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WB JEE Medical WB JEE Medical Solved Paper-2014

  • question_answer
    A piece of wood from an archaeological sample has 5.0 counts \[{{\min }^{-1}}\]per gram of \[C-14,\]while a fresh sample of wood has a count of \[15.0\,{{\min }^{-1}}{{g}^{-1}}.\] If half-life of C-14 is 5770 yr, the age of the archaeological sample is

    A)  8,500 yr           

    B)  9,200 yr

    C)  10,000 yr         

    D)  11. 000 yr

    Correct Answer: B

    Solution :

     Age of archaeological sample, \[t=\frac{2.303}{k}\log \left( \frac{{{N}_{0}}}{N} \right)\] (Here, \[{{N}_{0}}=\]initial activity, N = remaining activity) and       \[k=\frac{0.693}{{{t}_{1/2}}}\] (where \[{{t}_{1/2}}=\] half-life) \[=\frac{0.693}{5770}Y{{r}^{-1}}\] \[\therefore \] \[t=\frac{2.303\times 5770}{0.693}\log \left( \frac{15}{5} \right)\] \[=19175.0\log 3\,Yr\] \[=9148\,Yr\approx 9200\,Yr\]


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