[oscillate_wildly]

How much rotational energy would you expect one mole of a diatomic molecule to
possess on average at a temperature T?

I thought the answer would be (1/2RT) x 2 but the question is 3 marks so it can't be. Any help will be greatly appreciated.

Thanks.

[Yggdrasil]

You have the right idea.  From the equipartition theorem, we know that each degree of freedom contributes on average (1/2)RT of kinetic energy per mole [not 1/(2RT) as you have written].  Since linear molecules have only 2 rotational degrees of freedom, the rotational energy would be 2 * (1/2)RT = RT.