The correct option is **B**: "while resistance of metals decreases with temperature, the reverse is the case for semiconductors." ### Detailed Explanation To understand the differences between pure semiconductors and pure metals, we need to look at their electrical properties, particularly how their resistance changes with temperature. 1. **Electrical Conductivity**: - **Metals**: Metals are good conductors of electricity. They have a high density of free electrons that can move easily through the material. When the temperature of a metal increases, the metal atoms vibrate more vigorously, which leads to more collisions between the free electrons and the vibrating atoms. This increased scattering of electrons results in a decrease in conductivity and an increase in resistance. - **Semiconductors**: Semiconductors, such as silicon or germanium, have fewer free charge carriers at low temperatures. However, as the temperature increases, more electrons gain enough energy to jump from the valence band to the conduction band, creating more charge carriers. This increase in charge carriers leads to a decrease in resistance as temperature rises. 2. **Temperature Dependence**: - For metals, the relationship can be summarized as: \[ R(T) = R_0(1 + \alpha(T - T_0)) \] where \( R(T) \) is the resistance at temperature \( T \), \( R_0 \) is the resistance at a reference temperature \( T_0 \), and \( \alpha \) is the temperature coefficient of resistance (which is positive for metals). - For semiconductors, the relationship is more complex but can be generally stated as: \[ R(T) \propto \frac{1}{n(T)} \] where \( n(T) \) is the number of charge carriers, which increases with temperature. ### Why the Other Options are Incorrect - **Option A**: "Metals are harder than semiconductors." - This statement is not universally true. The hardness of a material depends on its atomic structure and bonding, not solely on whether it is a metal or a semiconductor. Some semiconductors can be quite hard (like diamond, which is a form of carbon). - **Option C**: "The resistance of metals increases with temperature, while for semiconductors, it is the reverse." - This option is incorrect because it incorrectly states the behavior of metals. In reality, the resistance of metals **increases** with temperature, while the resistance of semiconductors **decreases** with temperature. - **Option D**: "Metals have forbidden gaps while semiconductors have not." - This statement is misleading. Metals do not have a forbidden energy gap (band gap) in the same way that semiconductors do. Semiconductors have a small band gap that allows for the controlled conduction of electricity, while metals have overlapping conduction and valence bands, allowing for free electron movement. ### Summary of Key Points - **Metals**: Resistance increases with temperature due to increased atomic vibrations causing more electron scattering. - **Semiconductors**: Resistance decreases with temperature as more charge carriers are generated. - **Key Difference**: The temperature dependence of resistance is a fundamental distinction between metals and semiconductors. - **Common Pitfall**: Confusing the behavior of resistance in metals and semiconductors can lead to incorrect conclusions about their properties. This understanding is crucial for applications in electronics, where semiconductors are used in devices like diodes and transistors, while metals are often used for wiring and connections.