Question

The potential energy between two atoms in a molecule is given by u (x) = (a/x^12)-(b/x^6), where a and b are positive constant and x is the distance between the atoms. the atom is in stable equilibrium when?

Answer 1

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Answer 2

"The potential energy between two atoms is given as, $a /x^1^2 \quad and \quad b /x^6$respectively

here a and b are positive constants and x is the distance between the atoms.

$U(x)=a^{ [x-12] } - b^{ [x-6] }$

$\frac { du }{ dx } =a^{ [(-12)x-13] }- b^{ [(-6)x-7] }$

$=\frac { -12a }{ { x }^{ 13 } } \quad +\quad \frac { 6b }{ { x }^{ 7 } }$

For stable equilibrium, $F =\frac { du }{ dx } = 0$

Then $\frac { du }{ dx } = 0$

$\frac { -12a }{ { x }^{ 13 } } \quad +\quad \frac {6b}{{x}^{7}} =0$

$x^{ 6 }=\frac { 12a }{ 6b } =2\frac { a }{ b }$

Therefore

$x=6\frac { 2a }{ b } \times \frac { 1 }{ 2 }$"