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

A partial toy band keeps both filled and empty slots visible. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A partial band has some filled slots

Five electrons fill 5 of the 8 slots.

filled=electrons=5,\quad slots=8

The empty count closes the ledger

The remaining empty count is 3, so the occupancy verdict is partial.

empty=8 - 5=3,\quad occupancy=\mathrm{partial}