The potential energy (U) of a diatomic molecule is a function...

For equilibrium

$\dfrac{dU}{dr} = 0$

$\dfrac{- 10\alpha}{{r}^{11}} + \dfrac{5\beta}{{r}^{6}} = 0$

$\dfrac{5\beta}{{r}^{6}} = \dfrac{10\alpha}{{r}^{11}}$

${r}^{5} = \dfrac{2\alpha}{\beta}$

${r}^{5} = \dfrac{2\alpha}{\beta}$

$r = \left(\dfrac{2\alpha}{\beta}\right)\dfrac{1}{5}a = 1$