The observation for three materials shows: Material A absorbs all the visible light (opaque) Material B is transparent to all the visible light (transparent) Material C absorbs blue light but is transparent to red light. (Blue light has wavelength 0.4 �m, red light has wavelength 0.7 �m, and all other visible lights have wavelengths in between.) (5.a) Draw corresponding energy band diagram for each sample. (5.b) Rank materials A, B, and C on scale of increasing insulator behavior: (5.c) State the reasons why you ranked as you did in (5.b). (5.d) Predict trend of resistivity as function of increasing temperature for the three samples
To answer these questions, we need to understand the properties of materials in relation to their absorption of light and behavior as insulators. Let's break it down into the following steps:
Step 1: Drawing energy band diagrams
- Energy band diagrams visualize the energy levels of electrons in a material.
- For Material A, since it absorbs all visible light, it does not allow any photons to pass through. Therefore, it is an opaque material. In the energy band diagram, the valence band would be completely filled, and there would be a large energy gap to the conduction band.
- For Material B, being transparent to all visible light means it allows photons of all wavelengths to pass through without absorbing them. In the energy band diagram, the valence band would be partially filled, and the energy gap to the conduction band would be smaller than in Material A.
- For Material C, it absorbs blue light but is transparent to red light. This implies that blue light has enough energy to excite electrons across the energy gap, while red light does not. In the energy band diagram, the valence band would be partially filled, and there would be a smaller energy gap between the valence and conduction bands compared to Material A.
Step 2: Ranking materials based on insulator behavior
- To rank materials A, B, and C on a scale of increasing insulator behavior, we need to consider their band structures.
- Material A would have the largest energy gap between the valence and conduction bands, making it a better insulator compared to the other materials.
- Material C would have a smaller energy gap, allowing some electron excitation, which makes it a weaker insulator compared to Material A.
- Material B, being transparent to all visible light, would have the smallest energy gap, making it the weakest insulator among the three.
Step 3: Reasoning behind the ranking
- Material A absorbs all visible light, indicating a significant energy gap, which suggests strong insulator behavior.
- Material C absorbs blue light but is transparent to red light, indicating a smaller energy gap than Material A, making it a weaker insulator.
- Material B is transparent to all visible light, suggesting the smallest energy gap and the weakest insulator behavior.
Step 4: Predicting resistivity trends with increasing temperature
- Generally, as temperature increases, the resistivity of materials increases.
- For Material A, with a large energy gap and high insulator behavior, the resistivity is expected to increase the most with increasing temperature.
- Material C, with a smaller energy gap and weaker insulator behavior, would have a moderate increase in resistivity with increasing temperature.
- Material B, being the weakest insulator, would have the smallest increase in resistivity with increasing temperature.
By following these steps, you should be able to draw the energy band diagrams, rank the materials based on insulator behavior, and predict the trend of resistivity as a function of increasing temperature.
(5.a) To draw the corresponding energy band diagram for each sample, we need to understand the behavior of the materials with respect to absorption and transmission of light.
Material A (opaque): Since material A absorbs all visible light, it means it does not transmit any of the light waves. The energy band diagram for material A would show a complete bandgap, indicating that no electrons can transition from the valence band to the conduction band.
Material B (transparent): Material B is transparent to all visible light, which means it allows all light waves to pass through it without absorption. The energy band diagram for material B would show a small or no bandgap, indicating that electrons can transition easily from the valence band to the conduction band.
Material C (blue light absorber, red light transparent): Material C absorbs blue light while being transparent to red light. This suggests that it has a larger bandgap than material B but a smaller bandgap than material A. The energy band diagram for material C would show a larger bandgap than material B but a smaller bandgap than material A.
(5.b) Ranking materials A, B, and C on the scale of increasing insulator behavior:
1. Material A (opaque) - Highest insulator behavior: Since it absorbs all visible light, it likely has a wide bandgap and does not allow electron transitions from the valence band to the conduction band easily.
2. Material B (transparent) - Intermediate insulator behavior: It allows all visible light to pass through, indicating a smaller or no bandgap compared to material A.
3. Material C (blue light absorber, red light transparent) - Lowest insulator behavior: While it absorbs blue light, it still allows red light to pass through. This suggests a smaller bandgap compared to material A but a larger bandgap compared to material B.
(5.c) Reasons for the ranking in (5.b):
Material A is ranked highest as it absorbs all visible light, suggesting a wider bandgap and thus a higher insulator behavior.
Material B is ranked intermediate as it is transparent to all visible light, indicating a smaller or no bandgap compared to material A.
Material C is ranked lowest as it absorbs only blue light while allowing red light to pass through, indicating a smaller bandgap compared to material A but a larger bandgap compared to material B.
(5.d) Predicting the trend of resistivity as a function of increasing temperature for the three samples:
For all three materials, as the temperature increases, the resistivity is expected to increase. This is because higher temperature leads to increased lattice vibrations, which in turn increases the scattering of electrons. As a result, the resistance of the materials increases, leading to higher resistivity.