Question

The potential energy (U) of a diatomic molecule is a function dependent on $r$ (interatomic distance) as
$U=\frac{\alpha }{r^{10}}-\frac{\beta }{r^5}-3$
where, $\alpha$ and $\beta$ are positive constants. The equilibrium distance between two atoms will be
${\left(\frac{2\alpha }{\beta }\right)}^{\frac{a}{b}},$ where a =____.

Answer 1

Answer: 1

For equilibrium
$\frac{dU}{dr}=0$
$\frac{-10\alpha }{r^{11}}+\frac{5\beta }{r^6}=0$
$\frac{5\beta }{r^6}=\frac{10\alpha }{r^{11}}$
$r^5=\frac{2\alpha }{\beta }$
$r={\left(\frac{2\alpha }{\beta }\right)}^{\frac{1}{5}}$
$a=1$