Q.$\text{O}_2$ molecule consists of two oxygen atoms. In the molecule, nuclear force between the nuclei of the two atoms

The key idea is that nuclear forces are extremely short-ranged, acting only over distances of about $10^{-15}$ m (a few femtometers). The distance between the two oxygen nuclei in an $\text{O}_2$ molecule is roughly $10^{-10}$ m — tens of thousands of times larger.

1. Nuclear force (strong force) binds nucleons within a nucleus but falls to near zero beyond a few femtometers.
2. The separation between nuclei in a molecule is on the order of angstroms ($10^{-10}$ m), far beyond the range of nuclear force. …

The key to this question lies in understanding the range of the nuclear force. The nuclear force (also called the strong nuclear force) is what binds protons and neutrons together inside a nucleus. But it has a very short range — it only acts over distances on the order of a few femtometers ($1 \text{ fm} = 10^{-15} \text{ m}$). Beyond about 2–3 fm, it drops to essentially zero.

In contrast, the distance between the two oxygen nuclei in an O₂ molecule is about $1.2 \times 10^{-10} \text{ m}$ (120 pm). That's more than 100,000 times larger than the range of the nuclear force. So the nuclear force simply cannot reach from one nucleus to the other.

Let's walk through the options carefully.

1. Why option (A) is correct

   The nuclear force is indeed short-ranged. At the interatomic separation in a molecule, it is completely negligible. The bonding in O₂ is due to electrostatic (Coulomb) interactions between electrons and nuclei — the nuclear force plays no role.

2. Why option (B) is wrong

   The electrostatic force between the two positively charged nuclei is repulsive and significant at this distance. But the nuclear force is not "as important" — it is effectively zero. So the statement is false.

3. Why option (C) is wrong

   The nuclear force does not cancel the electrostatic repulsion between the nuclei. In fact, the two nuclei stay apart because the attractive forces from the shared electrons (covalent bonding) overcome the nuclear repulsion. The nuclear force is irrelevant here.

4. Why option (D) is wrong …

Method: The Range-vs-Distance Comparison Method

Whenever a question asks "is force X important at distance Y," you don't need detailed dynamics -- you only need to compare the CHARACTERISTIC RANGE of the force to the ACTUAL SEPARATION in the scenario. This generalises well beyond this one nuclear-force question.

Steps

Step 1: Identify the force's characteristic range

Every fundamental force other than gravity and electromagnetism has a distance beyond which it becomes negligible. Recall that scale -- for the strong nuclear force it is of order $1$-$3$ femtometres ($10^{-15}$ m).

Step 2: Identify the actual separation in the scenario

Determine the real distance between the two objects in question, in the same units. For two nuclei bonded in a molecule, the separation is the interatomic/bond distance, set by electron-cloud sizes -- of order $10^{-10}$ m (angstroms), not nuclear sizes.

Step 3: Compare the two length scales directly …