Doping of a semiconductor (with small impurity atoms) generally changes the resistivity as follows.

For pure $Ge$,the intrinsic carrier density is $10^{19} \ m^{-3}$. If donor impurity is added with a density of $10^{23} \ m^{-3}$,what will be the hole density (in $m^{-3}$)?

Indium impurity in germanium makes

$A$ semiconductor doped with a donor impurity is

$A$ semiconductor has equal electron and hole concentration of $2 \times 10^8 \ m^{-3}$. On doping with a certain impurity,the electron concentration increases to $4 \times 10^{10} \ m^{-3}$. What is the new hole concentration of the semiconductor?

The concentration of electrons in an intrinsic semiconductor is $6 \times 10^{15} \,m^{-3}$. On doping with an impurity, the electron concentration increases to $4 \times 10^{22} \,m^{-3}$. In thermal equilibrium, the concentration of the holes in the doped semiconductor is: