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 ?

Options

A. `(E_g)_(Si) lt (E_g)_(Ge) lt (E_g)_C`
B. `(E_g)_(C) lt (E_g)_(Ge) lt (E_g)_(Si)`
C. `(E_g)_(C) gt (E_g)_(Si) gt (E_g)_(Ge)`
D. `(E_g)_(C) = (E_g)_(Si) =(E_g)_(Ge)`

Answer

To determine which statements about the energy band gaps of carbon, silicon, and germanium are true, we can analyze the information provided about their respective energy band gaps.

### Step-by-Step Solution:

1. **Identify the Elements and Their Valence Electrons:**
- Carbon (C), Silicon (Si), and Germanium (Ge) each have four valence electrons.

2. **Understand the Concept of Energy Band Gap:**
- The energy band gap (E_g) is the energy difference between the valence band and the conduction band in a semiconductor. A larger band gap generally indicates a material that is less conductive at room temperature.

3. **List the Energy Band Gaps for Each Element:**
- From the information provided:
- For Carbon (C), the energy band gap (E_g) is approximately 5.4 eV.
- For Silicon (Si), the energy band gap (E_g) is approximately 1.1 eV.
- For Germanium (Ge), the energy band gap (E_g) is approximately 0.7 eV.

4. **Compare the Energy Band Gaps:**
- Now, we can compare the values:
- E_g (C) = 5.4 eV (highest)
- E_g (Si) = 1.1 eV (intermediate)
- E_g (Ge) = 0.7 eV (lowest)

5. **Determine the Correct Statement:**
- Based on the values:
- The order of energy band gaps from highest to lowest is: Carbon > Silicon > Germanium.
- Therefore, any statement asserting that carbon has the largest band gap, followed by silicon, and then germanium is true.

### Conclusion:
The correct statement is that the energy band gap for carbon is the largest, followed by silicon, and germanium has the smallest band gap.