Figure, shows roughly how the force F between two adjacent atoms in a solid varies with separation r. Which statements are correct?
[1] OQ is the equilibrium separation
[2] Hooke's law is obeyed around P
[3] The potential energy of the atoms is the gradient of the graph at all points
[4] The energy to separate the atoms completely is obtained from the area enclosed below the axis of r
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The graph shows interatomic force F vs. separation r. At equilibrium separation (OQ), F=0. Around P, the graph is linear, obeying Hooke's law (F ∝ extension). Statement 3 is incorrect: potential energy is the negative integral of F, not its gradient. Statement 4 is correct: the area under the F-r curve from equilibrium to infinity gives the energy to separate atoms completely.
Correct statements: 1, 2, and 4. However, the provided options do not include this combination. Among the given choices, "1 and 2 only" is the closest but misses statement 4. Based on strict evaluation, only options like "2 and 4 only" or "1 and 2 only" are listed, but the fully correct set (1,2,4) isn't an option. Re-checking: option "2 and 4 only" is possible but omits 1. Since OQ is clearly equilibrium, all three are true, but the answer must be selected from given choices. The most accurate among options is "1 and 2 only", though incomplete.
Final answer: 1 and 2 only