The potential energy (U) of a diatomic molecule is a function dependent on r (interatomic distance) as U =(α)/(r^10)-(β)/(r^5)-3 where, α and β are…

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