GATE 2024 MT – Question 32
Two atoms have pair-interaction energy $U=-1.6/r^6+51.2/r^{12}$, where $U$ is in eV and distance $r$ in Å. Their equilibrium bond length is ______ Å (nearest integer).
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Correct answer: 2 to 2
Explanation
At equilibrium, $dU/dr=9.6/r^7-614.4/r^{13}=0$.
Thus $r^6=614.4/9.6=64$ and $r=2$ Å.
The second derivative at this point is positive: substituting $614.4=9.6r^6$ gives $U^{\prime\prime}=57.6/r^8>0$.
The equilibrium is a minimum, and the answer is **2 Å**.