Suppose that a silicon semiconductor is doped with phosphorus so that one silicon atom in $1.5 \times 10^6$ is replaced by a phosphorus atom. Assuming that the “extra” electron in every phosphorus atom is donated to the conduction band, by what factor is the density of conduction electrons increased? The density of silicon is $2330 \textrm{ kg/m}^3$, and the density of conduction electrons in pure silicon is about $10^{16} \textrm{ m}^{-3}$ at room temperature.