If the potential energy between two molecules is given by
U = $- {A \over {{r^6}}} + {B \over {{r^{12}}}}$,
then at equilibrium,
separation between molecules, and the potential energy are :
Solution
U = $- {A \over {{r^6}}} + {B \over {{r^{12}}}}$
<br><br>F = - ${{dU} \over {dr}}$
<br><br>= – (A(–6r<sup>–7</sup>
)) + B(–12r<sup>–13</sup>)
<br><br>for equilibrium, F = 0
<br><br>$\therefore$ 0 = ${{6A} \over {{r^7}}} - {{12B} \over {{r^{13}}}}$
<br><br>$\Rightarrow$ ${{6A} \over {12B}} = {1 \over {{r^6}}}$
<br><br>$\Rightarrow$ r = ${\left( {{{2B} \over A}} \right)^{{1 \over 6}}}$
<br><br>$\therefore$ U = $- {A \over {{{2B} \over A}}} + {B \over {{{\left( {{{2B} \over A}} \right)}^2}}}$
<br><br>= $- {{{A^2}} \over {2B}} + {{{A^2}} \over {4B}}$
<br><br>= $- {{{A^2}} \over {4B}}$
About this question
Subject: Physics · Chapter: Work, Energy and Power · Topic: Work Done by a Force
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