The potential energy function for the force between two atoms in a diatomic molecule is approximately given by U(x)=x12a−x6b, where a and b are constants and x is the distance between the atoms. If the dissociation energy of the molecule is D=[U(x=∞)−Uat equilibrium ],D is

U=x12a−x6b F=−dxdU=+12x13a−x76b=0⇒x=(b2a)1/6 U(x=∞)=0Uequilibrium =(b2a)2a−(b2a)b=4ab2 ∴U(x=∞)−Uequilibrium =0−(−4ab2)=4ab2

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Work, Energy and Power

The concept of potential energy

The potential energy function for the force between two atoms

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The potential energy function for the force between two atoms in a diatomic molecule is approximately
given by $U (x) = \frac{a}{x ^{12}} - \frac{b}{x ^{6}}$ , where $a$ and $b$ are constants and $x$ is the distance between the atoms.
If the dissociation energy of the molecule is $D = [U (x = \infty) - U_{at equilibrium}], D$ is

\frac{b ^{2}}{6 a}

\frac{b ^{2}}{2 a}

\frac{b ^{2}}{12 a}

\frac{b ^{2}}{4 a}

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Updated on: May 9, 2023

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Elizabeth Discussed

The potential energy function for the force between two atoms in a diatomic molecule is approximately
given by

U (x) = \frac{a}{x ^{12}} - \frac{b}{x ^{6}}

, where

a

and

b

are constants and

x

is the distance between the atoms.
If the dissociation energy of the molecule is

D = [U (x = \infty) - U_{at equilibrium}], D

6 mins ago

Discuss this question LIVE

6 mins ago

Text solutionVerified

U = \frac{a}{x ^{12}} - \frac{b}{x ^{6}}

F = - \frac{d U}{d x} = + 12 \frac{a}{x ^{13}} - \frac{6 b}{x ^{7}} = 0 \Rightarrow x = (\frac{2 a}{b})^{1/6}

U (x = \infty) = 0

U_{equilibrium} = \frac{a}{( \frac{2 a}{b} ) ^{2}} - \frac{b}{( \frac{2 a}{b} )} = \frac{b ^{2}}{4 a}

∴ U (x = \infty) - U_{equilibrium} = 0 - (- \frac{b ^{2}}{4 a}) = \frac{b ^{2}}{4 a}

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Question Text	The potential energy function for the force between two atoms in a diatomic molecule is approximately given by $U (x) = \frac{a}{x ^{12}} - \frac{b}{x ^{6}}$ , where $a$ and $b$ are constants and $x$ is the distance between the atoms. If the dissociation energy of the molecule is $D = [U (x = \infty) - U_{at equilibrium}], D$ is
Updated On	May 9, 2023
Topic	Work, Energy and Power
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 9
Upvotes	904
Avg. Video Duration	9 min

Text solutionVerified

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The potential energy function for the force between two atoms in a diatomic molecule is approximately given by U(x)=x12a​−x6b​, where a and b are constants and x is the distance between the atoms. If the dissociation energy of the molecule is D=[U(x=∞)−Uat equilibrium ​],D is

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