The potential energy between two atoms, in a molecule, is given by U(x)=(a/x12)-(b/x6) where a and b are positive constants and x is the distance between the atoms. The atom is in stable equilibrium, when

Question

The potential energy between two atoms, in a molecule, is given by U(x)=(a/x12)-(b/x6) where a and b are positive constants and x is the distance between the atoms. The atom is in stable equilibrium, when (A) x=((2a/b))1/6 (B) x=((11 a/5b))1/6 (C) x=0 (D) x=((a/2b))1/6

Tardigrade Admin · Accepted Answer

U(x)=(a/x12)-(b/x6) or -(12 a/x13)-(-6 b/x7)=0 or x6=(2 a/b). Therefore x=((2 a/b))1 / 6.

Q. 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

$x = (\frac{2 a}{b})^{1/6}$

$x = (\frac{11 a}{5 b})^{1/6}$

$x = 0$

$x = (\frac{a}{2 b})^{1/6}$

$U (x) = \frac{a}{x ^{12}} - \frac{b}{x ^{6}}$
or $- \frac{12 a}{x ^{13}} - \frac{- 6 b}{x ^{7}} = 0$
or $x^{6} = \frac{2 a}{b}$ .
Therefore $x = (\frac{2 a}{b})^{1/6}$ .

Q. The potential energy between two atoms, in a molecule, is given by U(x)=x12a​−x6b​ where a and b are positive constants and x is the distance between the atoms. The atom is in stable equilibrium, when

x=(b2a​)1/6

x=(5b11a​)1/6

x=0

x=(2ba​)1/6