Question

The conduction band of a solid is partially filled at 0 K. Will it be a conductor, a semiconductor or an insulator?

Answer 1

It will be a conductor. As the elements having partially filled conduction band belong to the category of elements whose outermost subshell consists of an odd number of electrons, they are good conductors of electricity. When an electric field is applied, electrons in the partially filled band gain energy and start drifting. So, the conductor will conduct even at 0 K. A semiconductor behaves like an insulator at 0 K and an insulator conducts poorly only at very high temperatures.
As the given material has free electrons to conduct even at 0 K, it is a conductor.