If a small amount of antimony is added to germanium crystal,

$A$ pure semiconductor crystal has $5 \times 10^{22}$ atoms per $cm^3$. It is doped by $1$ ppm concentration of pentavalent element. The number of holes in the doped semiconductor is (given that $n_i = 1.5 \times 10^{10} cm^{-3}$):

What is the number density of donor atoms which must be added to a pure germanium semiconductor to make an $n$-type semiconductor of conductivity $6.4 \ \Omega^{-1} \ cm^{-1}$? The mobility of electrons in $n$-type germanium is $4 \times 10^3 \ cm^2 \ V^{-1} \ s^{-1}$. Neglect the contribution of holes to conductivity.

What is the relation between the number density of holes $(n_h)$ and free electrons $(n_e)$ in an intrinsic semiconductor at room temperature?

$N-$ type semiconductors are obtained when germanium is doped with:

In pure $Si$ at $300 \ K$,the concentration of electrons $(n_e)$ and holes $(n_h)$ is equal and is $1.5 \times 10^{16} \ m^{-3}$. If the concentration of holes $(n_h)$ increases to $3 \times 10^{22} \ m^{-3}$ after doping with Indium,calculate the concentration of electrons $(n_e)$ in the doped $Si$.