The potential energy of a system of two atoms as a function of their internuclear distance is shown — Bonding Chemistry Question

STEPS:

1. Understand the potential energy curve for a diatomic system: The graph represents the potential energy of two atoms as they interact at various internuclear distances. At very large distances (to the far right), the potential energy is zero because there is no interaction. As they approach, attractive forces pull them together, lowering the potential energy. At extremely close distances (to the far left), potential energy shoots up rapidly due to strong electrostatic repulsion between the positive nuclei and core electron clouds.
2. Identify the significance of the distance $x$: The distance $x$ marks the absolute minimum (the bottom of the well) of the potential energy curve. This minimum represents the most thermodynamically stable state of the diatomic system.
3. Relate potential energy to force: In physics and chemistry, the net force ($F$) acting on a system is mathematically defined as the negative derivative of the potential energy ($U$) with respect to distance ($r$):
$$F = -\frac{dU}{dr}$$
This means the net force is represented by the slope of the potential energy curve at any given point:
* If the slope is positive (to the right of $x$), there is a negative, attractive force pulling the atoms closer together.
* If the slope is negative (to the left of $x$), there is a positive, repulsive force pushing the atoms apart.
* If the slope is zero (exactly at the minimum, $x$), the net force is zero.
4. Determine the state of the forces at $x$: Since $x$ is at the flat bottom of the potential energy well, the slope of the curve is exactly zero ($\frac{dU}{dr} = 0$). Consequently, the net force acting on the atoms is zero because the attractive electrostatic forces and the repulsive electrostatic forces are perfectly balanced.
5. Conclude the behavior of the atoms: Because the forces are balanced at this distance, $x$ represents the equilibrium bond length of the molecule. The atoms will vibrate back and forth around this point, maintaining an average internuclear distance of $x$, which makes Option A the correct answer.

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WHY_OTHERS_WRONG:

• Option B is incorrect: A net repulsive force only dominates at internuclear distances less than $x$ (to the left of the minimum). In this region, the electron clouds and nuclei are forced too close together, causing the potential energy to rise steeply as they repel each other.
• Option C is incorrect: A net attractive force dominates at internuclear distances greater than $x$ (to the right of the minimum). In this region, the atoms are far apart and are pulled toward each other to maximize favorable nucleus-electron attractions, sliding down the energy well toward $x$.
• Option D is incorrect: The net force can be directly determined from a potential energy curve. Because force is the negative slope of the potential energy with respect to distance ($F = -\frac{dU}{dr}$), analyzing the slope at any point mathematically determines whether the forces are balanced (zero slope), attractive (positive slope), or repulsive (negative slope).