For a pure $Si$ crystal at $300 \ K$,the electron $(n_e)$ and hole $(n_h)$ concentrations are equal,being $1.5 \times 10^{16} \ m^{-3}$. On doping with Indium,the hole concentration increases to $4.5 \times 10^{22} \ m^{-3}$. Calculate the new electron concentration $(n_e)$ in the doped $Si$.
- A$4.3 \times 10^{10} \ m^{-3}$
- B$5 \times 10^{-7} \ m^{-3}$
- C$3.8 \times 10^6 \ m^{-3}$
- D$5 \times 10^9 \ m^{-3}$
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