1. Tardigrade
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  3. Physics
  4. 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 positive constants. The equilibrium distance between two atoms will be ((2 α/β))(a/b), where a =.

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Q. 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 =____.

JEE MainJEE Main 2021Work, Energy and Power

Solution:

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