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CGP EDU Academic Team
Published on: September 12, 2026
The potential energy between two atoms in a molecule is given by $U(x) = \frac{a}{x^{12}} - \frac{b}{x^{6}}$ ; where a and b are positive constants and x is the distance between the atoms. The atom is in stable equilibrium when
Text Solution
Verified by ExpertsThe correct answer is:
D
Condition for stable equilibrium $F = - \frac{dU}{dx} = 0$
⇒ ⇒ $-\frac{d}{dx}\left[\frac{a}{x^{12}}-\frac{b}{x^{6}}\right]=0$ ⇒ ⇒ $-12ax^{-13} + 6bx^{-7} = 0$
⇒ ⇒ $\frac{12a}{x^{13}} = \frac{6b}{x^{7}}$ ⇒ ⇒ $\frac{2a}{b} = x^{6}$ ⇒ ⇒ $x = \sqrt[6]{\frac{2a}{b}}$
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