Explanation:

Pure rotational microwave spectrum refers to the rotational transitions of a molecule in the microwave region of the electromagnetic spectrum. For a molecule to show a pure rotational microwave spectrum, it must meet certain criteria:

1. The molecule must have a permanent dipole moment.

2. The molecule must be a linear molecule or have a symmetric top structure.

Based on these criteria, the molecule that can show a pure rotational microwave spectrum is HCl.

Explanation for each option:

a) N2: Nitrogen is a diatomic molecule with a linear structure. However, it has no permanent dipole moment, so it cannot show a pure rotational microwave spectrum.

b) CO2: Carbon dioxide is a linear molecule with a permanent dipole moment. However, it has a symmetric top structure, so it cannot show a pure rotational microwave spectrum.

c) OCS: Carbonyl sulfide has a linear structure, but it has no permanent dipole moment. Thus, it cannot show a pure rotational microwave spectrum.

d) HCl: Hydrogen chloride has a linear structure and a permanent dipole moment. Therefore, it meets both criteria for showing a pure rotational microwave spectrum.

Conclusion:

In conclusion, out of the given options, HCl is the only molecule that can show a pure rotational microwave spectrum due to its linear structure and permanent dipole moment.