J & K CET Engineering J and K - CET Engineering Solved Paper-2008

  • question_answer
    The half-life period of a radioactive isotope is 4.8 min. Starting with 1 mg of the isotope, how much of it would remain after 10 min?

    A)  0.5 mg        

    B)  0.726 mg

    C)  0.126 mg      

    D)  0.236 mg

    Correct Answer: D

    Solution :

     Given, half-life period, \[{{t}_{1/2}}=4.8\,\,\min \] initial amount, \[{{N}_{0}}=1\,mg\] total time, \[t=10\text{ }min\] \[\Rightarrow \] \[k=\frac{0.693}{{{t}_{1/2}}}=\frac{0.693}{4.8}\] \[\Rightarrow \] \[k=\frac{2.303}{t}\log \frac{{{N}_{0}}}{N}\] or \[\frac{0.693}{4.8}=\frac{2.303}{10}\log \frac{1}{N}\] \[\log \frac{1}{N}=0.62689\] \[N=0.236\,mg\]


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