Explanation:

Oxygen gas (O2) is a diatomic molecule, meaning it consists of two oxygen atoms bonded together. Each oxygen atom has 6 valence electrons, and when they bond together, they share two pairs of electrons, forming a double bond. This double bond is what holds the two oxygen atoms together in the O2 molecule.

Translational degrees of freedom:

Translational degrees of freedom refer to the number of independent ways a molecule can move in space. In other words, it refers to the number of ways a molecule can move and translate as a whole.

For a diatomic molecule like O2, there are three translational degrees of freedom because the molecule can move in three independent directions in space: x, y, and z. These translational degrees of freedom correspond to the movement of the center of mass of the molecule.

Options:

Let's analyze each option given:

a) Monatomic, three: This option is incorrect because O2 is a diatomic molecule, not monatomic. Monatomic molecules consist of single atoms and have three translational degrees of freedom.

b) Diatomic, three: This option is correct. O2 is a diatomic molecule, and it indeed has three translational degrees of freedom.

c) Monatomic, one: This option is incorrect because O2 is a diatomic molecule, not monatomic. Monatomic molecules consist of single atoms and have one translational degree of freedom.

d) Diatomic, one: This option is incorrect. O2 is a diatomic molecule and has three translational degrees of freedom, not one.

Conclusion:

Based on the explanation above, the correct answer is option B, "Diatomic, three." O2 is a diatomic molecule, and it has three translational degrees of freedom.