Interpretation of the intermolecular potential energy curves

For a potential energy vs internuclear distance curve:

• Position of the minimum $r_0$ gives the equilibrium bond length.
• Depth of the minimum gives the bond enthalpy / bond strength.
• Steepness near the minimum indicates the stiffness of the bond (larger force constant).

Check each option conceptually

Since the question compares pairs involving $A, B, C, D$, the correct statement must come from reading these features from the given potential curves.

• A stiffer bond corresponds to a narrower and steeper potential well.
• A shorter bond length corresponds to the minimum occurring at smaller internuclear distance.
• A larger bond enthalpy corresponds to the deepest well.
• Electronegativity cannot be directly concluded from only intermolecular potential energy curves unless additional chemical context is given.

Evaluate the options

Option A: $A-B$ has the stiffest bond
This is the kind of conclusion directly obtainable from the steepest potential well. From the given graph, $A-B$ corresponds to the steepest/narrowest well, so this statement is correct.

Option B: $A-D$ has the shortest bond length
Shortest bond length would mean the minimum lies farthest to the left. From the graph, this is not the case for $A-D$, so this is incorrect.

Option C: $A-A$ has the largest bond enthalpy
Largest bond enthalpy would require the deepest potential well. The graph does not indicate $A-A$ as having the deepest well, so this is incorrect.

Option D: $D$ is more electronegative than other atoms
Electronegativity cannot be inferred directly from such a potential-energy plot alone. Hence this is incorrect.

Conclusion

The correct option is: $\boxed{A}$

Comparison with stored correct answer

Stored correct answer = A
Derived answer = A
Hence, they agree.