CUET UG Physics Booster Test 3- Band Theory and Intrinsic Properties -

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CUET UG Physics Booster Test 3- Band Theory and Intrinsic Properties

⏱️ 30 Minutes

❓ 20 Questions

📌 Answers are locked once submitted — results and explanations appear at the end.

CUET UG Physics Booster Test 3- Band Theory and Intrinsic Properties

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QUESTION 1 OF 20

Match List I with List II regarding solid formation

List I	List II
1. — Isolated atom	I. — 8N available energy states
2. — Atoms in a solid	II. — Energy decided by orbit
3. — Energy variation in band	III. — Outer orbits overlap
4. — Continuous band source	IV. — Continuous

Answer Review

1 Match List I with List II regarding solid formation

List I	List II
1. — Isolated atom	I. — 8N available energy states
2. — Atoms in a solid	II. — Energy decided by orbit
3. — Energy variation in band	III. — Outer orbits overlap
4. — Continuous band source	IV. — Continuous

A 1-II, 2-III, 3-IV, 4-I

B 1-III, 2-II, 3-I, 4-IV

C 1-I, 2-IV, 3-II, 4-III

D 1-II, 2-IV, 3-III, 4-I

💡 Short Explanation

Isolated atoms have discrete orbit-based energies. Overlapping outer orbits form bands. Energy becomes continuous in solids.

✅ Correct Answer Explanation

Correct matching: Isolated atom → Energy decided by orbit (II) Atoms in a solid → Outer orbits overlap (III) Energy variation in band → Continuous (IV) Continuous band source → 8N available energy states (I)

❓ Why Other Options Are Incorrect

Option B → Reverses isolated atom and solid properties.
Option C → Incorrect assignment of energy variation.
Option D → Incorrect matching of continuous variation.

🎯 Strategy

Used

Option Grouping

Application:

Match fundamental concepts of band formation.

Final Logic:

Only Option A correctly matches all entries.

🧠 Memory Trick

"Orbit → Overlap → Continuous Band."

📚 Class XII – Physics Part II – Chapter: Semiconductor Electronics: Materials, Devices and Simple Circuits – Topic: Energy Band Formation

2 The underlying reason that each electron has a different energy level forming a continuous variation is

A Each electron has a unique position and no two electrons see exactly the same pattern of surrounding charges

B Electrons are randomly distributed in the nucleus

C The Bohr model strictly applies to crystals without modification

D All atoms in the lattice share the exact same set of free electrons constantly

💡 Short Explanation

Electron surroundings differ slightly. Energy levels split into many values. Continuous bands are formed.

✅ Correct Answer Explanation

Inside a crystal, electrons experience slightly different surrounding charge environments. Consequently, their energies differ slightly, resulting in a very large number of closely spaced levels that form energy bands.

❓ Why Other Options Are Incorrect

Option B → Electrons are not distributed in the nucleus.
Option C → The Bohr model requires modification for solids.
Option D → Does not explain energy-level splitting.

🎯 Strategy

Used

Direct Concept Application

Application:

Identify the origin of continuous energy variation.

Final Logic:

Different charge environments create different energies.

🧠 Memory Trick

"Different Surroundings → Different Energies."

📚 Class XII – Physics Part II – Chapter: Semiconductor Electronics: Materials, Devices and Simple Circuits – Topic: Continuous Energy Bands

3 Correct statements about the valence band
1. It contains the energy levels of the valence electrons.
2. With no external energy, all valence electrons reside here.
3. At 0 K, it is partially filled in an intrinsic semiconductor.
4. Its top level is designated as EV.

A (A), (B), (C)

B (A), (B), (D)

C (B), (C), (D)

D (A), (C), (D)

💡 Short Explanation

Valence electrons occupy the valence band. It is full at absolute zero. EV denotes the top of the valence band.

✅ Correct Answer Explanation

The valence band contains the energy levels occupied by valence electrons. In an intrinsic semiconductor at 0 K, it is completely filled. The highest energy level of this band is represented by EV. Statement C is incorrect because the valence band is fully occupied at 0 K.

❓ Why Other Options Are Incorrect

Option A → Includes incorrect statement C.
Option C → Includes incorrect statement C.
Option D → Includes incorrect statement C.

🎯 Strategy

Used

Option Grouping

Application:

Evaluate each statement separately.

Final Logic:

Only A, B, and D are correct.

🧠 Memory Trick

"VB Full at 0 K."

📚 Class XII – Physics Part II – Chapter: Semiconductor Electronics: Materials, Devices and Simple Circuits – Topic: Valence Band

4 If the lowest level in the conduction band happens to be lower than the highest level of the valence band,

A the material is a perfect insulator

B the band gap becomes exactly 3 eV

C the 8N discrete energy levels are reduced to 4N

D electrons from the valence band can easily move into the conduction band

💡 Short Explanation

This represents band overlap. Electrons move freely. Metallic conduction becomes possible.

✅ Correct Answer Explanation

When the conduction band overlaps the valence band, electrons can move easily into available conduction states without requiring additional energy. This leads to high conductivity, characteristic of metals.

❓ Why Other Options Are Incorrect

Option A → Opposite of actual behavior.
Option B → Band overlap implies zero or negative effective gap.
Option C → Energy states do not reduce this way.

🎯 Strategy

Used

Conceptual Matching

Application:

Relate band overlap to conductivity.

Final Logic:

Band overlap enables free electron movement.

🧠 Memory Trick

"Overlap = Easy Conduction."

📚 Class XII – Physics Part II – Chapter: Semiconductor Electronics: Materials, Devices and Simple Circuits – Topic: Metallic Bands

5 At absolute zero, out of the 8N available energy states in a Si crystal, the number of completely unoccupied states in the upper band is:

A 0

B 2N

C 4N

D 8N

💡 Short Explanation

Total available states = 8N. 4N valence electrons occupy lower band. Upper band contains 4N empty states.

✅ Correct Answer Explanation

In a silicon crystal, there are 8N available energy states. At 0 K, the 4N valence electrons completely fill the lower band (valence band). Therefore, the upper band (conduction band) remains completely empty with 4N available states.

❓ Why Other Options Are Incorrect

Option A → Upper band is not occupied.
Option B → Only half the correct value.
Option D → Total states include both bands.

🎯 Strategy

Used

Substitution

Application:

Use the relation between available states and valence electrons.

Final Logic:

8N states − 4N occupied states = 4N empty states.

🧠 Memory Trick

"8N States, 4N Filled, 4N Empty."

📚 Class XII – Physics Part II – Chapter: Semiconductor Electronics: Materials, Devices and Simple Circuits – Topic: Band Occupancy

6 Incorrect statement regarding thermal excitation in intrinsic semiconductors

A Thermal energy at higher temperatures excites electrons to the conduction band.

B Thermally excited electrons at T > 0 K partially occupy the conduction band.

C The rate of generation of charge carriers exceeds the rate of recombination at equilibrium.

D The excited electrons leave an equal number of holes in the valence band.

💡 Short Explanation

At equilibrium, generation equals recombination. Electrons and holes are created together. Conduction band becomes partially occupied.

✅ Correct Answer Explanation

In thermal equilibrium, the rate of carrier generation equals the rate of recombination. Therefore, statement C is incorrect. If generation exceeded recombination continuously, carrier concentration would increase indefinitely.

❓ Why Other Options Are Incorrect

Option A → Correct.
Option B → Correct.
Option D → Correct.

🎯 Strategy

Used

Equilibrium Principle

Application:

Apply generation-recombination equilibrium.

Final Logic:

At equilibrium, generation = recombination.

🧠 Memory Trick

"Equilibrium Means Equal Rates."

📚 Class XII – Physics Part II – Chapter: Semiconductor Electronics: Materials, Devices and Simple Circuits – Topic: Thermal Excitation

7 Band gap comparison statements
1. The energy required to take out an electron is least for Ge, followed by Si, and highest for C.
2. Carbon has a band gap of 5.4 eV.
3. The band gap for Silicon is 0.7 eV.
4. Carbon (diamond) functions as an insulator due to its large gap.

A (A), (B), (D)

B (A), (B), (C)

C (B), (C), (D)

D (A), (C), (D)

💡 Short Explanation

Ge has the smallest gap. Diamond has the largest gap. Silicon has 1.1 eV, not 0.7 eV.

✅ Correct Answer Explanation

Germanium has the smallest energy gap (~0.7 eV), Silicon has ~1.1 eV, and diamond has ~5.4 eV. The large energy gap of diamond prevents thermal excitation and causes insulating behavior. Statement C is incorrect because 0.7 eV corresponds to Germanium.

❓ Why Other Options Are Incorrect

Option B → Includes incorrect statement C.
Option C → Includes incorrect statement C.
Option D → Includes incorrect statement C.

🎯 Strategy

Used

Option Grouping

Application:

Compare standard energy-gap values.

Final Logic:

A, B, and D are correct.

🧠 Memory Trick

"Ge 0.7 → Si 1.1 → C 5.4."

📚 Class XII – Physics Part II – Chapter: Semiconductor Electronics: Materials, Devices and Simple Circuits – Topic: Energy Gap Comparison

8 The energy gap between the top of the valence band and the bottom of the conduction band is essentially a region where

A infinitely large number of closely spaced energy levels exist

B no allowed electron energy states can exist for an intrinsic semiconductor

C overlapping levels create high conductivity

D all the 4N valence electrons reside at absolute zero

💡 Short Explanation

The gap is a forbidden region. No electron states exist there. Electrons must gain sufficient energy to cross it.

✅ Correct Answer Explanation

The forbidden energy gap is the region between the valence band and conduction band where no allowed electron energy states exist. Electrons must acquire energy equal to or greater than Eg to move across this region.

❓ Why Other Options Are Incorrect

Option A → Describes energy bands.
Option C → Describes metals.
Option D → Refers to valence-band occupancy.

🎯 Strategy

Used

Direct Recall

Application:

Recall the definition of forbidden energy gap.

Final Logic:

No allowed states exist in the band gap.

🧠 Memory Trick

"Forbidden Gap = No States."

📚 Class XII – Physics Part II – Chapter: Semiconductor Electronics: Materials, Devices and Simple Circuits – Topic: Forbidden Energy Gap

9 For metallic conductors, the energy gap between conduction and valence bands and the corresponding electrical conductivity are respectively:

A Large, Very low

B Small, Intermediate

C Zero or overlapping, Very high

D 3 eV, Zero

💡 Short Explanation

Bands overlap in metals. Electrons move freely. Conductivity is extremely high.

✅ Correct Answer Explanation

Metals have overlapping valence and conduction bands or effectively zero band gap. As a result, a large number of free electrons are available for conduction, giving metals very high conductivity.

❓ Why Other Options Are Incorrect

Option A → Describes insulators.
Option B → Describes semiconductors.
Option D → Incorrect relationship.

🎯 Strategy

Used

Conceptual Matching

Application:

Connect band structure to conductivity.

Final Logic:

Overlap produces very high conductivity.

🧠 Memory Trick

"Metal = Overlap = High Conductivity."

📚 Class XII – Physics Part II – Chapter: Semiconductor Electronics: Materials, Devices and Simple Circuits – Topic: Metallic Conductivity

10 The typical range of resistivity for a metal is:

A 10⁻⁵ to 10⁶ Ω m

B 10¹¹ to 10¹⁹ Ω m

C 10⁻² to 10⁻⁸ Ω m

D 10² to 10⁸ Ω m

💡 Short Explanation

Metals have very low resistivity. Free electrons move easily. They are excellent conductors.

✅ Correct Answer Explanation

Metals possess very low resistivity values, typically ranging from about 10⁻⁸ Ω m to 10⁻² Ω m. This low resistivity results from the availability of numerous free electrons for conduction.

❓ Why Other Options Are Incorrect

Option A → Semiconductor range.
Option B → Insulator range.
Option D → Not a standard metallic range.

🎯 Strategy

Used

Direct Recall

Application:

Recall standard resistivity classifications.

Final Logic:

Metals exhibit the lowest resistivity values.

🧠 Memory Trick

"Metal = Lowest Resistivity."

📚 Class XII – Physics Part II – Chapter: Semiconductor Electronics: Materials, Devices and Simple Circuits – Topic: Resistivity of Metals

11 Consider a material with a band gap of 5.4 eV

A It is classified as an intrinsic semiconductor at room temperature

B It is a metal because it belongs to group IV

C The energy gap is so large that thermal excitation cannot excite electrons to the conduction band

D Its conductivity is generally around 10⁵ S m⁻¹

💡 Short Explanation

A 5.4 eV gap is extremely large. Thermal energy at room temperature is insufficient. The material behaves as an insulator.

✅ Correct Answer Explanation

A band gap of 5.4 eV is characteristic of diamond (carbon), which behaves as an insulator. Because the gap is very large, room-temperature thermal energy cannot excite electrons from the valence band to the conduction band.

❓ Why Other Options Are Incorrect

Option A → Semiconductors typically have Eg < 3 eV.
Option B → Group IV membership does not automatically make a material metallic.
Option D → Such high conductivity is characteristic of good conductors, not insulators.

🎯 Strategy

Used

Substitution

Application:

Compare the given band gap with standard material classifications.

Final Logic:

A 5.4 eV gap prevents thermal excitation and conduction.

🧠 Memory Trick

"5.4 eV = Diamond Insulator."

📚 Class XII – Physics Part II – Chapter: Semiconductor Electronics: Materials, Devices and Simple Circuits – Topic: Insulating Bands

12 Correct statements regarding bound electrons in insulators
1. Electrons in the valence band all remain tightly bound.
2. No free electrons are available in the conduction band.
3. The forbidden gap completely prevents electron transitions at room temperature.
4. At room temperature, some bound electrons cross the gap easily.

A (A), (B), (C)

B (A), (B), (D)

C (B), (C), (D)

D (A), (C), (D)

💡 Short Explanation

Valence electrons remain bound. Conduction band remains empty. Large band gap prevents excitation.

✅ Correct Answer Explanation

Insulators possess a very large forbidden energy gap. As a result, electrons remain tightly bound in the valence band, the conduction band contains essentially no free electrons, and room-temperature thermal energy cannot bridge the gap. Statement D is incorrect because electrons do not cross the gap easily.

❓ Why Other Options Are Incorrect

Option B → Includes incorrect statement D.
Option C → Includes incorrect statement D.
Option D → Includes incorrect statement D.

🎯 Strategy

Used

Option Grouping

Application:

Evaluate each statement using insulating-band theory.

Final Logic:

A, B, and C are correct; D is incorrect.

🧠 Memory Trick

"Big Gap, Bound Electrons."

📚 Class XII – Physics Part II – Chapter: Semiconductor Electronics: Materials, Devices and Simple Circuits – Topic: Insulators

13 Incorrect statement about semiconducting gaps

A The gap is usually less than 3 eV.

B Thermal energy effectively ionises a few atoms in the lattice.

C Electrons can cross the gap and enter the valence band from the conduction band.

D The finite small gap leads to resistance lower than that of insulators.

💡 Short Explanation

Thermal excitation promotes electrons upward. Electrons move from valence band to conduction band. Option C reverses the process.

✅ Correct Answer Explanation

In semiconductors, thermal energy excites electrons from the valence band into the conduction band. Statement C incorrectly describes the direction of excitation. Although recombination can occur, thermal excitation itself is from valence to conduction band.

❓ Why Other Options Are Incorrect

Option A → Correct semiconductor property.
Option B → Correct description of carrier generation.
Option D → Correct comparison with insulators.

🎯 Strategy

Used

Direction Check

Application:

Verify the direction of electron excitation.

Final Logic:

Thermal excitation occurs from valence band to conduction band.

🧠 Memory Trick

"Electrons Go Up, Not Down."

📚 Class XII – Physics Part II – Chapter: Semiconductor Electronics: Materials, Devices and Simple Circuits – Topic: Semiconducting Gaps

14 At room temperature, the relation governing the dynamic equilibrium of electron-hole pairs generated intrinsically is:

A Rate of generation > Rate of recombination

B Rate of generation = Rate of recombination

C Rate of generation < Rate of recombination

D Rate of generation = 0

💡 Short Explanation

Equilibrium requires balance. Carrier concentration remains constant. Generation equals recombination.

✅ Correct Answer Explanation

In thermal equilibrium, electron-hole pairs are continuously generated and recombined. The carrier concentration remains constant because the rate of generation equals the rate of recombination.

❓ Why Other Options Are Incorrect

Option A → Carrier concentration would continuously increase.
Option C → Carrier concentration would continuously decrease.
Option D → Thermal generation exists at room temperature.

🎯 Strategy

Used

Equilibrium Principle

Application:

Apply equilibrium conditions for intrinsic semiconductors.

Final Logic:

Generation and recombination rates are equal.

🧠 Memory Trick

"Equilibrium = Equal Rates."

📚 Class XII – Physics Part II – Chapter: Semiconductor Electronics: Materials, Devices and Simple Circuits – Topic: Carrier Equilibrium

15 The thermal energy effectively ionises only a few atoms in the crystalline lattice, which directly

A destroys the diamond-like structure of the entire crystal

B forms a massive overlap of conduction and valence bands

C creates a vacancy in the bond while setting an electron free for conduction

D converts the intrinsic semiconductor into an insulator

💡 Short Explanation

Thermal energy breaks some covalent bonds. Free electrons are produced. Corresponding holes are created.

✅ Correct Answer Explanation

When thermal energy breaks a covalent bond, an electron becomes free to move in the conduction band. The bond vacancy left behind behaves as a hole. Together they form an electron-hole pair.

❓ Why Other Options Are Incorrect

Option A → The crystal structure remains intact.
Option B → Band overlap does not occur.
Option D → Carrier generation increases conductivity.

🎯 Strategy

Used

Cause-and-Effect Analysis

Application:

Determine the direct result of thermal ionisation.

Final Logic:

Thermal excitation produces free electrons and holes.

🧠 Memory Trick

"Broken Bond → Electron + Hole."

📚 Class XII – Physics Part II – Chapter: Semiconductor Electronics: Materials, Devices and Simple Circuits – Topic: Electron-Hole Pair Generation

16 Match List I with List II regarding Si/Ge lattice

List I	List II
1. — Outermost orbit of Si	I. — 4
2. — Outermost orbit of Ge	II. — n = 3
3. — Number of outer electrons per atom	III. — Diamond-like
4. — Lattice structure type	IV. — n = 4

A 1-II, 2-IV, 3-I, 4-III

B 1-IV, 2-II, 3-I, 4-III

C 1-II, 2-I, 3-IV, 4-III

D 1-I, 2-IV, 3-II, 4-III

💡 Short Explanation

Si outer orbit → n = 3. Ge outer orbit → n = 4. Both have four valence electrons.

✅ Correct Answer Explanation

Correct matching: Outermost orbit of Si → n = 3 (II) Outermost orbit of Ge → n = 4 (IV) Number of outer electrons → 4 (I) Structure type → Diamond-like (III)

❓ Why Other Options Are Incorrect

Option B → Reverses Si and Ge orbit numbers.
Option C → Incorrect electron assignment.
Option D → Incorrect orbit assignments.

🎯 Strategy

Used

Option Grouping

Application:

Match lattice characteristics of Si and Ge.

Final Logic:

Only Option A correctly matches all entries.

🧠 Memory Trick

"Si → 3, Ge → 4."

📚 Class XII – Physics Part II – Chapter: Semiconductor Electronics: Materials, Devices and Simple Circuits – Topic: Crystal Structure of Si and Ge

17 The mechanism of thermal energy affecting electron pairs in pure semiconductors implies

A Shared electron pairs stay permanently rigid at all temperatures

B More thermal energy allows some electrons to break away and become free

C The entire crystal lattice melts at room temperature

D The broken bonds leave a negatively charged vacancy

💡 Short Explanation

Increasing temperature breaks some bonds. Electrons become free carriers. Holes are simultaneously produced.

✅ Correct Answer Explanation

As temperature increases, some covalent bonds acquire enough energy to break. The released electrons enter the conduction band and become mobile charge carriers.

❓ Why Other Options Are Incorrect

Option A → Bonds can break with increasing temperature.
Option C → Lattice melting does not occur at room temperature.
Option D → Vacancies behave as positive holes.

🎯 Strategy

Used

Physical Interpretation

Application:

Analyze the effect of temperature on covalent bonds.

Final Logic:

Thermal energy frees some valence electrons.

🧠 Memory Trick

"Heat Frees Electrons."

📚 Class XII – Physics Part II – Chapter: Semiconductor Electronics: Materials, Devices and Simple Circuits – Topic: Thermal Excitation

18 Shared electron movement statements
1. Under an applied electric field, free electrons move completely independently as conduction electrons.
2. The electron originally set free is not involved in the process of hole motion.
3. Hole motion happens when an electron from a nearby covalent bond jumps to a vacant site.
4. The apparent movement of the hole is exactly the actual movement of a free electron.

A (A), (B), (C)

B (B), (C), (D)

C (A), (C), (D)

D (A), (B), (D)

💡 Short Explanation

Free electrons conduct independently. Hole motion occurs through bond-electron shifts. Hole motion is only an apparent movement.

✅ Correct Answer Explanation

Free electrons move through the conduction band under an electric field. Hole motion occurs when neighboring bond electrons successively fill vacancies. The original free electron is not responsible for hole movement. Statement D is incorrect because hole motion is an apparent movement, not the actual motion of a free conduction electron.

❓ Why Other Options Are Incorrect

Option B → Includes incorrect statement D.
Option C → Includes incorrect statement D.
Option D → Includes incorrect statement D.

🎯 Strategy

Used

Option Grouping

Application:

Distinguish between electron conduction and hole conduction.

Final Logic:

A, B, and C are correct.

🧠 Memory Trick

"Hole Moves by Bond Shifting."

📚 Class XII – Physics Part II – Chapter: Semiconductor Electronics: Materials, Devices and Simple Circuits – Topic: Hole Motion

19 Suppose an intrinsic semiconductor generates a free electron current Ie of 2 mA and a hole current Ih of 1 mA under an electric field. The total current I will be:

A 1 mA

B 2 mA

C 3 mA

D 0 mA

💡 Short Explanation

Total current is the sum of both currents. Electron and hole currents contribute together. Add the magnitudes directly.

✅ Correct Answer Explanation

For an intrinsic semiconductor: \(I=I_{e}+I_{h}\) Given: \(I_{e}=2 mAI_{h}=1 mA\) Therefore, \(I=2+1=3 mA\)

❓ Why Other Options Are Incorrect

Option A → Incorrect sum.
Option B → Ignores hole current.
Option D → Current is not zero.

🎯 Strategy

Used

Substitution

Application:

Apply the current relation directly.

Final Logic:

Total current = 3 mA.

🧠 Memory Trick

"Total Current = Electron + Hole."

📚 Class XII – Physics Part II – Chapter: Semiconductor Electronics: Materials, Devices and Simple Circuits – Topic: Current in Intrinsic Semiconductors

20 For an electron breaking free from a covalent bond, the charge of the free electron and the effective charge of the resulting hole are respectively:

A −q, −q

B +q, −q

C −q, +q

D +q, +q

💡 Short Explanation

Electron carries negative charge. Hole behaves as a positive charge carrier. They are generated as a pair.

✅ Correct Answer Explanation

When an electron leaves a covalent bond, it carries its natural charge of −q. The vacancy left behind behaves as a positively charged hole with effective charge +q.

❓ Why Other Options Are Incorrect

Option A → Hole is not negatively charged.
Option B → Electron is not positively charged.
Option D → Electron and hole have opposite charges.

🎯 Strategy

Used

Direct Recall

Application:

Recall the charges of electrons and holes.

Final Logic:

Electron = −q, Hole = +q.

🧠 Memory Trick

"Electron Negative, Hole Positive."

📚 Class XII – Physics Part II – Chapter: Semiconductor Electronics: Materials, Devices and Simple Circuits – Topic: Electron-Hole Pairs

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