The potential energy (U) of a diatomic molecule is a function dependent on r (interatomic distance) as
$U = {\alpha \over {{r^{10}}}} - {\beta \over {{r^5}}} - 3$
where, $\alpha$ and $\beta$ are positive constants. The equilibrium distance between two atoms will be ${\left( {{{2\alpha } \over \beta }} \right)^{{a \over b}}}$, where a = ___________.
Answer (integer)
1
Solution
$F = - {{dU} \over {dr}}$<br><br>$$F = - \left[ { - {{10\alpha } \over {{r^{11}}}} + {{5\beta } \over {{r^6}}}} \right]$$<br><br>for equilibrium, F = 0<br><br>${{10\alpha } \over {{r^{11}}}} = {{5\beta } \over {{r^6}}}$<br><br>${{2\alpha } \over \beta } = {r^5}$<br><br>$r = {\left( {{{2\alpha } \over \beta }} \right)^{1/5}}$<br><br>$\therefore$ $a = 1$
About this question
Subject: Physics · Chapter: Work, Energy and Power · Topic: Work Done by a Force
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