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 = ______ .

For equilibrium d U d r = 0 - 10 α r 11 + 5 β r 6 = 0 5 β r 6 = 10 α r 11 r 5 = 2 α β r 5 = 2 α β r = 2 α β 1 5 a = 1

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PhysicsW.E.P.Conservative force & potential energyMedium2 minQB

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The potential energy $(U)$ of a diatomic molecule is a function dependent on $r$ (interatomic distance) as $U = \frac{α}{r^{10}} - \frac{β}{r^{5}} - 3$ where, $α$ and $β$ are positive constants. The equilibrium distance between two atoms will be ${(\frac{2 α}{β})}^{\frac{a}{b}},$ where $a =$ ______ .

Answer:

1.00

Solution:

For equilibrium

$\frac{d U}{d r} = 0$

$\frac{- 10 α}{r^{11}} + \frac{5 β}{r^{6}} = 0$

$\frac{5 β}{r^{6}} = \frac{10 α}{r^{11}}$

$r^{5} = \frac{2 α}{β}$

$r = {(\frac{2 α}{β})}^{\frac{1}{5}} a = 1$

Stream:JEESubject:PhysicsTopic:W.E.P.Subtopic:Conservative force & potential energy

⏱ 2mℹ️ Source: QB

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