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KVPY Sample Paper KVPY Stream-SX Model Paper-1

  • question_answer
    A sample contains number of stable nuclei equal to \[{{N}_{s}}\] and number of unstable nuclei equal to \[{{N}_{u}}.\] After a time T the activity of the sample decreased to one third of the initial activity, while the total number of nuclei (excluding decayed nuclei) became half. The ratio \[{{N}_{s}}/{{N}_{u}}\] initially is:

    A) 1/3                   

    B) 1/4

    C) 3                                 

    D) 2

    Correct Answer: A

    Solution :

    Let N denote the total no of nuclei. Initially \[N={{N}_{u}}+{{N}_{s}}.\] After a time T since the activity decreased to one third, number of unstable nuclei will also become one third. So after a time T, \[N/2={{N}_{u}}/3+{{N}_{s}}.\] Solving the two equations we get \[{{N}_{s}}/{{N}_{u}}=1/3.\]        


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