A Si specimen is made into a p-type semiconductor by doping on an average one indium atom per \[6 \times {10^7}\] silicon atoms. If the number density of atoms in Si is $6 \times {10^{28}}/{m^3}$. What are indium atoms per $cm^3$?
(A) ${10^{12}}$
(B) ${10^{15}}$
(C) ${10^{18}}$
(D) ${10^{20}}$

Hint: Indium is not naturally found on the earth’s surface. In nature the indium is soft, malleable, ductile and post transition metal.
Indium atoms doped per $c{m^3}$ = number density of atoms in silicon specimen/ number of silicon atoms needed to dope 1 atom of indium.

Complete step by step answer:
Following information is given in the question.
Number of silicon atoms needed to dope 1 atom of indium =\[6 \times {10^7}\].
Number density of atoms in silicon specimen =$6 \times {10^{28}}/{m^3} = 6 \times {10^{22}}/{m^3}$
Now let us find the indium atoms doped per $c{m^3}$, using the following formula.
Indium atoms doped per $c{m^3}$ = number density of atoms in silicon specimen/ number of silicon atoms needed to dope 1 atom of indium
Let us substitute the values in the above formula.
Indium atoms doped per $c{m^3}$= $\dfrac{{6 \times {{10}^{22}}}}{{6 \times {{10}^7}}}$
Let us further simplify it.
Indium atoms doped per $c{m^3}$ $ = {10^{15}}$
Hence, option (B) ${10^{15}}$ is the correct option.

Additional information:
Semiconductors are the materials having electrical conductivity in between conductors and insulators. They are important as varying temperature and impurity can easily change their conductivity. So we can change their conductivity according to the need.
By the various combinations of semiconductor types, we can design a device of specific electrical property. Semiconductors are of two types, intrinsic semiconductors, and extrinsic semiconductors.
1. Intrinsic semiconductors are pure semiconductor materials. For example, germanium and silicon are the most common intrinsic semiconductors.
2. Extrinsic semiconductors are impurity added semiconductors. It was found that adding a small amount of impurity can increase the conductivity significantly. Extrinsic semiconductors are of two types N-TYPE and P-TYPE semiconductors.

When a pure semiconductor is doped by a pentavalent impurity, the fifth electron of dopant is set free. Hence the name n-type semiconductor.
Similarly, when the pure semiconductor is doped with a trivalent impurity, one electron of pure semiconductor, hence the name p-type semiconductor.

Note: Doping is a process of adding impurity to the pure semiconductor to increase their conductivity.