$A$ semiconductor doped with a donor impurity is

Why is it required to add impurity to a pure semiconductor? Mention its condition and explain what impure semiconductors are.

For an intrinsic semiconductor, if $n_h$ and $n_e$ represent the number of holes per unit volume and the number of free electrons per unit volume respectively, then:

If one indium atom is doped per $5 \times 10^7$ silicon atoms,and the number density of silicon atoms is $5 \times 10^{28} \, \text{atoms}/\text{m}^3$,find the number density of acceptor atoms in $\text{atoms}/\text{cm}^3$.

If $n_{e}$ and $n_{h}$ are the number of electrons and number of holes respectively in a semiconductor heavily doped with phosphorus,then:

$A$ potential difference of $2\,V$ is applied between the opposite faces of a $Ge$ crystal plate of area $1\,cm^{2}$ and thickness $0.5\,mm$. If the concentration of electrons in $Ge$ is $2 \times 10^{19}/m^{3}$ and mobilities of electrons and holes are $0.36\,m^{2}/(V\cdot s)$ and $0.14\,m^{2}/(V\cdot s)$ respectively,then the current flowing through the plate will be... (in $,A$)