In Germanium it is found that concentration of conducting electron is $3 \times 10^{19}$ per cubic meter. When Phosphorus impurity is doped the concentration of conducting electron increases to $2 \times 10^{23}$ per cubic meter. If product of hole concentration and conducting electron is independent of amount of impurity find the hole concentration in doped Germanium.

Question

$(a)\;2.8 \times 10^{15} \\ (b)\;4.5 \times 10^{16} \\ (c)\;1.8 \times 10^{16} \\ (d)\;4.5 \times 10^{15}$