Sn, C, and Si, Ge are all group XIV elements. Yet, Sn is a conductor, C is an insulator while Si and Ge are se

NCERT Exemplar · Q13

Q. Sn, C, and Si, Ge are all group XIV elements. Yet, Sn is a conductor, C is an insulator while Si and Ge are semiconductors. Why?

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Concept understanding — Band Gap Energy

What is Band Gap Energy? — A First Look

Imagine you have a single atom. Its electrons live in specific, fixed energy levels — like rungs on a ladder. You can't put an electron halfway between two rungs; it's either on one rung or another.

Now bring two atoms close together. Their electron rungs interact and split into two slightly different energies. Bring a billion atoms together — as in a solid crystal — and those original rungs spread into continuous bands of allowed energies, separated by gaps where no electron can exist.

That gap — the forbidden region between two bands — is the band gap.

The Intuition: A Wall Between Two Rooms

Think of the valence band as the ground floor of a building — electrons here are tightly bound to atoms, not free to move. The conduction band is the first floor above — electrons here can roam freely through the crystal, carrying current.

The band gap is the height of the ceiling between these two floors. An electron needs exactly that much energy to jump from the valence band to the conduction band. If you give it less energy, it stays stuck on the ground floor. If you give it exactly the gap energy or more, it can leap up and become a mobile charge carrier.

Note

In a metal, the valence and conduction bands overlap — there is no gap. That's why metals conduct electricity so easily: electrons already have free states available at no energy cost.

The Precise Statement

Band gap energy ( $E_g$ ) is the minimum energy required to excite an electron from the top of the valence band to the bottom of the conduction band in a solid.

E_g = E_{\text{conduction band minimum}} - E_{\text{valence band maximum}}

It is measured in electron volts (eV). One eV is the energy gained by an electron when accelerated through a potential difference of 1 volt — a tiny but convenient unit for atomic-scale energies.

Why Does It Matter?

The band gap determines almost everything about how a material behaves electrically and optically:

Material type	Typical $E_g$	Behaviour
Conductor (metal)	$E_g = 0$ (bands overlap)	Electrons flow freely at room temperature
Semiconductor	$0.1 \text{ eV} < E_g < 3 \text{ eV}$	Conducts only when given energy (heat, light)
Insulator	$E_g > 3 \text{ eV}$	Almost no conduction at normal conditions

Tip

A quick rule of thumb: if a material is transparent to visible light, its band gap is larger than about 3.1 eV (the energy of violet light). Diamond ( $E_g \approx 5.5$ eV) is transparent; silicon ( $E_g \approx 1.1$ eV) is opaque and shiny.

A Concrete Example: Silicon

Silicon has a band gap of 1.12 eV at room temperature. This means:

An electron in the valence band needs at least 1.12 eV to jump to the conduction band.
Visible light photons have energies between 1.8 eV (red) and 3.1 eV (violet). So silicon absorbs most visible light — that's why solar cells are dark. …

Why this formula?

Band Gap Energy: Why the Formula Holds

The band gap energy $E_g$ is the energy difference between the top of the valence band and the bottom of the conduction band in a solid. The key formula is:

E_g = E_c - E_v

where $E_c$ is the minimum energy of the conduction band and $E_v$ is the maximum energy of the valence band.

But why does this simple difference matter? The answer lies in how electrons behave in a crystal.

The Origin of Energy Bands

In an isolated atom, electrons occupy discrete energy levels. When atoms come together to form a solid, their atomic orbitals overlap. According to the Pauli exclusion principle, no two electrons can occupy the same quantum state. So the discrete levels split into a continuum of closely spaced levels — an energy band.

The valence band is formed from the outermost (valence) atomic orbitals. The conduction band is formed from the next higher set of orbitals (typically the empty orbitals above the valence orbitals). Between these bands lies the band gap — a region of forbidden energies where no electron states exist.

Why the Formula $E_g = E_c - E_v$ Is Not Trivial

You might think: "Of course the gap is the difference between the bottom of one band and the top of another." But the real insight is that $E_c$ and $E_v$ are not arbitrary points — they are the extrema of the band structure.

In a periodic crystal, the electron energy $E(\mathbf{k})$ depends on the wavevector $\mathbf{k}$ . The valence band has its maximum at some $\mathbf{k}$ -point (often at $\mathbf{k}=0$ for direct-gap semiconductors), and the conduction band has its minimum at some $\mathbf{k}$ -point. The band gap is:

E_g = \min_{\mathbf{k}_c} E_c(\mathbf{k}_c) - \max_{\mathbf{k}_v} E_v(\mathbf{k}_v)

This is not just a difference — it's a minimisation over all possible electron momenta.

Why This Difference Determines Conductivity

The band gap controls whether a material is an insulator, semiconductor, or conductor because of the Fermi-Dirac distribution:

f(E) = \frac{1}{1 + e^{(E - E_F)/k_B T}}

At absolute zero, all states below the Fermi level $E_F$ are filled, and all above are empty. For an intrinsic semiconductor, $E_F$ lies in the middle of the band gap. The probability that an electron is thermally excited from the valence band to the conduction band is proportional to $e^{-E_g/2k_B T}$ .

Important

The band gap energy $E_g$ appears in the exponent of the carrier concentration formula:

$n = p = N_c N_v e^{-E_g/2k_B T}$

This is why a small change in $E_g$ causes a huge change in conductivity — it's an exponential dependence.

The Physical Meaning of $E_g$

The band gap is not just a number — it's the minimum energy required to:

Break a covalent bond in the crystal (creating an electron-hole pair)
Promote an electron from a bonding state to an antibonding state
Create a mobile charge carrier

For example, in silicon ( $E_g = 1.12$ eV at 300 K), a photon with energy greater than 1.12 eV can be absorbed, exciting an electron from the valence band to the conduction band. This is why silicon is used in solar cells — the band gap matches the solar spectrum. …

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The electrical behaviour of group XIV elements (C, Si, Ge, Sn) is determined by the size of their band gap — the energy difference between the valence and conduction bands. Diamond (C) has a very large band gap ( $\approx 5.5\ \text{eV}$ ), making it an insulator. Si ( $\approx 1.1\ \text{eV}$ ) and Ge ( $\approx 0.7\ \text{eV}$ ) have moderate band gaps, making them semiconductors. Sn (grey tin) has a nearly zero or overlapping band gap, behaving as a conductor.

The key lies in how the band gap energy changes as you go down group XIV. Let’s understand why.

The Concept: Band Gap and Bonding

In a solid, atomic orbitals overlap to form energy bands. The valence band is filled with electrons; the conduction band is empty. The band gap ( $E_g$ ) is the energy an electron needs to jump from the valence band to the conduction band — to become free to conduct electricity.

For group XIV elements, each atom has four valence electrons. In the solid, these form covalent bonds. The strength of these bonds determines how wide the band gap is.

Bond strength and atomic size: As you go down the group (C → Si → Ge → Sn), atomic size increases. Larger atoms have valence electrons that are farther from the nucleus and more loosely held. This means the covalent bonds between atoms become weaker.
Weaker bonds → smaller band gap: A weaker bond means the energy required to break an electron free (to promote it to the conduction band) is smaller. So, the band gap decreases down the group.
The critical threshold: For electrical conduction, thermal energy at room temperature ( $k_B T \approx 0.025\ \text{eV}$ ) can promote a small number of electrons if the band gap is small enough (a few eV). If the band gap is huge, almost no electrons can jump — the material is an insulator. If the band gap is zero or negative (bands overlap), electrons flow freely — the material is a conductor.

E_g(\text{C}) \approx 5.5\ \text{eV},\quad E_g(\text{Si}) \approx 1.1\ \text{eV},\quad E_g(\text{Ge}) \approx 0.7\ \text{eV},\quad E_g(\text{Sn}) \approx 0\ \text{eV}

Now, let’s apply this to each element.

Step-by-Step Reasoning

Carbon (Diamond): Carbon is the smallest atom in the group. Its four valence electrons form extremely strong, directional covalent bonds (the diamond structure). This gives a very large band gap of about $5.5\ \text{eV}$ . At room temperature, thermal energy is far too small to excite electrons across this gap. Hence, diamond has almost no free electrons and is an insulator. …

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Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.

Showing the 12 most recent of 24 on this concept.

CBSE 2026Set ANNUAL1 markMCQ
$Q. If the energy band gaps for Carbon, Silicon and Germanium are E1, E2 and E3 respectively, then the correct relation between them will be$
(a) E1 > E2 > E3
(b) E1 = E2 = E3
(c) E1 < E2 < E3
(d) E1 > E2 < E3
›Reveal solutionSolution

Going from carbon (diamond) to silicon to germanium in Group 14, the energy band gap decreases, so E1 (carbon) > E2 (silicon) > E3 (germanium).

Carbon in its diamond form has a very wide energy gap (~5.4 eV), which is why it behaves as an insulator. Silicon has a moderate gap (~1.1 eV) and germanium has a smaller gap still (~0.7 eV), which is why both behave as semiconductors, with g …

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CBSE 2026Set ANNUAL1 markMCQ
$Q. The width of forbidden band is maximum for$
(a) metals
(b) non-conductors
(c) semi-conductors
(d) none of these
›Reveal solutionSolution
The forbidden gap (band gap) between valence and conduction bands is essentially zero for metals, small (~1 eV) for semiconductors, and large (>3 eV) for insulators.

In the band theory of solids, electrons occupy allowed energy bands, and the 'forbidden band' (band gap) is the energy range between the valence band (filled with electrons) and the conduction band (where electrons can move freely and conduct current).

In METALS/conductors, the valence and conduction bands overlap (essentially zero gap), so electrons move into the conduction band with negligible energy input - hence high conductivity.

In SEMICONDUCTORS, there is a small forbidden gap (of order 1 eV), so a modest amount of thermal or other energy can promote electrons across it. …
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CBSE 2026Set ANNUAL1 mark
$Q. What do you understand by energy band?$
›Reveal solutionSolution

In an isolated atom electrons occupy sharp, discrete energy levels; in a solid, the overlapping of countless such levels from ~10²³ closely packed atoms produces broad, continuous-looking bands of allowed energies.

In a single isolated atom, electrons can only have certain sharp, discrete energy values. When a huge number of atoms (of order Avogadro's number, ~ $10^{23}$ per cm³) are brought close together to form a solid, their outer electrons interact and each originally-discrete energy level splits into a large number of very closely spaced sub-levels — so close together that they appear to form a continuous range, called an energy band. The band formed from the valence electrons is the valence band, the next higher band (which may be empty or partly filled) is the conduction band, and the energy range between them where no allowed states exist is …

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CBSE 2025Set 55/4/11 markMCQ
$Q. Which of the following is an electrical conductor at room temperature? (A) Sn (B) Mica (C) Si (D) C$
›Reveal solutionSolution
The key idea is to classify each material by its electrical conductivity at room temperature. Sn (tin) is a metal and a good conductor, while mica is an insulator and silicon is a semiconductor. The correct option is (A).

Concept and Intuition

Electrical conductivity depends on how freely electrons can move through a material. At room temperature:

Metals (like tin) have a "sea" of delocalized electrons that flow easily — they are excellent conductors.

Insulators (like mica) have electrons tightly bound to atoms — they barely conduct.

Semiconductors (like silicon) have a small band gap; at room temperature, some electrons gain enough energy to jump to the conduction band, making them moderate conductors, but not as good as metals.

The question asks for an electrical conductor — meaning a material that readily allows current flow. Among the options, only one is a metal.

Step-by-Step Solution

Identify the nature of each substance

Sn (tin): A metal in Group 14 of the periodic table. It has metallic bonding with free electrons.

Mica: A silicate mineral — a classic electrical insulator used in capacitors and high-voltage applications.

Si (silicon): A metalloid, a semiconductor. Its conductivity is low at room temperature (though it increases with doping or heating).

C (carbon): Can exist as graphite (a conductor) or diamond (an insulator). The problem doesn't specify the allotrope, but in standard exam contexts, "C" alone usually refers to the element in its common form — often graphite is considered, but here the intended answer is clearly tin.

Compare conductivities at room temperature

Tin has a resistivity of about $1.1 \times 10^{-7} \, \Omega \cdot \text{m}$ — typical of a metal.

Mica has resistivity exceeding $10^{12} \, \Omega \cdot \text{m}$ — an insulator.

Silicon has resistivity around $2.3 \times 10^{3} \, \Omega \cdot \text{m}$ — a semiconductor, not a good conductor at room temperature. …
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CBSE 2025Set X11 markMCQ
$Q. The energy gap for silicon is :$
(a) 0.72 eV
(b) 1.1 eV
(c) 3 eV
(d) 5 eV
›Reveal solutionSolution

(b) 1.1 eV The forbidden energy gap between the valence band and conduction band in silicon is about $1.1\ \text{eV}$ at room temperature (for germanium it is about $0.72\ \text{eV}$ ). …

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CBSE 2025Set ANNUAL1 markMCQ
$Q. The conduction band is partially empty in$
(a) non-conductors
(b) semi-conductors
(c) metals
(d) super-conductors
›Reveal solutionSolution
Good conduction requires easily-available empty states just above the highest filled electron levels; in metals the conduction band itself is partially filled (or overlaps the valence band), giving electrons free states to move into under an applied field.

Band theory picture:

Non-conductors (insulators): a large energy gap separates a full valence band from an empty conduction band, so essentially no electrons can be thermally excited across - conduction band stays effectively empty.

Semiconductors: a small energy gap allows a few electrons to be thermally excited into an otherwise mostly-empty conduction band. …
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CBSE 2025Set ANNUAL1 markMCQ
$Q. If temperature of semiconductor is fall, the forbidden energy gap is -$
(a) increased
(b) remain unchanged
(c) decreased
(d) sometimes increased and sometimes decreased
›Reveal solutionSolution

The forbidden energy gap widens slightly as temperature falls.

For a semiconductor, the width of the forbidden energy gap $E_g$ typically has a small, gradual dependence on temperature: as temperature falls, the band gap increases slightly (e.g. silicon's gap rises from about 1.12 eV at 300 K to about 1.17 eV near 0 K), mainly due to reduced thermal expansion and reduced electron-phonon interaction narrowing the gap les …

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CBSE 2025Set ANNUAL1 markMCQ
$Q. The energy difference between valence band and conduction band of silicon at room temperature is about$
(a) 1.1 eV
(b) 0.15 eV
(c) 0.67 eV
(d) 6.7 eV
›Reveal solutionSolution

Silicon's band gap at room temperature is about 1.1 eV, distinguishing it from germanium (~0.7 eV).

…

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CBSE 2025Set ANNUAL1 mark
$Q. Distinguish between a semiconductor and an insulator based on their energy gap.$
›Reveal solutionSolution
The energy gap between the valence and conduction bands is small enough in a semiconductor for thermal energy to promote a few electrons across it, but far too large in an insulator.

In the band theory of solids, electrical conduction requires electrons in the (otherwise full) valence band to be excited across the energy gap $E_g$ into the empty conduction band.

Semiconductor: $E_g$ is small, typically about 1 eV or less (e.g. Si $\approx 1.1$ eV, Ge $\approx 0.7$ eV). At room temperature, thermal energy is enough to excite a small but significant number of electrons across this gap, giving the material a modest, temperature-dependent conductivity. …
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CBSE 2024Set A11 mark
$Q.The value of energy band in insulators is ———————— than 3 eV. Fill in the blank choosing the appropriate answer from the bracket: (decreasing, interference, helium, greater, diffraction, increasing)$
›Reveal solutionSolution

greater (more) than 3 eV. …

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CBSE 2024Set ANNUAL1 markMCQ
$Q. Assertion (A): Resistance of conductors is lower than semiconductors. Reason (R): In conductors, energy gap between conduction band and valence band is greater than 3 eV.$
(a) Both A and R are correct and R is the correct explanation of A.
(b) Both A and R are correct but R is not the correct explanation of A.
(c) A is correct but R is incorrect.
(d) Both A and R are incorrect.
›Reveal solutionSolution

Conductors do have lower resistance than semiconductors, but conductors have essentially zero (overlapping) energy gap, not a gap greater than 3 eV.

Assertion (A) is correct: conductors have much lower resistance (and much higher conductivity) than semiconductors, because conductors have a very large number of free charge carriers. Reason (R) is incorrect: in conductors, the conduction band and valence band actually overlap (energy gap $E_g \approx 0$ ) -- there is no forbidd …

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CBSE 2024Set A1 markMCQ
$Q. The width of forbidden energy gap in the semiconductor is approximately (A) 1 eV (B) 10 eV (C) 100 eV (D) 0.01 eV$
›Reveal solutionSolution

A semiconductor's forbidden energy gap is approximately 1 eV → option (A).

The energy gap between the top of the valence band and the bottom of the conduction band determines whether a material is a conductor, insulator or semiconductor. For semiconductors this gap is small, of the order of ~1 eV (e.g. ≈1.1 eV for silicon, ≈0.7 eV …

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Q.Sn, C, and Si, Ge are all group XIV elements. Yet, Sn is a conductor, C is an insulator while Si and Ge are semiconductors. Why?

Concept understanding — Band Gap Energy

What is Band Gap Energy? — A First Look

The Intuition: A Wall Between Two Rooms

The Precise Statement

Why Does It Matter?

A Concrete Example: Silicon

Why this formula?

Band Gap Energy: Why the Formula Holds

The Origin of Energy Bands

Why the Formula $E_g = E_c - E_v$ Is Not Trivial

Why This Difference Determines Conductivity

The Physical Meaning of $E_g$

The Concept: Band Gap and Bonding

Step-by-Step Reasoning

Method: Tracking How Bond Strength (and Hence Band Gap) Changes Down a Group

Concept and Intuition

Step-by-Step Solution

Q.Sn, C, and Si, Ge are all group XIV elements. Yet, Sn is a conductor, C is an insulator while Si and Ge are semiconductors. Why?

The Concept: Band Gap and Bonding

Step-by-Step Reasoning

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