2. Sample Papers
  3. JEE Main & Advanced

JEE Main & Advanced Sample Paper JEE Main Sample Paper-7

  • question_answer
    The potential energy function of a diatomic molecule is given by \[U(x)=\frac{a}{{{x}^{12}}}-\frac{b}{{{x}^{6}}}\]. The position \[x\] of stable equilibrium is

    A)  \[\sqrt{\frac{a}{b}}\]                                    

    B)  \[{{\left( \frac{2a}{b} \right)}^{1/3}}\]

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

    D)  \[{{\left( \frac{a}{b} \right)}^{1/3}}\]

    Correct Answer: C

    Solution :

    \[F=0\] and \[U\] is \[-ve\] for stable equilibrium. \[U(x)=\frac{a}{{{x}^{12}}}-\frac{b}{{{x}^{6}}}\] \[F=-\frac{dU}{dx}=-\left[ -12a{{x}^{-13}}+6b{{x}^{-7}} \right]=0\] \[\Rightarrow \,\,12a{{x}^{-13}}=6b{{x}^{-7}}\Rightarrow \,\frac{2a}{b}={{x}^{6}}\] \[\therefore \,\,x={{\left( \frac{2a}{b} \right)}^{1/6}}\]


You need to login to perform this action.
You will be redirected in 3 sec spinner