Suppose a pure Si crystal has \(5\times10^{28}\) atoms per \(\text{m}^3\). It is doped with \(5\times10^{22}\) atoms per \(\text{m}^3\) of Arsenic. Calculate the majority and minority carrier concentration in the doped silicon.
Given:
\[
n_i=1.5\times10^{16}\,\text{m}^{-3}
\]