The number density of conduction electrons in pure silicon at room temperature is about $$10^{16}\ \text{m}^{-3}$$. The number density of conduction electrons is increased by a factor of $$10^6$$ by doping the silicon lattice with phosphorus. Assume that at room temperature every phosphorus atom contributes one electron to the conduction band. The fraction of silicon atoms replaced by phosphorus atoms is, given the density of silicon as $$2.33\ \text{g cm}^{-3}$$ and the molar mass of silicon as $$28.1\ \text{g mol}^{-1}$$,