A $1 \mathrm{~cm}^{3} \mathrm{~Si}$ cube is doped with As with a concentration of $1$ atom per $10^{9} \mathrm{~Si}$ atoms. The resistance of the doped $\mathrm{Si}$ cube in $\mathrm{Ohms}$ is $\_\_\_\_$ (rounded off to one decimal place).
Given:
Atomic concentration of $\mathrm{Si}=5 \times 10^{22} \mathrm{~cm}^{-3}$
Intrinsic concentration of electrons in $\mathrm{Si}=1 \times 10^{10} \mathrm{~cm}^{-3}$
Electron mobility in $\mathrm{Si}=1350 \mathrm{~cm}^{2} \cdot \mathrm{~V}^{-1} \cdot \mathrm{~s}^{-1}$
Hole mobility in $\mathrm{Si}=450 \mathrm{~cm}^{2} \cdot \mathrm{~V}^{-1} \cdot \mathrm{~s}^{-1}$
Electronic charge $=1.6 \times 10^{-19} \mathrm{C}$
