The n-type semiconductor has equal concentration of free electron and donor atoms.

Answer:

Introduction:
In order to understand the answer to this question, we need to have a basic understanding of the different types of materials and their electronic structures.

Materials and their Electronic Structures:
1. Metals: Metals are materials that have a high concentration of free electrons. These free electrons are responsible for the high electrical conductivity of metals. In metals, the number of free electrons is much greater than the number of donor atoms.

2. Insulators: Insulators are materials that have a very low concentration of free electrons. In insulators, the valence band is completely filled and the conduction band is empty. The number of free electrons is negligible compared to the number of donor atoms.

3. Semiconductors: Semiconductors are materials that have an intermediate concentration of free electrons. They can be classified into two types: P-type and N-type.

- P-type semiconductors: In P-type semiconductors, the concentration of free electrons is low. This is achieved by introducing impurity atoms with fewer valence electrons than the host material. These impurity atoms are called acceptor atoms. The number of donor atoms in P-type semiconductors is much greater than the number of free electrons.

- N-type semiconductors: In N-type semiconductors, the concentration of free electrons is high. This is achieved by introducing impurity atoms with more valence electrons than the host material. These impurity atoms are called donor atoms. The number of donor atoms in N-type semiconductors is equal to the number of free electrons.

Explanation:
Based on the above information, we can conclude that the number of free electron concentration is equal to the number of donor atoms in N-type semiconductors (option C). In N-type semiconductors, the impurity atoms (donor atoms) introduce additional electrons into the material, which become free to move and contribute to the electrical conductivity. The number of free electrons in N-type semiconductors is equal to the number of donor atoms, as each donor atom contributes one free electron.

Therefore, option C is the correct answer.