The nucleus of deuterium, known as the deuteron, is a bound state of a proton and a neutron, both of which are spin-1/2, isospin- 1/2 particles. Experimentally, the spin of the deuteron is measured to be 1 , while its isospin is 0 . (a) What does this tell us about the symmetries of the spin and isospin parts of the deuteron wavefunction? (b) The S z​ -projection of a given deuteron is observed to be 0 . Write down its spin ⊗ isospin wavefunction interms of those of its component nucleons and motivate why it takes this form. [Note that in this question you don't need to consider the quark wavefunctions at all, only those of the proton and neutron based on their overall spin and isospin.]