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
5.a) The energy band diagram for each sample can be represented as follows:
Material A:
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Valence Band Conduction Band
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Visible Light Range
Material B:
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Valence Band Conduction Band
Material C:
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Valence Band Blue Light Absorbing Level Conduction Band
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Red Light Transparent Level
5.b) Ranking materials A, B, and C on the scale of increasing insulator behavior:
1) Material B (Transparent to all visible light)
2) Material C (Absorbs blue light but is transparent to red light)
3) Material A (Absorbs all visible light)
5.c) Reasons for the ranking in 5.b:
Material A is ranked lowest because it absorbs all visible light, suggesting it has a high conductivity and behaves more like a conductor than an insulator.
Material C is ranked in the middle because it absorbs blue light but is transparent to red light. This indicates that it has a certain level of energy absorption but still allows some light to pass through, indicating some insulating behavior.
Material B is ranked first because it is transparent to all visible light. This suggests that it has the least energy absorption and behaves more like a typical insulator.
5.d) Predicted trend of resistivity as a function of increasing temperature for the three samples:
Generally, the resistivity of materials increases with an increase in temperature. The trend can be predicted as follows:
Material A: As a conductor, its resistivity might decrease with increasing temperature due to the increased mobility of charge carriers. However, without specific information about its conductivity, it is difficult to make an accurate prediction.
Material B: As an insulator, its resistivity is expected to increase with increasing temperature. The increased thermal energy will cause more atomic vibrations and disruptions, hindering the flow of charge carriers.
Material C: Similar to Material B, its resistivity is expected to increase with increasing temperature due to the same reasons mentioned above. However, it could also be influenced by any specific properties related to the absorption of blue light and transparency to red light, which are not mentioned in the given information.
To answer the question, we'll go through each part step by step:
(5.a) Drawing energy band diagrams for each sample:
To draw the energy band diagram for each sample, we need to understand the behavior of these materials. Here are the characteristics of each material:
- Material A absorbs all visible light, so it does not allow any light to pass through. This suggests that it has a completely filled valence band and an empty conduction band.
- Material B is transparent to all visible light, which indicates that its valence band is filled, and there is a gap between the valence and conduction bands.
- Material C absorbs blue light but is transparent to red light. This implies that it has a partially filled valence band and a partially filled conduction band.
Now, let's draw the energy band diagrams for each material based on the given information. Note that we'll use simplified diagrams with only the valence and conduction bands:
Energy Band Diagram:
| A |
__ |________|__ --> Valence Band
__ | |__ --> Conduction Band
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| B |
__ |________|__ --> Valence Band
--> Band Gap
__ | |__ --> Conduction Band
| C |
__ |________|__ --> Valence Band
--> Partially Filled Band Gap
__ | |__ --> Conduction Band
(5.b) Ranking materials A, B, and C based on increasing insulator behavior:
To rank these materials in terms of increasing insulator behavior, we need to consider the characteristics of insulators. Insulators have a large band gap, which hampers the movement of electrons from the valence to conduction band. Based on this, the ranking from least insulating to most insulating is as follows:
Rank: B < C < A
(5.c) Reasons for the ranking in (5.b):
The reasons behind this ranking are as follows:
- Material B is transparent to all visible light, suggesting that it has a moderate band gap. This indicates that it allows some electron movement but is not a good conductor.
- Material C absorbs blue light and is transparent to red light, implying that it has a smaller band gap compared to Material B. Thus, it has better insulating behavior than Material B but is less insulating than Material A.
- Material A absorbs all visible light, indicating it has a completely filled valence band and an empty conduction band. This implies a large band gap and makes it the most insulating material among the three.
(5.d) Predicting the trend of resistivity with increasing temperature:
To predict the trend of resistivity with increasing temperature, we need to consider the behavior of different materials. Generally, as the temperature increases, the resistivity of conductors increases, while the resistivity of semiconductors and insulators decreases.
Based on the ranking (B < C < A), we can predict the trend of resistivity for each material:
- Material B: As temperature increases, its resistivity is likely to increase moderately since it behaves more like a conductor.
- Material C: With increasing temperature, its resistivity will decrease because it behaves like a semiconductor with a smaller band gap.
- Material A: Its resistivity is expected to increase significantly with increasing temperature since it behaves like an insulator, and insulators have a larger band gap.
Keep in mind that these predictions are based on the general behavior of conductors, semiconductors, and insulators. Actual materials can exhibit different behavior depending on their specific properties.
I hope this explanation helps! Let me know if you have any further questions.