The potential energy (U) of a diatomic molecule is a function dependent on r (interatomic distance) as U = αr¹⁰ - (β)/(r⁵) - 3 where, α and β are positive constants. The equilibrium distance between two atoms will be ((2α)/(β))a/b, where a = ___________. Numerical answer type. Work it out, then open the answer.

Answer: 1. The constant -3 does not affect dU/dr. dU/dr = -10αr¹¹ + (5β)/(r⁶) = 0 ⇒ r⁵ = (2α)/(β) r = ((2α)/(β))1/5, so a/b = 1/5 and a = 1.

The potential energy (U) of a diatomic molecule is a function… | JEE Main 2021 (25 Feb, Shift 1)

Q8JEE Main 2021 · 25 FEB · SHIFT 1Medium

Potential Energy & Equilibrium

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 = ___________.

Numerical answer type. Work it out, then open the answer.

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Answer: 1

The constant $-3$ does not affect $\frac{dU}{dr}$ .
$\frac{dU}{dr} = -\frac{10\alpha}{r^{11}} + \frac{5\beta}{r^6} = 0 \Rightarrow r^5 = \frac{2\alpha}{\beta}$
$r = \left(\frac{2\alpha}{\beta}\right)^{1/5}$ , so $\frac{a}{b} = \frac{1}{5}$ and $a = 1$ .

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