                 \[M={{M}_{0}}\,{{e}^{-\lambda t}}\]                 \[=10\,{{e}^{-\lambda +\frac{2}{\lambda }}}(\because \,\,{{M}_{0}}=10g)\]                 \[=10\,{{e}^{-2}}=\frac{10}{{{e}^{2}}}=1.35\,g\]


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