CUET UG Physics Booster Test 2- Band Theory and Intrinsic Properties -

🚀

CUET UG Physics Booster Test 2- 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 2- Band Theory and Intrinsic Properties

1 / 20

QUESTION 1 OF 20

The formation of energy bands in solids instead of discrete energy levels

Answer Review

1 The formation of energy bands in solids instead of discrete energy levels

A occurs because atoms in a solid are far apart

B occurs because outer orbits of neighbouring atoms come very close or overlap

C results in every electron seeing the exact same pattern of surrounding charges

D makes electron motion identical to that in an isolated atom

💡 Short Explanation

Atoms in solids are closely packed. Outer electron orbits overlap. Energy levels split into bands.

✅ Correct Answer Explanation

In a solid, atoms are packed very closely together. As a result, the outer electron orbits of neighboring atoms overlap. This overlap causes the discrete energy levels of isolated atoms to split into a very large number of closely spaced energy levels, forming energy bands.

❓ Why Other Options Are Incorrect

Option A → Atoms in solids are not far apart.
Option C → Electrons experience different surrounding charge patterns.
Option D → Electron motion in solids differs from isolated atoms.

🎯 Strategy

Used

Contextual/Tonal Matching

Application:

Identify the physical cause of energy-band formation.

Final Logic:

Overlapping outer orbits produce energy bands.

🧠 Memory Trick

"Orbit Overlap → Energy Bands."

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

2 Each electron in a crystal has a unique position and surrounding charge pattern,

A only one discrete energy level is formed

B energy levels disappear entirely

C each electron will have a different energy level, forming a continuous energy variation

D the valence band overlaps with the inner core levels

💡 Short Explanation

Electrons experience different surroundings. Energy levels split slightly. Continuous bands are formed.

✅ Correct Answer Explanation

Inside a crystal, no two electrons experience exactly the same surrounding charge distribution. Consequently, their energies differ slightly. These numerous closely spaced energy levels merge into continuous energy bands.

❓ Why Other Options Are Incorrect

Option A → Many energy levels are formed.
Option B → Energy levels do not disappear.
Option D → Inner core levels do not overlap with the valence band.

🎯 Strategy

Used

Direct Concept Application

Application:

Relate electron surroundings to energy-level splitting.

Final Logic:

Different environments create different energy levels.

🧠 Memory Trick

"Different Charges → Different Energies."

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

3 Valence band characteristics statements
Valence band characteristics statements
A. It includes the energy levels of the valence electrons.
B. It is completely occupied at absolute zero temperature.
C. It is always partially empty in insulators.
D. Its highest energy level is denoted 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 0 K. EV denotes the top of the valence band.

✅ Correct Answer Explanation

The valence band contains the energy levels occupied by valence electrons. At absolute zero temperature, it is completely filled. The highest energy level of the valence band is represented by EV. Statement C is incorrect because in insulators the valence band is completely filled, not partially empty.

❓ 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 individually.

Final Logic:

Only A, B, and D are correct.

🧠 Memory Trick

"Valence Band: Full at 0 K."

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

4 Incorrect statement about the conduction band

A It is the energy band above the valence band.

B It is normally completely filled with electrons at absolute zero temperature.

C The lowest energy level in the conduction band is shown as EC.

D When it overlaps on the valence band, electrons can move freely into it.

💡 Short Explanation

Conduction band is above the valence band. It is empty at 0 K in semiconductors. EC denotes its lower edge.

✅ Correct Answer Explanation

For semiconductors at absolute zero, the conduction band is empty because no electrons possess enough energy to enter it. Therefore, stating that it is completely filled is incorrect.

❓ Why Other Options Are Incorrect

Option A → Correct definition.
Option C → EC denotes the conduction-band minimum.
Option D → Band overlap enables conduction in metals.

🎯 Strategy

Used

Elimination

Application:

Identify the statement inconsistent with band occupancy.

Final Logic:

The conduction band is empty at 0 K.

🧠 Memory Trick

"0 K → Empty Conduction Band."

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

5 If N is the number of atoms in a Si crystal, the total number of outer electrons occupying the lower band at absolute zero is:

A N

B 2N

C 4N

D 8N

💡 Short Explanation

Each Si atom contributes 4 valence electrons. At 0 K all remain in the valence band. Total electrons = 4N.

✅ Correct Answer Explanation

A silicon atom possesses four valence electrons. Therefore, N silicon atoms contribute 4N valence electrons. At absolute zero, all of these electrons occupy the lower energy band (valence band).

❓ Why Other Options Are Incorrect

Option A → Too few electrons.
Option B → Does not match silicon valency.
Option D → Represents available states, not electrons.

🎯 Strategy

Used

Substitution

Application:

Multiply the number of atoms by four valence electrons.

Final Logic:

N atoms × 4 valence electrons = 4N.

🧠 Memory Trick

"Si Has Four Valence Electrons."

📚 Class XII – Physics Part II – Chapter: Semiconductor Electronics: Materials, Devices and Simple Circuits – Topic: Band Occupancy at 0 K

6 With thermal excitation, electrons move to the conduction band and create vacancies in the valence band. The conduction particles are respectively:

A Free electrons, Positive holes

B Positive holes, Bound electrons

C Core ions, Free electrons

D Bound electrons, Core ions

💡 Short Explanation

Thermal energy creates electron-hole pairs. Electrons become mobile. Holes act as positive carriers.

✅ Correct Answer Explanation

When a valence electron gains thermal energy, it moves to the conduction band and becomes a free electron. The vacancy left behind behaves like a positively charged particle called a hole.

❓ Why Other Options Are Incorrect

Option B → Holes are not produced first.
Option C → Core ions do not participate in conduction.
Option D → Bound electrons cannot conduct.

🎯 Strategy

Used

Direct Recall

Application:

Apply the concept of electron-hole pair generation.

Final Logic:

Thermal excitation creates free electrons and holes.

🧠 Memory Trick

"Electron Up → Hole Left."

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

7 What is the respective energy gap value for Silicon and Germanium?

A 5.4 eV and 1.1 eV

B 1.1 eV and 0.7 eV

C 0.7 eV and 1.1 eV

D 3.0 eV and 0 eV

💡 Short Explanation

Silicon has a larger gap than Germanium. Both are semiconductors. Standard NCERT values are 1.1 eV and 0.7 eV.

✅ Correct Answer Explanation

The energy gap of Silicon is approximately 1.1 eV, while that of Germanium is approximately 0.7 eV. These values explain why both materials behave as semiconductors.

❓ Why Other Options Are Incorrect

Option A → 5.4 eV corresponds to diamond.
Option C → Values are reversed.
Option D → Incorrect values.

🎯 Strategy

Used

Direct Recall

Application:

Recall standard semiconductor energy gaps.

Final Logic:

Si = 1.1 eV; Ge = 0.7 eV.

🧠 Memory Trick

"Si-1.1, Ge-0.7."

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

8 Match List I (Gap Description) with List II (Condition)

List I	List II
1. Eg > 3 eV	I. Metal (Sn)
2. Eg = 0	II. Silicon
3. Eg ≈ 1.1 eV	III. Germanium
4. Eg ≈ 0.7 eV	IV. Insulator

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

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

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

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

💡 Short Explanation

Large gap → Insulator. Zero gap → Metal. Silicon → 1.1 eV. Germanium → 0.7 eV.

✅ Correct Answer Explanation

Correct matching: Eg > 3 eV → Insulator Eg = 0 → Metal Eg ≈ 1.1 eV → Silicon Eg ≈ 0.7 eV → Germanium

❓ Why Other Options Are Incorrect

Option B → Incorrectly reverses assignments.
Option C → Incorrect metal assignment.
Option D → Incorrect insulator assignment.

🎯 Strategy

Used

Option Grouping

Application:

Match standard energy-gap values with materials.

Final Logic:

Only Option A correctly matches all pairs.

🧠 Memory Trick

"0–Metal, 0.7–Ge, 1.1–Si, >3–Insulator."

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

9 Correct statements about metalsCorrect statements about metals
A. Conduction band is partially filled.
B. Valence band is partially empty.
C. Conduction and valence bands may overlap.
D. Thermal excitation is required to create an overlap.

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

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

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

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

💡 Short Explanation

Metals possess free electrons. Bands may overlap. Thermal excitation is unnecessary.

✅ Correct Answer Explanation

Metals conduct electricity because the conduction band may be partially filled, the valence band may be partially empty, or both bands may overlap. These conditions already exist naturally and do not require thermal excitation.

❓ 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:

Identify the actual causes of metallic conductivity.

Final Logic:

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

🧠 Memory Trick

"Metal = Overlap and Free Electrons."

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

10 The resistance of metallic materials is low because
A. the energy gap is strictly larger than 3 eV
B. electrons from the valence band can easily move into the conduction band due to overlap
C. thermal excitation ionises all the core atoms
D. holes move freely in the conduction band

A the energy gap is strictly larger than 3 eV

B electrons from the valence band can easily move into the conduction band due to overlap

C thermal excitation ionises all the core atoms

D holes move freely in the conduction band

💡 Short Explanation

Band overlap provides free electrons. Electrons move with little energy. Conductivity becomes very high.

✅ Correct Answer Explanation

In metals, the conduction band and valence band overlap or the conduction band is partially filled. Therefore, electrons can move easily under an applied electric field, resulting in low resistance and high conductivity.

❓ Why Other Options Are Incorrect

Option A → Describes insulators.
Option C → Core atoms are not ionized.
Option D → Conduction is mainly due to free electrons.

🎯 Strategy

Used

Contextual/Tonal Matching

Application:

Relate metallic conductivity to band overlap.

Final Logic:

Band overlap allows easy electron movement.

🧠 Memory Trick

"Overlap = Low Resistance."

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

11 In insulators, the energy gap is large. Consequently

A Electrons can be excited by thermal excitation at room temperature.

B Electrons from the valence band all remain bound.

C There is an abundant supply of free electrons in the conduction band.

D The resistivity is roughly 10⁻² to 10⁻⁸ Ω m.

💡 Short Explanation

Insulators have very large band gaps. Thermal energy cannot excite electrons easily. Electrons remain bound in the valence band.

✅ Correct Answer Explanation

In insulators, the energy gap is typically greater than 3 eV. The thermal energy available at room temperature is insufficient to move electrons from the valence band to the conduction band. Therefore, electrons remain tightly bound and conduction does not occur.

❓ Why Other Options Are Incorrect

Option A → Thermal excitation is insufficient.
Option C → Conduction band is essentially empty.
Option D → This resistivity range belongs to metals.

🎯 Strategy

Used

Elimination

Application:

Identify the consequence of a large energy band gap.

Final Logic:

Large gaps keep electrons bound in the valence band.

🧠 Memory Trick

"Large Gap = Bound Electrons."

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

12 Insulator conduction statements
Insulator conduction statements
A. There are no electrons in the conduction band.
B. No electrical conduction is possible.
C. Energy gap is so large that thermal excitation cannot bridge it.
D. Holes provide high conductivity in insulators.

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

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

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

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

💡 Short Explanation

Conduction band is empty. Large band gap prevents excitation. Electrical conduction is negligible.

✅ Correct Answer Explanation

Insulators possess a large forbidden energy gap. Electrons cannot acquire sufficient thermal energy to reach the conduction band, leaving it effectively empty. Hence, electrical conduction is practically impossible. Statement D is incorrect because holes do not provide high conductivity in insulators.

❓ 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 insulator band theory.

Final Logic:

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

🧠 Memory Trick

"Empty CB + Big Gap = Insulator."

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

13 The approximate energy gap for Silicon is:

A 0 eV

B 0.7 eV

C 1.1 eV

D 5.4 eV

💡 Short Explanation

Silicon is a semiconductor. It has a moderate energy gap. Standard value is 1.1 eV.

✅ Correct Answer Explanation

Silicon possesses an energy band gap of approximately 1.1 eV. This value is large enough to prevent excessive conduction yet small enough to allow controlled carrier generation at room temperature.

❓ Why Other Options Are Incorrect

Option A → Corresponds to metals.
Option B → Approximate value for Germanium.
Option D → Approximate value for diamond.

🎯 Strategy

Used

Direct Recall

Application:

Recall standard energy-gap values.

Final Logic:

Silicon → 1.1 eV.

🧠 Memory Trick

"Si = 1.1 eV."

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

14 Incorrect statement about semiconductors at room temperature

A Some electrons acquire enough energy to cross the energy gap.

B Resistance is as high as that of insulators.

C A finite but small band gap exists.

D Electrons can move in the conduction band.

💡 Short Explanation

Semiconductors have moderate resistance. Some electrons are thermally excited. Conductivity is greater than in insulators.

✅ Correct Answer Explanation

At room temperature, thermal energy excites some electrons into the conduction band. Therefore, semiconductors conduct electricity better than insulators and have much lower resistance than insulating materials.

❓ Why Other Options Are Incorrect

Option A → Correct statement.
Option C → Correct characteristic.
Option D → Conduction electrons move in the conduction band.

🎯 Strategy

Used

Odd One Out

Application:

Identify the statement inconsistent with semiconductor behavior.

Final Logic:

Semiconductor resistance is lower than insulator resistance.

🧠 Memory Trick

"Semiconductor ≠ Insulator."

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

15 Match List I (Symbol) with List II (Meaning) in intrinsic semiconductors

List I	List II
1. ne	I. Total current
2. nh	II. Intrinsic carrier concentration
3. ni	III. Free electron concentration
4. I	IV. Hole concentration

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

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

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

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

💡 Short Explanation

ne → electron concentration. nh → hole concentration. ni → intrinsic carrier concentration.

✅ Correct Answer Explanation

Correct matching: ne → Free electron concentration nh → Hole concentration ni → Intrinsic carrier concentration I → Total current Hence Option A is correct.

❓ Why Other Options Are Incorrect

Option B → Interchanges ne and nh.
Option C → Incorrect assignment of ni.
Option D → Incorrect assignment of nh.

🎯 Strategy

Used

Option Grouping

Application:

Match standard semiconductor symbols with meanings.

Final Logic:

Only Option A matches all definitions correctly.

🧠 Memory Trick

"e = Electron, h = Hole, i = Intrinsic."

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

16 In the diamond-like structure of pure Silicon, the number of valence electrons per atom and the number of nearest neighbours are respectively:

A 4, 8

B 8, 4

C 4, 4

D 2, 4

💡 Short Explanation

Silicon is tetravalent. Each atom has four neighbours. Four covalent bonds are formed.

✅ Correct Answer Explanation

Each silicon atom possesses four valence electrons and forms covalent bonds with four nearest neighbouring atoms arranged tetrahedrally.

❓ Why Other Options Are Incorrect

Option A → Nearest neighbours are not eight.
Option B → Silicon does not have eight valence electrons.
Option D → Silicon is not divalent.

🎯 Strategy

Used

Direct Recall

Application:

Recall the diamond crystal structure.

Final Logic:

Silicon → 4 valence electrons and 4 neighbours.

🧠 Memory Trick

"Silicon = 4 and 4."

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

17 The two shared electrons in a covalent bond can be assumed to

A be completely transferred from one atom to another

B escape the crystal lattice entirely at 0 K

C shuttle back-and-forth between the associated atoms holding them strongly

D reside exclusively in the conduction band

💡 Short Explanation

Covalent bonds involve electron sharing. Shared electrons bind neighbouring atoms. They are not permanently transferred.

✅ Correct Answer Explanation

In a covalent bond, the shared electron pair is common to both atoms and effectively moves between them, providing the attractive force that holds the crystal structure together.

❓ Why Other Options Are Incorrect

Option A → Describes ionic bonding.
Option B → Electrons remain bound at 0 K.
Option D → Bond electrons belong to the valence structure.

🎯 Strategy

Used

Conceptual Matching

Application:

Identify the nature of covalent bonding.

Final Logic:

Shared electrons strengthen the bond between atoms.

🧠 Memory Trick

"Shared Electrons Hold Atoms Together."

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

18 Correct statements about covalent bonds in Si/Ge
Correct statements about covalent bonds in Si/Ge
A. At low temperatures, an idealised picture shows all bonds intact.
B. As temperature increases, no bonds can be broken.
C. Shared electrons form a valence bond.
D. Each atom takes a share of one electron from each of its four neighbours.

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

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

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

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

💡 Short Explanation

Covalent bonds exist between neighbours. Shared electrons form valence bonds. Thermal energy can break some bonds.

✅ Correct Answer Explanation

At low temperatures, nearly all covalent bonds remain intact. Shared electrons form valence bonds, and each atom shares electrons with four neighbouring atoms. As temperature rises, some bonds can break due to thermal excitation. Statement B is incorrect because thermal energy can break covalent bonds.

❓ Why Other Options Are Incorrect

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

🎯 Strategy

Used

Option Grouping

Application:

Evaluate each bonding statement independently.

Final Logic:

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

🧠 Memory Trick

"Heat Breaks Some Bonds."

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

19 What is the effective charge of the vacancy (hole) created when an electron breaks away from a covalent bond?

A −q

B +q

C 0

D +2q

💡 Short Explanation

A missing electron leaves a positive vacancy. The vacancy behaves like a charge carrier. This carrier is called a hole.

✅ Correct Answer Explanation

When an electron leaves a covalent bond, a vacancy is created. Since a negative charge is missing, the vacancy behaves as an effective positive charge of magnitude +q.

❓ Why Other Options Are Incorrect

Option A → Electron charge is −q.
Option C → Hole carries effective charge.
Option D → Hole charge is not doubled.

🎯 Strategy

Used

Direct Recall

Application:

Recall the definition of a hole.

Final Logic:

A hole behaves as a positive charge carrier.

🧠 Memory Trick

"Missing Electron = Positive Hole."

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

20 The total current I in an intrinsic semiconductor is given by the sum of electron current (Ie) and hole current (Ih) as:

A I = Ie − Ih

B I = Ie × Ih

C I = Ie + Ih

D I = Ih / Ie

💡 Short Explanation

Both electrons and holes conduct. Their currents add together. Total current is their sum.

✅ Correct Answer Explanation

In an intrinsic semiconductor, electrical conduction occurs through both electrons and holes. Therefore, the total current is the sum of the electron current and the hole current: I=I_e+I_h

❓ Why Other Options Are Incorrect

Option A → Currents do not subtract.
Option B → Current is not a product.
Option D → No such relation exists.

🎯 Strategy

Used

Formula Recall

Application:

Apply the total-current relation for intrinsic semiconductors.

Final Logic:

Total current equals electron current plus hole current.

🧠 Memory Trick

"Electron Current + Hole Current = Total Current."

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

CUET UG Physics Booster Test 2- Band Theory and Intrinsic Properties

Test Complete!

Answer Review