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 questions 5.a, 5.b, 5.c, and 5.d, we need to understand the concepts of energy band diagrams, insulator behavior, and resistivity.
5.a) Drawing the corresponding energy band diagram for each sample:
An energy band diagram shows the energy levels of electrons in a material. For Material A, which absorbs all visible light, the energy band diagram would have a completely filled valence band and an empty conduction band, showing that it is an insulator. For Material B, which is transparent to all visible light, the energy band diagram would show a small band gap between the valence and conduction bands, indicating that it is a semiconductor. For Material C, which absorbs blue light but is transparent to red light, the energy band diagram would show a smaller band gap for blue light absorption.
5.b) Ranking materials A, B, and C on the scale of increasing insulator behavior:
To rank the materials on the scale of increasing insulator behavior, we compare their ability to conduct electricity. Material A absorbs all visible light and is the most opaque, indicating that it does not allow electron flow. Therefore, Material A exhibits the highest insulator behavior. Material B is transparent to all visible light, suggesting that it has some conductivity. However, it is not as insulating as Material A, so it falls in the middle. Material C absorbs blue light and is transparent to red light, indicating that it has some conductivity, but less than Material B. Therefore, Material C exhibits the least insulator behavior among the three materials.
5.c) Reasons for the ranking in 5.b:
The ranking in question 5.b is based on the transparency of the materials to visible light. Material A absorbs all visible light, meaning it has high absorption and low conductivity. Material B is transparent to all visible light, which suggests it has some conductivity. Material C absorbs blue light but is transparent to red light, indicating that it has some conductivity, but less than Material B.
5.d) Predicting the trend of resistivity as a function of increasing temperature for the three samples:
The resistivity of a material is a measure of how strongly it opposes the flow of electric current. In general, as the temperature of a material increases, its resistivity also increases. This is true for most conductors and semiconductors.
For Material A, which is the most insulating, its resistivity is expected to increase as the temperature increases. For Material B, which is a semiconductor, its resistivity will also increase with increasing temperature, but typically at a slower rate compared to insulators. Material C, being less insulating than Material A and B, will also have an increasing resistivity with temperature, but again, at a slower rate compared to the other two.
Please note that the actual resistivity-temperature relationship might depend on the specific properties of each material and should be verified experimentally or with more detailed information about the materials.
5.a) The energy band diagrams for each material can be roughly drawn as follows:
Material A (Opaque):
```
| Energy |
| Gap |
| |
| |
|-----------| Valence Band
| |
| ↓ |
| |
|-----------| Conduction Band
```
Material B (Transparent):
```
| Energy |
| Gap |
| |
| |
| | Valence Band
| |
| |
|-----------| Conduction Band
```
Material C (Blue light absorber, transparent to red light):
```
| Energy |
| Gap |
| |
| |
|-----------| Valence Band
| |
| ↓ |
|-----------| Conduction Band
```
Note: These are simplified energy band diagrams and not drawn to scale.
5.b) Ranking the materials based on increasing insulator behavior:
1. Material B (Transparent)
2. Material C (Blue light absorber, transparent to red light)
3. Material A (Opaque)
5.c) Reasons for the rankings:
- Material B is transparent because it has a relatively wide band gap, which allows electrons to easily transition from the valence band to the conduction band when exposed to visible light.
- Material C is a partial absorber of blue light but transparent to red light. It has a smaller band gap than Material B, allowing blue light (with shorter wavelength) to excite electrons and transition to the conduction band. Red light (with longer wavelength) does not have enough energy to cause such transitions.
- Material A is opaque because it absorbs all visible light. It has a very small or no band gap, making it difficult for electrons to transition to the conduction band, resulting in high absorption and low transmission of visible light.
5.d) Predicting the trend of resistivity with increasing temperature for the three samples is not possible based on the given information about their optical properties. Resistivity is related to the electrical behavior of materials and requires information about their charge carrier concentration, mobility, and temperature coefficients, which are not provided in the question.