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Experimentally it is observed that neutron (n)-proton(p) system (deuteron) is bound, but the proton-proton and neutron-neutron systems are not bound. This is due to :

  • A.unequal nuclear force between n-p, n-n and p-p systems
  • B.unequal total charges of n-p, n-n and p-p systems
  • C.Pauli's principle
  • D.non-conservation of angular momentum

Answer: C

The difference is due to Pauli's principle.

The nuclear force is spin dependent: it is strong enough to bind two nucleons only in the spin-triplet state (S = 1). The deuteron's ground state is exactly this, an L = 0, S = 1 state of a neutron and a proton, which are different particles and face no restriction.

Two protons or two neutrons are identical fermions, so their total wave function must be antisymmetric. In the lowest, L = 0 state the space part is symmetric, which forces the spin part to be the antisymmetric singlet (S = 0), and the singlet force is too weak to bind. So the Pauli principle keeps p-p and n-n out of the one state that binds.

The nuclear force itself is charge independent to a good approximation, so 'unequal nuclear force' is not the reason, and charge only adds Coulomb repulsion for p-p, which cannot explain why n-n is unbound. Angular momentum is conserved throughout.

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