Empty Band Has Only Empty Slots - Solid-State Physics: Lattices, Phonons, and Band Filling Step by Step

The empty boundary case has zero filled slots. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

The slot count comes from sites times states per site

Four repeating cells with two states per cell make 8 toy slots. This cell count is distinct from the endpoint-site count.

slots=4\cdot 2=8

Zero electrons leaves every slot empty

With 0 electrons, the empty count is 8 and the occupancy verdict is empty.

filled=0,\quad empty=8,\quad occupancy=\mathrm{empty}