Which of the following graphs correctly shows the relationship between potential energy and internuc — Bonding Chemistry Question

STEPS:

1. Understand the electrostatic forces at play: As two isolated hydrogen atoms ($\text{H}$) approach each other to form a covalent bond, three primary electrostatic forces act within the system:
* Attraction between the nucleus of one atom and the electron cloud of the other.
* Repulsion between the two positively charged nuclei.
* Repulsion between the two negatively charged electron clouds.
2. Analyze the potential energy at large internuclear separation (far right of the x-axis): When the hydrogen atoms are relatively far apart, they do not interact. At this infinite separation, the electrostatic forces are negligible, and the potential energy of the system is conventionally defined as zero.
3. Analyze the potential energy as the atoms approach (moving right-to-left): As the distance decreases, the attractive forces between the nucleus of one atom and the electron cloud of the other begin to dominate over repulsive forces. Because attraction stabilizes the system, the potential energy decreases, dropping below the zero line (becoming negative).
4. Identify the equilibrium bond distance (the potential energy well): As the atoms move closer, they reach a specific internuclear distance where the attractive and repulsive forces are perfectly balanced. This is the most thermodynamically stable state of the system, represented by the minimum potential energy (the bottom of the well). The depth of this well corresponds to the bond energy (energy released when the bond forms), and the distance at this minimum corresponds to the bond length of the stable $\text{H}_2$ molecule.
5. Analyze the potential energy at extremely short distances (far left of the x-axis): If the nuclei are forced closer together than the equilibrium bond length, the repulsive forces (especially the powerful electrostatic repulsion between the two positively charged nuclei) dominate exponentially. This causes the potential energy to rise sharply and become highly positive.
6. Select the matching graph: A correct graph must start extremely high and positive on the far left, dip down into a negative well representing the stable bond, and asymptotically approach zero from below as separation increases to the right. This describes Graph D.

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WHY_OTHONG_WRONG:

• Graph A is incorrect: This graph shows potential energy that is always negative and simply rises to zero as separation increases. It completely lacks a minimum well (no stable bond length) and fails to depict the rapid rise in potential energy caused by nuclear repulsion at very short distances.
• Graph B is incorrect: This graph shows potential energy that is always positive and decreases asymptotically to zero. This represents a purely repulsive system (such as two like charges) where a stable chemical bond cannot form.
• Graph C is incorrect: This graph displays a potential energy maximum (a hill) at intermediate distances and a decrease at close separation, which is the exact opposite of physical reality (attraction stabilizes at intermediate distances, and repulsion destabilizes at close distances).
• Graph E is incorrect: Although it shows a minimum well, it incorrectly includes a potential energy peak (an activation barrier) as the atoms separate. In reality, pulling two neutral hydrogen atoms apart from their equilibrium distance simply requires overcoming the bond energy, and the potential energy rises smoothly toward zero without any intermediate barrier.