CUET UG Physics Booster Test 3-Dual Nature of Matter and De Broglie -

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CUET UG Physics Booster Test 3-Dual Nature of Matter and De Broglie

⏱️ 30 Minutes

❓ 20 Questions

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

CUET UG Physics Booster Test 3-Dual Nature of Matter and De Broglie

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QUESTION 1 OF 20

When visually observing an object, which mechanisms require which physical description?
1. Gathering and focussing light by the eye-lens utilizes the wave picture.
2. Absorption of light by the retina's rods and cones utilizes the photon picture.
3. The choice of description is fundamentally dependent on the nature of the interacting experiment.
4. All visual phenomena are purely described by continuous wave mechanics.

Answer Review

1 When visually observing an object, which mechanisms require which physical description?
1. Gathering and focussing light by the eye-lens utilizes the wave picture.
2. Absorption of light by the retina's rods and cones utilizes the photon picture.
3. The choice of description is fundamentally dependent on the nature of the interacting experiment.
4. All visual phenomena are purely described by continuous wave mechanics.

A (1), (3), (4)

B (2), (3), (4)

C (1), (2), (3)

D (1), (2), (4)

💡 Short Explanation

�� Vision involves both wave and particle aspects. �� Lens action is explained by wave optics. �� Retinal absorption involves photons.

✅ Correct Answer Explanation

Statement 1 is correct because image formation and focusing by the eye lens are explained using the wave nature of light. → Statement 2 is correct because rods and cones absorb light through photon interactions. → Statement 3 is correct because the appropriate description depends on the phenomenon being studied. → Statement 4 is incorrect because photon interactions are essential in light absorption.

❓ Why Other Options Are Incorrect

�� Statement 4 → Continuous wave mechanics alone cannot explain absorption at the retinal receptors.

🎯 Strategy

Used

�� Elimination

Application:

�� Remove the statement claiming wave theory alone explains all visual processes.

Final Logic:

�� Statements 1, 2 and 3 correctly describe vision.

🧠 Memory Trick

Lens = Wave, Retina = Photon

📚 Class XII – Physics Part II – Chapter: Dual Nature of Radiation and Matter – Topic: Context-Dependent Description of Light

2 Correct statements about radiation duality interactions in physical effects
1. The transfer of energy and momentum in discrete amounts demonstrates particle nature.
2. The photoelectric effect strictly involves energy transfer via photons.
3. The Compton effect strictly involves momentum transfer via photons.
4. The phenomenon of interference proves the localized absorption of photons.

A (1), (2), (4)

B (1), (3), (4)

C (2), (3), (4)

D (1), (2), (3)

💡 Short Explanation

�� Photoelectric effect supports photon energy transfer. �� Compton effect supports photon momentum transfer. �� Interference supports wave nature.

✅ Correct Answer Explanation

Statement 1 is correct because discrete energy and momentum transfer are signatures of particle behavior. → Statement 2 is correct because photoelectric emission occurs through photon-electron interaction. → Statement 3 is correct because Compton scattering demonstrates momentum transfer by photons. → Statement 4 is incorrect because interference is evidence of wave behavior, not localized photon absorption.

❓ Why Other Options Are Incorrect

�� Statement 4 → Interference demonstrates wave superposition, not photon absorption.

🎯 Strategy

Used

�� Elimination

Application:

�� Separate wave-based phenomena from particle-based phenomena.

Final Logic:

�� Statements 1, 2 and 3 are correct.

🧠 Memory Trick

Photoelectric = Energy, Compton = Momentum

📚 Class XII – Physics Part II – Chapter: Dual Nature of Radiation and Matter – Topic: Radiation Duality Evidence

3 Symmetry arguments utilized by de Broglie
1. Nature inherently favors symmetry in its physical entities.
2. Matter and energy, the two basic physical entities, must have symmetrical character.
3. If electromagnetic radiation exhibits dual aspects, matter must also mirror this.
4. Matter waves are theorized to exist only for electrically charged sub-atomic particles.

A (1), (2), (3)

B (1), (3), (4)

C (2), (3), (4)

D (1), (2), (4)

💡 Short Explanation

�� de Broglie relied on symmetry arguments. �� Matter and energy are treated analogously. �� Matter waves are universal.

✅ Correct Answer Explanation

Statements 1, 2 and 3 correctly describe de Broglie's reasoning. → Statement 4 is incorrect because matter waves are associated with all moving particles, not only charged subatomic particles.

❓ Why Other Options Are Incorrect

�� Statement 4 → Neutral particles also possess de Broglie wavelengths.

🎯 Strategy

Used

�� Elimination

Application:

�� Remove the statement restricting matter waves to charged particles.

Final Logic:

�� Statements 1, 2 and 3 are correct.

🧠 Memory Trick

Radiation Dual → Matter Dual

📚 Class XII – Physics Part II – Chapter: Dual Nature of Radiation and Matter – Topic: Symmetry in Nature

4 In formulating his revolutionary 1924 hypothesis, Louis de Broglie primarily relied on the conceptual argument that

A since nature is symmetrical, moving material particles should exhibit wave-like properties just as radiation exhibits particle-like properties

B emerging experimental evidence from Compton scattering directly and undeniably proved the wave nature of electrons

C explaining the photoelectric effect required all matter to behave continuously like a wave

D Planck's constant was mathematically unmeasurable without assuming matter waves existed

💡 Short Explanation

�� de Broglie's argument was conceptual. �� Symmetry between matter and radiation was central. �� Matter waves were proposed theoretically.

✅ Correct Answer Explanation

de Broglie argued that if radiation exhibits both wave and particle properties, matter should also possess dual characteristics. → This symmetry argument led to the matter-wave hypothesis. → Therefore option A is correct.

❓ Why Other Options Are Incorrect

�� Option B → Compton scattering concerned photons, not electron waves.
�� Option C → Opposite of quantum reasoning.
�� Option D → Incorrect historical and conceptual statement.

🎯 Strategy

Used

�� Contextual/Tonal Matching

Application:

�� Recall the fundamental reasoning behind the hypothesis.

Final Logic:

�� Symmetry motivated matter-wave theory.

🧠 Memory Trick

Symmetry → Matter Waves

📚 Class XII – Physics Part II – Chapter: Dual Nature of Radiation and Matter – Topic: de Broglie's Hypothesis

5 Match List I with List II regarding proportionality inside de Broglie's equation

List I	List II
1. λ versus p	a. Inversely proportional
2. λ versus m (for constant v)	b. Inversely proportional
3. λ versus v (for constant m)	c. Inversely proportional
4. p versus v (for constant m)	d. Directly proportional

A 1-d, 2-c, 3-b, 4-a

B 1-a, 2-b, 3-c, 4-d

C 1-a, 2-d, 3-c, 4-b

D 1-c, 2-a, 3-d, 4-b

💡 Short Explanation

�� λ = h/p. �� p = mv. �� Wavelength decreases as mass or velocity increases.

✅ Correct Answer Explanation

Correct Match: List I — List II 1. λ versus p — a. Inversely proportional 2. λ versus m — b. Inversely proportional 3. λ versus v — c. Inversely proportional 4. p versus v — d. Directly proportional → Hence option B is correct.

❓ Why Other Options Are Incorrect

�� Options A, C and D contain incorrect proportionality relations.

🎯 Strategy

Used

�� Option Grouping

Application:

�� Use λ = h/mv and p = mv.

Final Logic:

�� λ varies inversely with p, m and v.

🧠 Memory Trick

Bigger p → Smaller λ

📚 Class XII – Physics Part II – Chapter: Dual Nature of Radiation and Matter – Topic: de Broglie Relation

6 Incorrect statement about the functional role of h

A It directly links the physical momentum of a material particle to its matter wavelength

B It acts as the mathematical proportionality constant between energy and frequency for photons

C Its magnitude ensures that heavy macroscopic objects possess easily observable and large wavelengths

D It relates the classical wave attributes and particle attributes for both matter and radiation uniformly

💡 Short Explanation

�� h is extremely small. �� Large masses give tiny wavelengths. �� Macroscopic matter waves are unobservable.

✅ Correct Answer Explanation

Since h is very small, macroscopic objects with large momentum have extremely small de Broglie wavelengths. → Therefore heavy objects do not possess easily observable wavelengths. → Hence option C is correct.

❓ Why Other Options Are Incorrect

�� Option A → Correct role in λ = h/p.
�� Option B → Correct role in E = hν.
�� Option D → Correctly describes the significance of h.

🎯 Strategy

Used

�� Elimination

Application:

�� Identify the statement contradicting de Broglie wavelength behavior.

Final Logic:

�� Heavy objects have tiny, not large, wavelengths.

🧠 Memory Trick

Small h → Tiny Macroscopic λ

📚 Class XII – Physics Part II – Chapter: Dual Nature of Radiation and Matter – Topic: Role of Planck's Constant

7 If an electron translates with speed v = 5.4 × 10⁶ m/s, what is its explicit momentum p?
(Using m = 9.11 × 10⁻³¹ kg)

A 4.92 × 10⁻²⁴ kg m/s

B 4.92 × 10⁻²⁵ kg m/s

C 4.92 × 10⁻²⁶ kg m/s

D 4.92 × 10⁻²³ kg m/s

💡 Short Explanation

�� Use p = mv. �� Multiply mass and velocity. �� Express answer in scientific notation.

✅ Correct Answer Explanation

p = mv = (9.11 × 10⁻³¹)(5.4 × 10⁶) = 4.92 × 10⁻²⁴ kg m/s → Therefore option A is correct.

❓ Why Other Options Are Incorrect

�� Option B → One power of ten too small.
�� Option C → Two powers of ten too small.
�� Option D → One power of ten too large.

🎯 Strategy

Used

�� Substitution

Application:

�� Apply p = mv directly.

Final Logic:

�� p = 4.92 × 10⁻²⁴ kg m/s.

🧠 Memory Trick

Momentum = mv

📚 Class XII – Physics Part II – Chapter: Dual Nature of Radiation and Matter – Topic: Electron Momentum

8 For the fundamental relation linking matter and wave properties, the specific attributes unified by h are respectively:

A c, λ

B E, m

C v, F

D λ, p

💡 Short Explanation

�� λ is a wave property. �� p is a particle property. �� h connects them.

✅ Correct Answer Explanation

In the de Broglie equation: λ = h/p → λ represents wavelength (wave aspect). → p represents momentum (particle aspect). → Thus h unifies λ and p.

❓ Why Other Options Are Incorrect

�� Option A → Not the wave-particle pair connected by h.
�� Option B → Not related by de Broglie's relation.
�� Option C → Not involved.

🎯 Strategy

Used

�� Contextual/Tonal Matching

Application:

�� Identify the quantities appearing in λ = h/p.

Final Logic:

�� h links wavelength and momentum.

🧠 Memory Trick

λ ↔ p through h

📚 Class XII – Physics Part II – Chapter: Dual Nature of Radiation and Matter – Topic: Wave-Particle Integration

9 The analytical relation for the momentum of a light quantum having wavelength λ is directly derived as:

A h(λ)⁻¹

B λ(h)⁻¹

C h(λ)²

D λ(h)²

💡 Short Explanation

�� Photon momentum depends on wavelength. �� Use de Broglie relation. �� Inverse dependence exists.

✅ Correct Answer Explanation

From: λ = h/p Therefore: p = h/λ = h(λ)⁻¹ → Hence option A is correct.

❓ Why Other Options Are Incorrect

�� Option B → Represents λ/h.
�� Option C → Incorrect square dependence.
�� Option D → Incorrect dimensions.

🎯 Strategy

Used

�� Substitution

Application:

�� Rearrange λ = h/p.

Final Logic:

�� p = h/λ.

🧠 Memory Trick

Photon Momentum = h/λ

📚 Class XII – Physics Part II – Chapter: Dual Nature of Radiation and Matter – Topic: Photon Momentum

10 When correctly substituting p = hν/c into the de Broglie matter wave relation for a photon

A The resulting effective mass of the photon becomes physically measurable

B The resulting de Broglie wavelength conceptually and numerically equals the electromagnetic wavelength of the photon itself

C It yields an inconsistent result that contradicts the established wave nature of light

D It logically proves that photons travel mathematically slower than the theoretical speed of light

💡 Short Explanation

�� Use λ = h/p. �� Substitute photon momentum. �� Result equals c/ν.

✅ Correct Answer Explanation

Using: λ = h/p and p = hν/c → λ = h/(hν/c) = c/ν → This is exactly the electromagnetic wavelength of the photon. → Hence option B is correct.

❓ Why Other Options Are Incorrect

�� Option A → Effective mass is not obtained from this derivation.
�� Option C → The derivation is perfectly consistent.
�� Option D → No such conclusion follows.

🎯 Strategy

Used

�� Substitution

Application:

�� Substitute photon momentum into de Broglie's equation.

Final Logic:

�� de Broglie wavelength equals electromagnetic wavelength.

🧠 Memory Trick

Photon: λ = c/ν

📚 Class XII – Physics Part II – Chapter: Dual Nature of Radiation and Matter – Topic: Applicability of de Broglie Relation to Photons

11 Regarding the calculated de Broglie values of a 0.12 kg ball moving at 20 m/s:
1. The calculated particle momentum is 2.40 kg m s⁻¹.
2. The associated matter wavelength is 2.76 × 10⁻³⁴ m.
3. The resulting wavelength is practically beyond any physical measurement.
4. The matter wave character dominates and is highly significant.

A (1), (2), (3)

B (1), (2), (4)

C (2), (3), (4)

D (1), (3), (4)

💡 Short Explanation

�� Macroscopic objects have large momentum. �� Their de Broglie wavelengths are extremely small. �� Wave effects are practically unobservable.

✅ Correct Answer Explanation

Momentum: p = mv = 0.12 × 20 = 2.40 kg m s⁻¹ → Wavelength: λ = h/p = (6.63 × 10⁻³⁴)/(2.40) = 2.76 × 10⁻³⁴ m → Such a tiny wavelength is far beyond present experimental detection. → Statement 4 is incorrect because wave effects are negligible for macroscopic objects.

❓ Why Other Options Are Incorrect

�� Statement 4 → Matter-wave effects do not dominate for macroscopic objects.

🎯 Strategy

Used

�� Substitution

Application:

�� Calculate p and λ directly using standard formulas.

Final Logic:

�� Statements 1, 2 and 3 are correct.

🧠 Memory Trick

Big Mass → Tiny λ

📚 Class XII – Physics Part II – Chapter: Dual Nature of Radiation and Matter – Topic: Matter Waves of Macroscopic Objects

12 Correct statements about unmeasurable matter waves in daily life
1. The relative heaviness (large m) of a macroscopic particle drastically decreases its de Broglie wavelength.
2. High-energy macroscopic objects exhibit clear quantum diffraction natively.
3. The extreme smallness of Planck's constant forces macroscopic λ to be tiny.
4. The de Broglie wavelengths of macroscopic objects are generally considered unmeasurable.

A (1), (2), (3)

B (1), (3), (4)

C (2), (3), (4)

D (1), (2), (4)

💡 Short Explanation

�� λ = h/mv. �� Large mass reduces wavelength. �� Macroscopic diffraction is not observed.

✅ Correct Answer Explanation

Statements 1, 3 and 4 correctly explain why macroscopic matter waves are unobservable. → Statement 2 is incorrect because quantum diffraction is not observable for ordinary macroscopic bodies.

❓ Why Other Options Are Incorrect

�� Statement 2 → Macroscopic objects do not show clear quantum diffraction.

🎯 Strategy

Used

�� Elimination

Application:

�� Remove the statement inconsistent with observed macroscopic behavior.

Final Logic:

�� Statements 1, 3 and 4 are correct.

🧠 Memory Trick

Large m → Small λ

📚 Class XII – Physics Part II – Chapter: Dual Nature of Radiation and Matter – Topic: Unmeasurable Matter Waves

13 Statements detailing the sub-atomic domain's wave mechanics
1. The wave character of sub-atomic particles is both significant and measurable.
2. Measurable wavelengths are typically of the order of atomic-plane spacing in crystals.
3. Sub-atomic particles possess unmeasurably small wavelengths due to high velocities.
4. Accelerated electron wavelengths are mathematically comparable to X-ray wavelengths.

A (1), (2), (3)

B (2), (3), (4)

C (1), (3), (4)

D (1), (2), (4)

💡 Short Explanation

�� Electron wavelengths are measurable. �� They are comparable to crystal spacing. �� They are similar to X-ray wavelengths.

✅ Correct Answer Explanation

Statements 1, 2 and 4 are correct. → Electron wavelengths are typically around 10⁻¹⁰ m, comparable to crystal lattice spacing. → Statement 3 is incorrect because sub-atomic wavelengths are measurable and experimentally observed.

❓ Why Other Options Are Incorrect

�� Statement 3 → Contradicts electron diffraction experiments.

🎯 Strategy

Used

�� Elimination

Application:

�� Identify the statement inconsistent with matter-wave observations.

Final Logic:

�� Statements 1, 2 and 4 are correct.

🧠 Memory Trick

Electron λ ≈ X-ray λ

📚 Class XII – Physics Part II – Chapter: Dual Nature of Radiation and Matter – Topic: Wave Nature of Sub-Atomic Particles

14 Using the calculated wavelengths from Example 11.3, what is the exact wavelength λ for the electron?

A 0.135 × 10⁻⁹ m

B 0.135 × 10⁻¹⁰ m

C 0.135 × 10⁻¹¹ m

D 0.135 × 10⁻¹² m

💡 Short Explanation

�� Use λ = h/p. �� Electron momentum is very small. �� Result lies in atomic dimensions.

✅ Correct Answer Explanation

For the electron: p = 4.92 × 10⁻²⁴ kg m s⁻¹ → Therefore, λ = h/p = (6.63 × 10⁻³⁴)/(4.92 × 10⁻²⁴) ≈ 1.35 × 10⁻¹⁰ m = 0.135 × 10⁻⁹ m → Hence option A is correct.

❓ Why Other Options Are Incorrect

�� Option B → Ten times smaller.
�� Option C → Hundred times smaller.
�� Option D → Thousand times smaller.

🎯 Strategy

Used

�� Substitution

Application:

�� Apply λ = h/p.

Final Logic:

�� λ = 0.135 × 10⁻⁹ m.

🧠 Memory Trick

Electron λ ≈ 10⁻¹⁰ m

📚 Class XII – Physics Part II – Chapter: Dual Nature of Radiation and Matter – Topic: Electron de Broglie Wavelength

15 Match List I with List II regarding foundational contributions in quantum mechanics

List I	List II
1. Proposed 1924 hypothesis of matter waves	a. Louis Victor de Broglie
2. Developed full-fledged theory of wave mechanics	b. Erwin Schrodinger
3. Awarded Nobel Prize in 1929 for electron wave nature	c. Louis Victor de Broglie
4. Reasoned nature was fundamentally symmetrical	d. Louis Victor de Broglie

A 1-a, 2-b, 3-c, 4-d

B 1-b, 2-a, 3-d, 4-c

C 1-d, 2-c, 3-a, 4-b

D 1-c, 2-d, 3-b, 4-a

💡 Short Explanation

�� de Broglie proposed matter waves. �� Schrodinger developed wave mechanics. �� Nobel Prize recognized de Broglie's contribution.

✅ Correct Answer Explanation

Correct Match: List I — List II 1. Proposed 1924 hypothesis of matter waves — a. Louis Victor de Broglie 2. Developed full-fledged theory of wave mechanics — b. Erwin Schrodinger 3. Awarded Nobel Prize in 1929 for electron wave nature — c. Louis Victor de Broglie 4. Reasoned nature was fundamentally symmetrical — d. Louis Victor de Broglie → Hence option A is correct.

❓ Why Other Options Are Incorrect

�� Options B, C and D contain incorrect scientist-contribution pairings.

🎯 Strategy

Used

�� Option Grouping

Application:

�� Associate scientists with their known contributions.

Final Logic:

�� Only Option A gives all correct matches.

🧠 Memory Trick

de Broglie → Matter Waves, Schrodinger → Wave Mechanics

📚 Class XII – Physics Part II – Chapter: Dual Nature of Radiation and Matter – Topic: Development of Quantum Mechanics

16 Incorrect statement about Louis de Broglie's Nobel Prize

A It was officially awarded in the year 1929

B It recognized his revolutionary discovery of the wave nature of electrons

C It was awarded primarily for his derivation of the photoelectric emission equation

D It validated his bold 1924 hypothesis proposing the dual nature of matter

💡 Short Explanation

�� Photoelectric equation is associated with Einstein. �� de Broglie proposed matter waves. �� Nobel Prize was awarded in 1929.

✅ Correct Answer Explanation

de Broglie received the Nobel Prize for proposing the wave nature of matter. → The photoelectric equation was formulated by Einstein. → Therefore option C is correct.

❓ Why Other Options Are Incorrect

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

🎯 Strategy

Used

�� Elimination

Application:

�� Distinguish Einstein's work from de Broglie's contribution.

Final Logic:

�� Photoelectric equation was not de Broglie's achievement.

🧠 Memory Trick

Einstein → Photoelectric, de Broglie → Matter Waves

📚 Class XII – Physics Part II – Chapter: Dual Nature of Radiation and Matter – Topic: Nobel Prize Recognition

17 The expression for momentum p of a photon, which was confirmed scattered in the Compton effect, is formulated with h and c as:

A hc(ν)²

B cν(h)⁻¹

C hν(c)⁻¹

D hν(c)²

💡 Short Explanation

�� Photon momentum depends on frequency. �� Derived from E = pc. �� Important in Compton scattering.

✅ Correct Answer Explanation

Photon energy: E = hν → Also: E = pc → Therefore: p = hν/c = hν(c)⁻¹ → Hence option C is correct.

❓ Why Other Options Are Incorrect

�� Option A → Incorrect dimensions.
�� Option B → Incorrect arrangement.
�� Option D → Incorrect dependence on c.

🎯 Strategy

Used

�� Substitution

Application:

�� Use E = hν and E = pc.

Final Logic:

�� p = hν/c.

🧠 Memory Trick

Photon Momentum = hν/c

📚 Class XII – Physics Part II – Chapter: Dual Nature of Radiation and Matter – Topic: Photon Momentum

18 The structural order of atomic-planes spacing inside crystals

A provides a dimensional scale where the de Broglie wavelength of sub-atomic particles is significantly measurable

B makes it structurally impossible to measure the wavelength of moving electrons

C is dimensionally too large to meaningfully interact with X-ray wavelengths

D is directly proportional to the physical mass of traversing macroscopic balls

💡 Short Explanation

�� Crystal spacing is about 10⁻¹⁰ m. �� Electron wavelengths are similar. �� Diffraction becomes possible.

✅ Correct Answer Explanation

Atomic plane spacing and electron wavelengths are of comparable magnitude. → This allows diffraction experiments and measurement of matter waves. → Therefore option A is correct.

❓ Why Other Options Are Incorrect

�� Option B → Electron wavelengths can be measured.
�� Option C → X-rays interact strongly with crystal planes.
�� Option D → No such proportionality exists.

🎯 Strategy

Used

�� Contextual/Tonal Matching

Application:

�� Relate crystal spacing to diffraction conditions.

Final Logic:

�� Comparable scales enable measurement.

🧠 Memory Trick

Crystal Scale ≈ Electron Scale

📚 Class XII – Physics Part II – Chapter: Dual Nature of Radiation and Matter – Topic: Crystal Diffraction and Matter Waves

19 When analyzing the dual attributes for a propagating matter wave, the physically meaningful velocity and the unmeaningful velocity are respectively:

A Group velocity, Phase velocity

B Phase velocity, Group velocity

C Light velocity, Particle velocity

D Particle velocity, Light velocity

💡 Short Explanation

�� Group velocity equals particle velocity. �� Phase velocity lacks direct physical significance. �� Matter waves travel as wave packets.

✅ Correct Answer Explanation

Group velocity represents the actual velocity of the particle. → Phase velocity does not represent physical transport of matter. → Hence option A is correct.

❓ Why Other Options Are Incorrect

�� Option B → Reversed order.
�� Option C → Not the standard interpretation.
�� Option D → Incorrect classification.

🎯 Strategy

Used

�� Contextual/Tonal Matching

Application:

�� Recall definitions of group and phase velocity.

Final Logic:

�� Group velocity is meaningful; phase velocity is not.

🧠 Memory Trick

Group = Real, Phase = Formal

📚 Class XII – Physics Part II – Chapter: Dual Nature of Radiation and Matter – Topic: Group and Phase Velocity

20 Detailed statements about electron energy distribution in metals
1. Free electrons are not entirely free to leave the constant potential of the metal.
2. The specific energy distribution differs fundamentally from Maxwell's theory.
3. Pauli's exclusion principle mathematically explains the energy distribution difference.
4. All free electrons require identical supplementary work function energy to escape.

A (1), (2), (3)

B (1), (3), (4)

C (2), (3), (4)

D (1), (2), (4)

💡 Short Explanation

�� Electrons are bound within the metal. �� They obey quantum statistics. �� Pauli exclusion principle is important.

✅ Correct Answer Explanation

Statement 1 is correct because electrons remain confined by the metal's potential barrier. → Statement 2 is correct because electrons follow Fermi-Dirac statistics rather than Maxwell-Boltzmann statistics. → Statement 3 is correct because the exclusion principle governs electron occupancy of energy states. → Statement 4 is incorrect because electrons possess different initial energies inside the metal.

❓ Why Other Options Are Incorrect

�� Statement 4 → Different electrons require different additional energies depending on their initial energy states.

🎯 Strategy

Used

�� Elimination

Application:

�� Remove the statement assuming identical electron energies.

Final Logic:

�� Statements 1, 2 and 3 are correct.

🧠 Memory Trick

Metal Electrons → Fermi + Pauli

📚 Class XII – Physics Part II – Chapter: Dual Nature of Radiation and Matter – Topic: Electron Energy Distribution in Metals

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