JEE Main & Advanced Chemistry Nuclear chemistry Question Bank Critical Thinking Nuclear chemistry

  • question_answer The half-life period of \[P{{b}^{210}}\] is 22 years. If 2 gm of \[P{{b}^{210}}\] is taken, then after 11 years how much of \[P{{b}^{210}}\] will be left [KCET 2001]

    A)            1.414 gm                                

    B)            2.428 gm

    C)            3.442 gm                                

    D)            4.456 gm

    Correct Answer: A

    Solution :

           \[{{N}_{t}}={{N}_{o}}{{\left( \frac{1}{2} \right)}^{2}}\][\[\therefore {{t}_{1/2}}\]= 22 years, T = 11 years, \[{{N}_{o}}\]=2, \[{{N}_{t}}\]=?]                    \[T={{t}_{1/2}}\times n,\] 11= 2 × n or \[n=\frac{11}{22}=\frac{1}{2}\]                    \[\therefore {{N}_{t}}=2gm\times {{\left( \frac{1}{2} \right)}^{1/2}}=1.414gm\].

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