The intrinsic charge carrier density in germanium crystal at $300K\ is\ 2.5\times \dfrac{{{10}^{13}}}{c{{m}^{3}}}$. Density is an n-type germanium crystal at $300K\ be\ 5\times \dfrac{{{10}^{16}}}{c{{m}^{3}}}$, the hole density in this n-type crystal at 300 K would be
(A) $2.5\times \dfrac{{{10}^{13}}}{c{{m}^{3}}}$
(B) $5\times \dfrac{{{10}^{6}}}{c{{m}^{3}}}$
(C) $1.25\times \dfrac{{{10}^{10}}}{c{{m}^{3}}}$
(D) $0.2\times \dfrac{{{10}^{4}}}{c{{m}^{3}}}$

Hint: We know that intrinsic carrier concentration is the number of electrons in the conduction band or the number of holes in the valence band in intrinsic material. This number of carriers depends on the band gap of the material and on the temperature of the material. In an intrinsic semiconductor, which does not contain any impurity, the concentrations of both types of carriers are ideally equal. If an intrinsic semiconductor is doped with a donor impurity then the majority carriers are electrons. On the basis of this concept we have to solve this question.

Complete step-by-step answer:
We know that law of mass action, law stating that the rate of any chemical reaction is proportional to the product of the masses of the reacting substances, with each mass raised to a power equal to the coefficient that occurs in the chemical equation.
$nP=n{{i}^{2}}$[By Mass Action law]
$n=\dfrac{2.5\times 2.5\times {{10}^{26}}}{5\times {{10}^{16}}}$
$n=1.25\times \dfrac{{{10}^{10}}}{c{{m}^{3}}}$
It is known that the rate law is composed of rate constant and concentration of the reactants with the order of overall reaction. The law of mass action equation consists of a concentration of reactants and products raised to the power of the stoichiometric coefficient.

Hence, the correct answer is Option C.

Note: We should know that semiconductors are materials which have a conductivity between conductors (generally metals) and non-conductors or insulators (such as most ceramics). Semiconductors can be pure elements, such as silicon or germanium, or compounds such as gallium arsenide or cadmium selenide. Semiconductors are especially important as varying conditions like temperature and impurity content can easily change their conductivity. The combination of various semiconductor types together generates devices with special electrical properties, which allow control of electrical signals.
It is known that an extrinsic semiconductor is a semiconductor doped by a specific impurity which is able to deeply modify its electrical properties, making it suitable for electronic applications (diodes, transistors, etc.) or optoelectronic applications (light emitters and detectors).