Answer
See answers.
Work Step by Step
a. See page 830. Consider a neutral He atom, which has two electrons in the ground state, the 1s shell. The two electrons must have opposite spins, by the Pauli exclusion principle. If we were to try to bond this atom covalently to another He atom, each electron from the first atom would find that it had the same quantum numbers as an electron in the second atom. From the exclusion principle, this is not allowed. The electrons would stay away from the other nucleus. Electrons between 2 neutral helium atoms cannot be shared covalently.
b. Consider the $He_2^+$ molecular ion to be formed from a neutral He atom and a $He^+$ion. The two electrons in the neutral atom must have opposite spins, by the Pauli exclusion principle. Therefore, the single electron belonging to the ion can find an electron of opposite spin that belongs to the neutral atom. These two electrons, because their quantum numbers are not the same, can come close together and spend time between the two nuclei. The two positively charged nuclei are attracted to the electron cloud, and this forms the bond that makes a $He_2^+$ molecular ion.
