Carbon , silicon and germanium have four valence elcectrons each . These are characterised by valence and conduction bands separated by energy band - gap respectively equal to ` (E_g)_(c) (E_g)_(si) ` and ` (E_g)_(Ge) `. Which of the following statements ture ?
Carbon , silicon and germanium have four valence elcectrons each . These are characterised by valence and conduction bands separated by energy band - gap respectively equal to ` (E_g)_(c) (E_g)_(si) ` and ` (E_g)_(Ge) `. Which of the following statements ture ?
A
(a) ` (E__g)_(Si) lt (E_g)_(Ge) lt (E_g) _C `
B
(b ) ` (E__g)_(C ) lt (E_g)_(Ge) gt (E_g)_Si `
C
(c ) ` (E__g)_(C ) gt (E_g)_(Si) gt (E_g) _(Ge) `
D
(d)`(E_g)_C = (E_g)_(Si) = (E_g)_(Ge)`
Text Solution
AI Generated Solution
The correct Answer is:
To solve the question regarding the energy band gaps of carbon, silicon, and germanium, we will analyze the properties of each material based on their electronic structure.
### Step-by-Step Solution:
1. **Identify the Valence Electrons**:
- Carbon, silicon, and germanium all have four valence electrons. This is a key characteristic that influences their electrical properties.
2. **Understand the Concept of Energy Band Gap**:
- The energy band gap (E_g) is the energy difference between the valence band (where the electrons are present) and the conduction band (where electrons can move freely to conduct electricity).
- Materials can be classified as conductors, semiconductors, or insulators based on the size of their band gap.
3. **Classify the Materials**:
- **Carbon**: Carbon is primarily an insulator (in its diamond form) and has a large energy band gap. This means it does not conduct electricity well.
- **Silicon**: Silicon is a semiconductor with a moderate energy band gap, allowing it to conduct electricity under certain conditions (like doping).
- **Germanium**: Germanium is also a semiconductor, but it has a smaller energy band gap compared to silicon, which allows it to conduct electricity more easily.
4. **Compare the Energy Band Gaps**:
- Based on the classification:
- The energy band gap of carbon (E_g(c)) is the largest.
- The energy band gap of silicon (E_g(si)) is smaller than that of carbon but larger than that of germanium.
- The energy band gap of germanium (E_g(Ge)) is the smallest.
- Therefore, the order of the energy band gaps is:
\[
E_g(Ge) < E_g(si) < E_g(c)
\]
5. **Conclusion**:
- The correct statement regarding the energy band gaps is that the band gap of germanium is less than that of silicon, and the band gap of silicon is less than that of carbon.
### Final Answer:
- The correct order of the energy band gaps is:
\[
E_g(Ge) < E_g(si) < E_g(c)
\]
To solve the question regarding the energy band gaps of carbon, silicon, and germanium, we will analyze the properties of each material based on their electronic structure.
### Step-by-Step Solution:
1. **Identify the Valence Electrons**:
- Carbon, silicon, and germanium all have four valence electrons. This is a key characteristic that influences their electrical properties.
2. **Understand the Concept of Energy Band Gap**:
...
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Knowledge Check
Which of the following equations correctly represents the temperature variation of energy gap between the conduction and valence bands for Si?
Which of the following equations correctly represents the temperature variation of energy gap between the conduction and valence bands for Si?
A
`E_g(T)=0.70-2.23xx10^(-4)` T eV
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`E_g(T)=0.70+2.23xx10^(-4)` T eV
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`E_g(T)=1.10+3.60xx10^(-4)` T eV
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