Zone-refined Si contains residual P at 0.1 parts per billion by weight. Find conductivity in Ω⁻¹ m⁻¹ to 2 decimals. Given $N_A=6.02\times10^{23}$, Si density 2.33 g/cm³, P atomic weight 30.97, electron charge $1.6\times10^{-19}$ C and mobility 0.2 m²/(V s).
One m³ of Si has mass $2.33\times10^6$ g. Its phosphorus mass is $0.1\times10^{-9}(2.33\times10^6)=2.33\times10^{-4}$ g. Assuming one mobile electron per donor, $n=(2.33\times10^{-4}/30.97)(6.02\times10^{23})=4.529\times10^{18}$ m⁻³. Then $\sigma=ne\mu=0.14493$ Ω⁻¹ m⁻¹, approximately 0.14. The intended extrinsic model assumes ionized donors and neglects other carriers.
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