J & K CET Medical J & K - CET Medical Solved Paper-2011

  • question_answer
    One gram atom of a radioactive isotope\[({{t}_{1/2}}=10\,h)\]that emits alpha particle was placed in a sealed container. The time taken for 0.875 g atom of helium to accumulate in the container is

    A)  10 h                                      

    B)  20 h

    C)  30 h                                      

    D)  40 h

    Correct Answer: C

    Solution :

                    \[\frac{N}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{n}}\] \[{{N}_{0}}=1\,g\] \[N=1-0.875=0.125\text{ }g\]                 \[\frac{0.125}{1}={{\left( \frac{1}{2} \right)}^{n}}\]                 \[\frac{125}{1000}={{\left( \frac{1}{2} \right)}^{n}}\]                 \[\frac{1}{8}={{\left( \frac{1}{2} \right)}^{n}}\]                 \[{{\left( \frac{1}{2} \right)}^{3}}={{\left( \frac{1}{2} \right)}^{n}}\] \[n=3\] \[\therefore \]Total time\[\text{(T)}=n\times {{t}_{1/2}}\] \[=3\times 10\] \[=30h\]


You need to login to perform this action.
You will be redirected in 3 sec spinner