Chapter 10 classified a crystal by counting its valence electrons per primitive cell: silicon's eight electrons fill exactly four bands, leaving no partly filled band and so no metal. A phosphorus-doped silicon crystal, Nd=1.0×1015cm−3, does add one extra electron per dopant atom beyond that exact count. Explain, with a numeric comparison, why this doped crystal is still described by this chapter's dilute, hydrogen-like picture rather than by Chapter 10's rule that a partly filled band is a metal, even though an electron really has been added beyond the closed-shell count.