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NEET AIPMT SOLVED PAPER 2003

  • question_answer
                    The radioisotope, tritium \[(\,_{1}^{3}H)\] has a half-life of 12.3 years. If the initial amount of tritium is 32 mg, how many milligrams of it would remain after 49.2 years?                                                                            

    A)                 4 mg                      

    B)                 8 mg

    C)                 1 mg

    D)                 2 mg

    Correct Answer: D

    Solution :

                    \[{{t}_{1/2}}=12.3\,y.\]                 Initial amount \[({{N}_{0}})=32\,mg\]                 Amount left (N) = ?                 Total time (T) = 49.2 y                 \[\frac{N}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{n}}\]                 where n = total number of half-life                 \[n=\frac{Total\,time}{Half\,-\,life}\]                 \[\frac{49.2}{12.3}=4\]                 \[So,\frac{N}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{n}}\]                  \[\frac{N}{32}={{\left( \frac{1}{2} \right)}^{4}}\]                  \[\frac{N}{32}=\frac{1}{16}\]                  \[N=\frac{32}{16}\,=2mg\]


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