In pure $Si$ at $300 \ K$,the concentration of electrons $(n_e)$ and holes $(n_h)$ is equal and is $1.5 \times 10^{16} \ m^{-3}$. If the concentration of holes $(n_h)$ increases to $3 \times 10^{22} \ m^{-3}$ after doping with Indium,calculate the concentration of electrons $(n_e)$ in the doped $Si$.

• A
  $3.5 \times 10^5 \ m^{-3}$
• B
  $7.5 \times 10^9 \ m^{-3}$
• C
  $2.5 \times 10^{-9} \ m^{-3}$
• D
  $5.5 \times 10^{12} \ m^{-3}$