MPSC 2026 Prelims Paper-I · Question 56 of 100

Correct — option (1), "The force is stronger". The nuclear force between two nucleons is spin-dependent: it is stronger when their intrinsic spins are parallel than when they are antiparallel. This is one of the defining properties of the force, listed alongside its short range, its charge independence and its saturation, and it is not a theoretical nicety — it is read directly off the simplest nuclear system there is. The evidence is the deuteron. A deuteron is one proton bound to one neutron, and it is the only bound two-nucleon system in nature. Its total spin is 1 in units of ħ, which means the proton and neutron spins are parallel — the triplet configuration — and its binding energy is about 2.22 MeV, small but real. Now take the same proton and neutron with their spins antiparallel, the singlet configuration. That system has no bound state at all. The two particles are identical in every respect except the relative orientation of their spins, and one arrangement binds while the other does not. Nothing but a spin dependence in the force itself can account for that, and the direction of the dependence is fixed by which arrangement binds: parallel spins, stronger attraction, a bound nucleus. The point is reinforced from the other side. There is no bound di-proton and no bound di-neutron. In each of those pairs the two nucleons are identical fermions, so the Pauli exclusion principle bars them from occupying the same lowest state with parallel spins; they are forced into the antiparallel arrangement, and in that arrangement the attraction is too weak to bind. Only the neutron-proton pair, which is free to take the parallel-spin configuration because the two particles are distinguishable, forms a bound two-body nucleus. The pattern of what exists and what does not in the lightest nuclei is itself the measurement. So the answer is option (1). The force is stronger when the spins are parallel — which is why the deuteron exists, why its spin is 1, and why the periodic table has a starting point at all.

• (2)The force is weaker — Option (2) reverses the dependence. If the attraction were weaker with spins parallel, the bound two-nucleon state would be the singlet, with proton and neutron spins antiparallel, and the deuteron would have total spin zero. It does not — the deuteron's spin is 1, its nucleons are in the parallel-spin triplet configuration, and it is the singlet neutron-proton system that fails to bind. The observed facts of the lightest bound nucleus point squarely against this option.
• (3)The force remains constant — Option (3) denies that the nuclear force depends on spin at all. That is a substantive claim and it is contradicted by the plainest evidence available: a proton and a neutron bind when their spins are parallel and do not bind when they are antiparallel. A spin-independent force could not distinguish the two cases, so both would bind or neither would. Spin dependence is a standard listed property of the nucleon-nucleon interaction precisely because this comparison forces it.
• (4)The force become repulsive — Option (4) attaches a real property of the nuclear force to the wrong variable. The force does turn strongly repulsive — it has a hard repulsive core at very short separations, below roughly 0.7 femtometre, which is what stops nuclear matter from collapsing and gives nuclei their almost constant density. But that repulsion is a function of the DISTANCE between nucleons, not of the relative orientation of their spins. Parallel spins strengthen the attraction; they do not turn it into a repulsion, and if they did the deuteron could not exist.

The nuclear force is the attraction that binds protons and neutrons into a nucleus against the electrostatic repulsion of the protons. Its standard properties form a compact list that examiners return to. It is the strongest of the known interactions at nuclear distances, roughly a hundred times stronger than the electromagnetic force. It is extremely short-ranged, effective over one or two femtometres and negligible beyond about two and a half, which is why nuclear forces play no part in chemistry or in everyday physics. It is charge-independent: the neutron-neutron, proton-proton and neutron-proton attractions are essentially equal once the Coulomb repulsion between protons is set aside. It saturates — each nucleon interacts only with its nearest neighbours rather than with every other nucleon in the nucleus, which is why the binding energy per nucleon stays close to 8 MeV across most of the periodic table instead of growing with mass number. It has a repulsive hard core at very small separations, which keeps nuclear density nearly constant. It is spin-dependent, stronger for parallel spins, which is the property tested here. And it is non-central: the deuteron has a small but non-zero electric quadrupole moment, showing that its ground state is not perfectly spherical and that the force contains a tensor component depending on the orientation of the spins relative to the line joining the nucleons.

At a deeper level the nuclear force is not fundamental. Protons and neutrons are themselves composites of quarks bound by the strong interaction through the exchange of gluons, and the force between whole nucleons is a residual effect of that interaction leaking beyond the boundary of each nucleon — analogous to the way van der Waals forces between neutral molecules are a residue of the electromagnetic forces binding each molecule together. The first successful description came from Hideki Yukawa, who proposed in 1935 that the force is carried by a then-unknown massive particle exchanged between nucleons, and who inferred its mass from the observed range of the force, since a shorter range implies a heavier exchange particle. The particle, the pion, was found in cosmic rays in 1947. For MPSC purposes the examinable material stays at this descriptive level: the properties of the nuclear force, the meson-exchange picture, the binding energy per nucleon curve with its maximum in the iron-nickel region, and the consequence that fusion releases energy for light nuclei while fission does so for heavy ones.

• The nuclear force is spin-dependent and is stronger when the spins of two nucleons are parallel than when they are antiparallel.
• The deuteron — one proton and one neutron with parallel spins, total spin 1, binding energy about 2.22 MeV — is the only bound two-nucleon system. The corresponding antiparallel-spin neutron-proton state is unbound, and there is no bound di-proton or di-neutron.
• Other standard properties: strongest known force at nuclear range; very short range, effective within about 1 to 2 femtometres; charge-independent; saturating, so binding energy per nucleon stays near 8 MeV across most nuclei; and repulsive at separations below roughly 0.7 femtometre.
• The force is non-central. The deuteron's non-zero electric quadrupole moment shows its ground state is not perfectly spherical, evidence of a tensor component in the nucleon-nucleon interaction.
• Hideki Yukawa proposed in 1935 that the nuclear force is mediated by the exchange of a massive particle, inferring its mass from the range of the force; the pion was discovered in cosmic rays in 1947. The nuclear force is a residual effect of the strong interaction between quarks, which is mediated by gluons.

• Confusing the spin dependence of the nuclear force with its distance dependence. Parallel spins make the attraction stronger; very small separations make it repulsive. Two different variables, two different effects.
• Assuming the deuteron's spin is zero. It is 1, because the proton and neutron spins are parallel — and that single fact is the evidence for the answer to this question.
• Thinking the nuclear force is a fundamental interaction. It is a residual effect of the strong interaction between quarks, in the way that intermolecular forces are a residue of electromagnetism.
• Explaining the absence of a bound di-neutron by the nuclear force alone. The Pauli exclusion principle forces two identical nucleons into the antiparallel-spin configuration, in which the attraction is too weak to bind.

Nuclear physics in MPSC's general science section stays descriptive. The commonest shape is a properties question — which of the following is true of the nuclear force, or which property explains a stated observation such as the near-constant binding energy per nucleon. The second shape is the fundamental-forces comparison, ranking the four interactions by strength and range and naming their exchange particles. The third is applied: fission and fusion, the binding energy curve, radioactivity and half-life, and nuclear power. Because the material is qualitative, the reliable preparation is the properties list itself, held together with the single observation that supports each item — saturation from the flat binding energy curve, the hard core from constant nuclear density, spin dependence from the deuteron, and the tensor component from the deuteron's quadrupole moment.

No directly related past PYQ was found.

• practice — not a real PYQ

  The deuteron, the nucleus of heavy hydrogen, has a total spin of 1 in units of ħ. This tells us that :

  • (a)the proton and neutron spins are antiparallel
  • (b)the proton and neutron spins are parallel
  • (c)the deuteron contains two protons
  • (d)the nuclear force is spin-independent

  Answer(b) the proton and neutron spins are parallel. Each nucleon has spin one-half, so the pair can combine to total spin 1 only if the two spins add rather than cancel. Since the parallel-spin state binds and the antiparallel one does not, the deuteron is direct evidence that the nuclear force is spin-dependent and stronger for parallel spins.

• practice — not a real PYQ

  The near-constant value of the binding energy per nucleon, close to 8 MeV, across most of the periodic table is explained by which property of the nuclear force ?

  • (a)Charge independence
  • (b)Saturation
  • (c)Spin dependence
  • (d)The repulsive hard core

  Answer(b) Saturation. Each nucleon interacts only with its nearest neighbours rather than with every other nucleon in the nucleus, so total binding energy grows roughly in proportion to the number of nucleons and the ratio stays nearly constant. Were every nucleon bound to every other, binding energy would rise as the square of the mass number and the per-nucleon figure would climb steadily with atomic mass, which is not what is observed.