In a non-degenerate bulk semiconductor with electron density $n = 10^{16} \; \text{cm}^{-3},$ the value of $E_{c} – E_{Fn} = 200 \; \text{meV},$ where $E_{c}$ and $E_{Fn}$ denote the bottom of the conduction band energy and electron Fermi level energy, respectively. Assume thermal voltage as $26 \; \text{meV}$ and the intrinsic carrier concentration is $10^{10} \; \text{cm}^{-3}.$ For $ n = 0.5 \times 10^{16} \; \text{cm}^{-3},$ the closest approximation of the value of $(E_{c} – E_{Fn}),$ among the given options, is ____________.
- $226 \; \text{meV}$
- $174 \; \text{meV}$
- $218 \; \text{meV}$
- $182 \; \text{meV}$