Suppose a pure Si crystal has $5 \times 10^{28}$ atoms per $\text{m}^3$. It is doped with $5 \times 10^{22}$ atoms per $\text{m}^3$ of Arsenic. Calculate the majority and minority carrier concentration in the doped silicon. (Given : $n_i = 1\cdot5 \times 10^{16} \text{ m}^{-3}$)