Silicon (at 300 K) has hole concentration (and equal electron concentration) of 1.5 × $$10^{16}$$​ $$\text m^{-3}$$​. After indium is doped, the new hole concentration is 4.5 × $$10^{22}$$​ $$\text m^{-3}$$​. The value of electron concentration in the doped silicon is:

Correct option is A

​$$\text{Given:} \\\text{Initially, the hole concentration (and electron concentration) in silicon is } 1.5 \times 10^{16} \, \text{m}^{-3}, \\\text{After doping with indium, the new hole concentration is } 4.5 \times 10^{22} \, \text{m}^{-3}. \\\text{In the case of a p-type semiconductor, the electron concentration } n \text{ can be determined using the equation for the product of the electron and hole concentrations,} \\\text{which is constant at a given temperature for intrinsic semiconductors:} \\n \cdot p = n_i^2 \\\text{Where:} \\n \text{ is the electron concentration,} \\p \text{ is the hole concentration,} \\n_i \text{ is the intrinsic carrier concentration of silicon (at 300 K, } n_i \approx 1.5 \times 10^{16} \, \text{m}^{-3}). \\\text{Given that the hole concentration is now } p = 4.5 \times 10^{22} \, \text{m}^{-3}, \text{ we can calculate the electron concentration as:} \\n = \frac{n_i^2}{p} \\\text{Substitute the known values:} \\n = \frac{(1.5 \times 10^{16})^2}{4.5 \times 10^{22}} \\n = \frac{2.25 \times 10^{32}}{4.5 \times 10^{22}} \\n = 5.0 \times 10^9 \, \text{m}^{-3}$$​​