Q.Fusion processes, like combining two deuterons to form a He nucleus are impossible at ordinary temperatures and pressure. The reasons for this can be traced to the fact:

Fusion needs two deuterons to get within about $1\ \text{fm}$ of each other, because the nuclear force that can bind them acts only over that short range — this is option (A). But both deuterons are positively charged, so Coulomb repulsion strongly resists them getting that close at ordinary thermal energies — this is option (B). Both facts together — short range and positive charge — are needed to explain why fusion is blocked at ordinary temperature and pressure (the Coulomb-barrier argument). Options (C) (complete ionisation) and (D) (nuclei breaking up first) are not correct reasons. …

This is an NCERT Exemplar multiple-correct-answer (MCQ-II) question — more than one option can be correct, and here (A) and (B) are both needed together to fully explain why fusion doesn't happen at ordinary temperature and pressure.

Step 1 — Why closeness matters: option (A).

The strong nuclear force that binds nucleons together is attractive, but it acts only over an extremely short range — roughly $1\ \text{fm}$ ($10^{-15}\ \text{m}$), comparable to the size of a nucleus itself. Beyond this range it drops off essentially to zero. So for two deuterons to fuse into a helium nucleus, they must first be brought within about $1\ \text{fm}$ of each other — only then does the nuclear force take over and pull them together. This is exactly what option (A), "nuclear forces have short range," is telling you.

Step 2 — Why that closeness is blocked: option (B).

A deuteron nucleus carries a net positive charge ($+e$, from its single proton). Two deuterons approaching each other therefore repel electrostatically, via Coulomb's law:

As the separation $r$ shrinks toward the $\sim 1\ \text{fm}$ distance the nuclear force needs, this repulsion grows very large. The height of this "Coulomb barrier" at $r \approx 1\ \text{fm}$ works out to roughly

At ordinary temperature (say $300\ \text{K}$), the average thermal kinetic energy of a particle is only $k_B T \approx 0.025\ \text{eV}$ — many millions of times too small to climb this barrier. This is exactly what option (B), "nuclei are positively charged," is telling you: it is that positive charge which sets up the barrier in the first place.

Step 3 — Why (A) and (B) must be taken together.

Neither fact alone tells the whole story:

• (A) alone says the nuclear force's range is short — it explains what the deuterons need to achieve (get to within $\sim 1\ \text{fm}$ of each other), but not why that is hard to do.
• (B) alone says the nuclei repel each other — it explains why closeness is resisted, but not how close they actually need to get before that repulsion becomes the deciding obstacle. …

Method: Identifying the Root Physical Cause in a Conceptual MCQ (Separating the Barrier from Merely Necessary Conditions)

This method applies to conceptual multiple-choice questions that ask "why" a process is impossible/possible, where several options each state something true but only one of them is the actual mechanism responsible.

Steps

Step 1: Restate precisely what needs explaining

Pin down the exact physical fact the question wants explained — here, why two nuclei do not spontaneously fuse under ordinary conditions (room temperature and pressure), even though fusion releases energy and is therefore energetically "downhill" once it happens.

Step 2: Identify what has to happen at the microscopic level for the process to occur

For fusion, the nuclei must get close enough (within about $10^{-15}$ m, the range of the strong nuclear force) for the short-range attractive force to take over and bind them.

Step 3: For each answer option, ask "is this the obstacle itself, or just a separate/necessary fact that doesn't explain the block"?

Go through each option and test it against Step 2: does keeping or removing this fact directly change whether the nuclei can get close enough? A fact can be true and even necessary for the process (like the short range of the nuclear force, which is a precondition for what happens once nuclei are close) without being the actual thing standing in the way of getting close in the first place. …