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NEET AIPMT SOLVED PAPER 2000

  • question_answer
                    The half-life of a radioactive isotope is three hours. If the initial mass of the isotope was 300g, the mass which remained undecayed after 18 hours would be:                                                                 

    A)                 4.68 g   

    B)                 2.34 g   

    C)                 1.17 g   

    D)                 9.36 g

    Correct Answer: A

    Solution :

                    Given                 Half-life \[({{t}_{1/2}})=3\,h\]                 Initial mass \[({{N}_{0}})=300g\]                 Total time (T) = 18 h                 Mass left (N) = ?                 We know that,                 \[\frac{N}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{n}}\]                 where n = number of half life                 \[n=\frac{Total\,time}{Half-life}=\frac{18}{3}=6\] So,          \[\frac{N}{300}={{\left( \frac{1}{2} \right)}^{6}}\] \[or\frac{N}{300}=\frac{1}{64}\]              \[N=\frac{300}{64}=4.68\,g\]


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