Discuss the stability of an atom in a molecule possessing Lennard-joners potential energy function
`U(x)=4epsi[((alpha)/(x))^(12)-((alpha)/(x))^(6)]`
where x=separation between the atoms, `alpha=0.263` nm and `epsi=1.5xx10^(-22)J`

Explanation

To discuss the stability of an atom in a molecule possessing the Lennard-Jones potential energy function, we need to analyze the given potential energy function:

\[ U(x) = 4\epsilon \left( \left( \frac{\alpha}{x} \right)^{12} - \left( \frac{\alpha}{x} \right)^{6} \right) \]

where \( x \) is the separation between the atoms, \( \alpha = 0.263 \) nm, and \( \epsilon = 1.5 \times 10^{-22} \) J.

### Step 1: Find the Equilibrium Position
To find the equilibrium position, we need to differentiate the potential energy function \( U(x) \) with respect to \( x \) and set the derivative equal to zero.
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