Q.Carbon, silicon and germanium have four valence electrons 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 is true?

Concept: Band Gap Energy — the energy gap between the valence and conduction bands determines whether a material behaves as an insulator, semiconductor, or conductor. For group 14 elements, the band gap decreases as we move down the group.

Reasoning:

1. Carbon (diamond) is an insulator with a very large band gap (~5.5 eV).
2. Silicon and germanium are semiconductors; their band gaps are smaller and decrease down the group: Si (~1.1 eV), Ge (~0.7 eV).
3. Therefore, the order is: $(E_g)_C > (E_g)_{Si} > (E_g)_{Ge}$.

The key idea here is that the band gap energy in semiconductors and insulators is not arbitrary — it is directly linked to the strength of the covalent bond and the size of the atom. Carbon, silicon, and germanium all belong to Group 14 and have four valence electrons each. In their solid state, they form a diamond-like crystal structure where each atom is covalently bonded to four neighbours.

Why does the band gap change as we go down the group? The valence electrons in a solid occupy bands — the valence band (filled with bonding electrons) and the conduction band (empty, higher energy). The energy gap between them, $E_g$, is the minimum energy needed to promote an electron from a bonding state to a conducting state. A larger gap means the material is more insulating; a smaller gap means it is more semiconducting.

The trend is governed by two factors that work together:

1. Atomic size and bond length: As we go from C to Si to Ge, the atomic radius increases. This means the distance between neighbouring atoms in the crystal also increases. A longer bond is weaker — the shared electrons are less tightly held. This reduces the splitting between bonding and antibonding energy levels, which directly shrinks the band gap.

2. Electronegativity: Carbon is the most electronegative in the group. It holds its valence electrons very tightly, requiring more energy to free them. Silicon and germanium are less electronegative, so their electrons are more easily excited into the conduction band.

The result is a clear, monotonic decrease: diamond (carbon) has a band gap of about 5.5 eV (making it an insulator), silicon has about 1.1 eV, and germanium has about 0.67 eV. So the order is $(E_g)_C > (E_g)_{Si} > (E_g)_{Ge}$.

Now let’s check the options:

1. Option (a) says $(E_g)_{Si} < (E_g)_{Ge} < (E_g)_C$. This is wrong because it places germanium’s gap above silicon’s — the actual order is the reverse.

2. Option (b) says $(E_g)_C < (E_g)_{Ge} > (E_g)_{Si}$. This is nonsense — it claims carbon has the smallest gap, which is completely false, and also gives germanium the largest, which is also false.

3. Option (c) says $(E_g)_C > (E_g)_{Si} > (E_g)_{Ge}$. This matches the known trend exactly.

4. Option (d) says all three are equal. This is clearly wrong — the materials have very different electrical properties (diamond is an insulator, silicon and germanium are semiconductors).

Method: Trend Analysis Using Periodic Table Position

The band gap energy of an element depends on how tightly the valence electrons are bound to the nucleus. For elements in the same group (Group 14: C, Si, Ge), as you go down the group, the atomic size increases and the valence electrons become less tightly held. This means less energy is needed to jump from the valence band to the conduction band — so the band gap decreases.

Steps:

1. Identify the group: Carbon, silicon, and germanium all belong to Group 14 of the periodic table.
2. Recall the order of increasing atomic size: C (smallest) → Si → Ge (largest).
3. Larger atoms have weaker hold on valence electrons → smaller band gap.
4. Therefore, band gap decreases as we move down the group: C has the largest gap, Ge the smallest.

Answer: Option (c)

Common Mistakes Students Make on This Band Gap Question

Mistake 1: Confusing the trend of band gap with atomic size

Many students think that since carbon is smaller than silicon, and silicon smaller than germanium, the band gap should follow the same order — decreasing with size. That part is actually correct. The mistake comes from reversing the inequality or mixing up which element has the largest gap.

Carbon (diamond) has the largest band gap (~5.5 eV), germanium the smallest (~0.67 eV), and silicon sits in between (~1.12 eV). So the correct order is:

That matches option (c).

Mistake 2: Thinking band gap increases down the group

Some students memorise that conductivity increases down Group 14 (C → Si → Ge → Sn → Pb) and then incorrectly conclude that band gap must also increase. This is backwards. Conductivity increases because band gap decreases — more electrons can jump to the conduction band at room temperature.

Mistake 3: Forgetting that carbon (diamond) is an insulator

Carbon in its diamond form has a band gap so large (~5.5 eV) that at room temperature, almost no electrons cross it. That makes it an insulator, not a semiconductor. Students sometimes treat all four elements as semiconductors and then guess wrong.

Mistake 4: Picking option (a) because it "looks like" a decreasing trend

Option (a) says $(E_g)_{Si} < (E_g)_{Ge} < (E_g)_C$. This has silicon's gap smaller than germanium's — which is false. The actual decreasing order is C > Si > Ge. Students who vaguely remember "band gap decreases down the group" sometimes write the elements in the wrong sequence.

How to avoid: Always write the elements in order of increasing atomic number: C (6), Si (14), Ge (32). Then recall that band gap decreases as atomic size increases. So C has the largest, Ge the smallest.

Mistake 5: Not recognising that option (b) is nonsense

Option (b) says $(E_g)_C < (E_g)_{Ge} > (E_g)_{Si}$. This claims carbon's gap is smaller than germanium's — which is wildly wrong. Yet some students pick it because they see a "greater than" sign and think it matches some trend they half-remember.

How to avoid: Test the extreme values. If you know diamond is an insulator and germanium is a semiconductor, then carbon's gap must be larger. Any option that says otherwise is automatically wrong.

Final answer: Option (c) $(E_g)_C > (E_g)_{Si} > (E_g)_{Ge}$ is correct.