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  • The potential energy (U) of diatomic molecule is a function dependent on r (interatomic distance) as <img alt="U= \frac{\alpha }{r^{10}} -\frac{\beta}{r^5}-3" src="https://entrancecorner.codecogs.com/gif.latex?U%3D%20%5Cfrac%7B%5Calpha%20%7D%7Br%5E%7B1

The potential energy (U) of 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 = _______
Option: 1 1
Option: 2 2
Option: 3 3
Option: 4 4

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\begin{aligned} &\text { For equilibrium }\\ &\frac{\mathrm{dU}}{\mathrm{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}}\\ &\mathrm{a}=1 \end{aligned}

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