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RAJASTHAN ­ PET Rajasthan PET Solved Paper-2006

  • question_answer
    The relative energy of two atoms of a molecule is expressed by the following expression. \[U(x)=\left( \frac{a}{{{x}^{12}}} \right)-\left( \frac{b}{{{x}^{6}}} \right)\] Here \[\alpha \] and b are positive constants and\[x\]is the distance between these atoms. If atom is at a state of permanent equilibrium, then

    A)  \[x={{\left( \frac{2a}{b} \right)}^{1/6}}\]

    B)  \[x={{\left( \frac{a}{2b} \right)}^{1/6}}\]

    C)  \[x=0\]

    D)  \[x={{\left( \frac{11a}{b} \right)}^{1/6}}\]

    Correct Answer: A

    Solution :

     For stable equilibrium position of atom \[\frac{dU}{dx}=0\] \[\Rightarrow \] \[-12a{{x}^{-13}}+6b{{x}^{-7}}=0\] \[\Rightarrow \] \[{{x}^{6}}=\frac{2a}{b}\] \[\Rightarrow \] \[x={{\left( \frac{2a}{b} \right)}^{1/6}}\]


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