JEE Main & Advanced Physics Nuclear Physics And Radioactivity Question Bank Assertion and Reason

  • question_answer
    Assertion             :       Radioactivity of \[{{10}^{8}}\] undecayed radioactive nuclei of half-life of 50 days is equal to that of \[1.2\times {{10}^{8}}\] number of undecayed nuclei of some other material with half-life of 60 days   Reason                 :       Radioactivity is proportional to half-life.

    A)             If both assertion and reason are true and the reason is the correct explanation of the assertion.

    B)             If both assertion and reason are true but reason is not the correct explanation of the assertion.

    C)             If assertion is true but reason is false.

    D)             If the assertion and reason both are false.

    E)             If assertion is false but reason is true.

    Correct Answer: C

    Solution :

                       Radioactivity \[=-\frac{dN}{dt}=\lambda N=\frac{0.693N}{T}\] \[=\frac{0.693\times {{10}^{8}}}{50}=\frac{0.693\times 1.2\times {{10}^{8}}}{60}\]\[=0.693\times 2\times {{10}^{6}}.\] Radioactivity is proportional to 1/T1/2, and not to T1/2.


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