### Correct Option: B. equal to the number of holes in the valence band #### Detailed Explanation: In a pure semiconductor, the behavior of charge carriers—electrons and holes—is fundamental to understanding its electrical properties. Let's break down the concepts involved: 1. **Understanding Semiconductors**: - A semiconductor is a material that has electrical conductivity between that of a conductor and an insulator. Common examples include silicon and germanium. - In a pure (intrinsic) semiconductor, the number of charge carriers is determined solely by the properties of the material itself, without any impurities or doping. 2. **Charge Carriers**: - **Electrons** are negatively charged particles that can move freely in the conduction band, allowing for electrical conduction. - **Holes** are the absence of electrons in the valence band, which can also contribute to conduction. When an electron leaves its position in the valence band, it creates a hole, which can be thought of as a positive charge carrier. 3. **Electron-Hole Pair Generation**: - When thermal energy is supplied to a pure semiconductor, some electrons gain enough energy to jump from the valence band to the conduction band. This process creates an equal number of electrons in the conduction band and holes in the valence band. - Therefore, for every electron that moves to the conduction band, a corresponding hole is created in the valence band. 4. **Equilibrium Condition**: - In thermal equilibrium, the number of electrons in the conduction band (n) is equal to the number of holes in the valence band (p). This relationship can be expressed mathematically as: \[ n = p \] - This equality holds true for intrinsic semiconductors because the generation of electron-hole pairs is a balanced process. 5. **Conclusion**: - Since the number of electrons in the conduction band is equal to the number of holes in the valence band, the correct answer is **B**. #### Why Other Options Are Incorrect: - **Option A: less than the number of holes in the valence band**: - This option suggests that there are fewer electrons than holes. However, as explained, for every electron that jumps to the conduction band, a hole is created. Thus, this statement is incorrect. - **Option C: greater than the number of holes in the valence band**: - This option implies that there are more electrons than holes. This would only be true in a doped semiconductor (n-type), where additional electrons are introduced. In a pure semiconductor, this is not the case. - **Option D: twice the number of holes in the valence band**: - This option suggests a specific ratio that does not apply to intrinsic semiconductors. The relationship is one-to-one, not two-to-one, making this option incorrect. #### Summary of Key Points: - In a pure semiconductor, the number of electrons in the conduction band is equal to the number of holes in the valence band. - This equality arises from the process of thermal excitation, where each electron that moves to the conduction band creates a corresponding hole. - The relationship can be expressed as \( n = p \) for intrinsic semiconductors. - Understanding this concept is crucial for grasping the behavior of semiconductors in electronic devices.