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JIPMER Jipmer Medical Solved Paper-2015

  • question_answer
    The potential energy between two atoms, in a molecule, is given by\[U(x)=\frac{a}{{{x}^{12}}}-\frac{b}{{{x}^{6}}}\]where a and b are positive and x is the distance between the atoms. The atom is in stable equilibrium, when:

    A)  \[x=0\]

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

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

    D)         \[x={{\left( \frac{11a}{5b} \right)}^{1/16}}\]

    Correct Answer: C

    Solution :

    Given: \[U(x)=\frac{a}{{{x}^{12}}}-\frac{b}{{{x}^{6}}}\] or\[-\frac{12a}{{{x}^{13}}}-\frac{-6b}{{{x}^{7}}}=0\]or \[{{x}^{6}}=\frac{2a}{b}.\] Therefore \[x={{\left( \frac{2a}{b} \right)}^{1/6}}\]


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