CUET UG Physics Booster Test 3- Einstein’s Quantum Theory and Photons
📌 Answers are locked once submitted — results and explanations appear at the end.
QUESTION 1 OF 20
Wave theory failure statements
1. Greater intensity implies greater energy continuously absorbed per electron.
2. Sufficiently intense radiation should overcome the work function eventually, regardless of frequency.
3. A threshold frequency arises naturally from continuous wave absorption.
4. Absorption occurs continuously over the entire wavefront.
QUESTION 2 OF 20
Incorrect statement about emission delay in classical theory versus experiment
QUESTION 3 OF 20
Match List I with List II concerning quantum versus classical properties
| List I | List II |
|---|---|
| 1. Continuous energy distribution | a. Quantum hypothesis |
| 2. Discrete energy units | b. Wave theory |
| 3. Group velocity of matter wave | c. Single photon absorption |
| 4. Instantaneous emission | d. Velocity of the particle |
QUESTION 4 OF 20
The power emitted by a source is 2.0 × 10⁻³ W with photon energy 3.98 × 10⁻¹⁹ J. What will be the total number of photons emitted per second?
QUESTION 5 OF 20
Einstein's radical assumption fundamentally differed from classical physics because
QUESTION 6 OF 20
In Einstein's photoelectric equation, if the maximum kinetic energy is set to zero, the expression for the threshold frequency ν₀ will be
QUESTION 7 OF 20
The photoelectric equation shows that an increase in incident frequency leads to a _______ in maximum kinetic energy, while an increase in intensity leads to _______ in maximum kinetic energy.
QUESTION 8 OF 20
In evaluating the stopping potential V₀ corresponding to maximum kinetic energy,
QUESTION 9 OF 20
Correct statements about single quantum absorption
1. Low intensity does not imply a delay in emission.
2. A single electron absorbs only a single quantum of radiation.
3. The basic elementary process depends directly on the total intensity.
4. High intensity ensures multiple quanta are absorbed by one electron.
QUESTION 10 OF 20
Match List I with List II for electron emission energies
| List I | List II |
|---|---|
| 1. Maximum kinetic energy | a. Energy absorbed < φ₀ |
| 2. Lower kinetic energy | b. Least tightly bound electrons |
| 3. Zero kinetic energy | c. Tightly bound electrons |
| 4. Cannot escape | d. Incident frequency equals threshold |
QUESTION 11 OF 20
If the threshold frequency for caesium is 5.16 × 10¹⁴ Hz, what will be its work function?
(h = 6.63 × 10⁻³⁴ J s, 1 eV = 1.6 × 10⁻¹⁹ J)
QUESTION 12 OF 20
Minimum emission condition statements
1. Requires ν > ν₀.
2. Dictates that photoelectric emission cannot occur if hν < φ₀.
3. Shows that threshold frequency is exactly the same for all metals.
4. Ensures Kmax is positive for emission.
QUESTION 13 OF 20
Incorrect statement about Millikan's slope measurements
QUESTION 14 OF 20
The experimental verification of the photoelectric equation by Millikan
QUESTION 15 OF 20
Let an electric field be E and the charge of a photon be q. Since photons are electrically neutral, their electrostatic force in the field will be
QUESTION 16 OF 20
For a fixed frequency, an increase in intensity results in a _______ in the number of photons per second, but _______ in the energy of each photon.
QUESTION 17 OF 20
Correct statements about the momentum of light
1. The momentum of a photon is given by p = h/λ.
2. All photons of a particular wavelength have the exact same momentum.
3. Photon momentum is directly proportional to intensity.
4. Momentum confirms a particle-like nature of light.
QUESTION 18 OF 20
Match List I with List II regarding radiation interaction
| List I | List II |
|---|---|
| 1. Wavelength λ | a. Wave picture |
| 2. Group velocity of matter wave | b. Velocity of the particle |
| 3. Compton effect | c. Scattering of X-rays from electrons |
| 4. Eye-lens gathering light | d. Momentum p = h/λ |
QUESTION 19 OF 20
In analyzing a photon-electron collision process, it is essential to note that
QUESTION 20 OF 20
Non-conservation of photon number statements
1. A photon may be entirely absorbed by an electron.
2. The total number of photons before and after a collision may completely differ.
3. A new photon may be created during emission or collision.
4. Photons possess rest mass which must be rigorously conserved.
Test Complete!
Answer Review
1 Wave theory failure statements
1. Greater intensity implies greater energy continuously absorbed per electron.
2. Sufficiently intense radiation should overcome the work function eventually, regardless of frequency.
3. A threshold frequency arises naturally from continuous wave absorption.
4. Absorption occurs continuously over the entire wavefront.
�� Classical theory assumes continuous energy absorption. �� Higher intensity means greater energy transfer. �� Threshold frequency cannot be explained classically.
- Statement 1 is correct according to classical wave theory because energy absorption is continuous and increases with intensity. → Statement 2 is correct because classical theory predicts that sufficiently intense radiation should eventually provide enough energy for emission, irrespective of frequency. → Statement 4 is correct because wave theory assumes energy is distributed continuously over the wavefront. → Statement 3 is incorrect because classical theory cannot naturally explain the existence of a threshold frequency.
- �� Statement 3 → Threshold frequency is unexplained by classical wave theory.
Used
- �� Elimination
Application:
- �� Remove the statement inconsistent with classical wave predictions.
Final Logic:
- �� Statements 1, 2 and 4 correctly describe the classical picture.
- Wave Theory = Continuous + No Threshold
2 Incorrect statement about emission delay in classical theory versus experiment
�� Classical theory predicted delay. �� Experiments showed immediate emission. �� This was a major failure of wave theory.
- Classical wave theory predicted that electrons would require time to accumulate sufficient energy before emission. → Experiments showed photoemission begins almost instantaneously (≈10⁻⁹ s or less). → Therefore wave theory did not accurately predict instantaneous emission. → Hence option B is incorrect.
- �� Option A → Correct classical prediction.
- �� Option C → Correct experimental observation.
- �� Option D → Correct consequence of classical theory.
Used
- �� Elimination
Application:
- �� Compare theoretical prediction with experimental results.
Final Logic:
- �� Instantaneous emission contradicted classical wave theory.
- Wave Theory → Delay, Experiment → Instant
3 Match List I with List II concerning quantum versus classical properties
| List I | List II |
|---|---|
| 1. Continuous energy distribution | a. Quantum hypothesis |
| 2. Discrete energy units | b. Wave theory |
| 3. Group velocity of matter wave | c. Single photon absorption |
| 4. Instantaneous emission | d. Velocity of the particle |
�� Continuous distribution belongs to wave theory. �� Quanta belong to quantum theory. �� Group velocity equals particle velocity.
Correct matching: List I — List II 1. Continuous energy distribution — b. Wave theory 2. Discrete energy units — a. Quantum hypothesis 3. Group velocity of matter wave — d. Velocity of the particle 4. Instantaneous emission — c. Single photon absorption → Therefore Option A is correct.
- �� Options B, C and D contain incorrect pairings between wave and quantum concepts.
Used
- �� Option Grouping
Application:
- �� Match each concept with its defining principle.
Final Logic:
- �� Only Option A provides all correct associations.
- Wave → Continuous, Quantum → Discrete
4 The power emitted by a source is 2.0 × 10⁻³ W with photon energy 3.98 × 10⁻¹⁹ J. What will be the total number of photons emitted per second?
�� Power = Energy per second. �� Number of photons = Power ÷ Photon energy. �� Direct substitution.
- Number of photons emitted per second: N = P/E = (2.0 × 10⁻³)/(3.98 × 10⁻¹⁹) ≈ 5.03 × 10¹⁵ s⁻¹ ≈ 5.0 × 10¹⁵ s⁻¹ → Therefore option C is correct.
- �� Option A → Wrong order of magnitude.
- �� Option B → Incorrect division.
- �� Option D → Excessively large value.
Used
- �� Substitution
Application:
- �� Apply N = P/E.
Final Logic:
- �� N ≈ 5.0 × 10¹⁵ photons/s.
- Photon Count = Power ÷ Photon Energy
5 Einstein's radical assumption fundamentally differed from classical physics because
�� Einstein introduced photons. �� Energy exchange is discrete. �� Conservation laws remain valid.
- Einstein proposed that radiation consists of discrete packets of energy called quanta or photons. → This was fundamentally different from the classical continuous-wave picture. → Therefore option B is correct.
- �� Option A → Classical, not Einsteinian, view.
- �� Option C → Einstein's theory obeys conservation laws.
- �� Option D → Photon energy depends on frequency.
Used
- �� Elimination
Application:
- �� Identify the key distinction between quantum and classical theories.
Final Logic:
- �� Einstein replaced continuity with discreteness.
- Einstein = Photons
6 In Einstein's photoelectric equation, if the maximum kinetic energy is set to zero, the expression for the threshold frequency ν₀ will be
�� At threshold, Kmax = 0. �� Photon energy equals work function. �� Use Einstein's equation.
- Einstein's equation: Kmax = hν − φ₀ At threshold: Kmax = 0 Therefore: hν₀ = φ₀ ν₀ = φ₀/h → Hence option A is correct.
- �� Option B → Reciprocal form.
- �� Option C → Incorrect dimensions.
- �� Option D → Not physically meaningful.
Used
- �� Substitution
Application:
- �� Set Kmax = 0 in Einstein's equation.
Final Logic:
- �� ν₀ = φ₀/h.
- Threshold = φ/h
7 The photoelectric equation shows that an increase in incident frequency leads to a _______ in maximum kinetic energy, while an increase in intensity leads to _______ in maximum kinetic energy.
�� Kmax depends on frequency. �� Kmax is independent of intensity. �� Einstein's equation gives a linear relation.
- From: Kmax = hν − φ₀ → Increasing frequency increases Kmax linearly. → Intensity changes the number of emitted electrons, not their maximum kinetic energy. → Therefore option A is correct.
- �� Option B → Opposite frequency dependence.
- �� Option C → Incorrect for both quantities.
- �� Option D → Intensity does not affect Kmax.
Used
- �� Elimination
Application:
- �� Separate frequency effects from intensity effects.
Final Logic:
- �� Frequency affects energy; intensity affects count.
- Frequency → Energy, Intensity → Number
8 In evaluating the stopping potential V₀ corresponding to maximum kinetic energy,
�� Stopping potential measures Kmax. �� eV₀ equals maximum kinetic energy. �� Frequency increases V₀.
- At stopping potential: eV₀ = Kmax → Thus the product of electronic charge and stopping potential gives the maximum kinetic energy. → Therefore option B is correct.
- �� Option A → V₀ increases with frequency.
- �� Option C → V₀ is independent of intensity.
- �� Option D → V₀ is a retarding, not accelerating, potential.
Used
- �� Substitution
Application:
- �� Use the stopping potential relation directly.
Final Logic:
- �� Kmax = eV₀.
- Stop Voltage = Electron Energy
9 Correct statements about single quantum absorption
1. Low intensity does not imply a delay in emission.
2. A single electron absorbs only a single quantum of radiation.
3. The basic elementary process depends directly on the total intensity.
4. High intensity ensures multiple quanta are absorbed by one electron.
�� Emission is instantaneous. �� One photon interacts with one electron. �� Intensity affects photon number only.
- Statement 1 is correct because photoelectric emission occurs almost instantaneously even at low intensity. → Statement 2 is correct because the elementary process involves absorption of a single photon by a single electron. → Statements 3 and 4 are incorrect.
- �� Statement 3 → Intensity affects emission rate, not the elementary process.
- �� Statement 4 → High intensity does not guarantee multi-photon absorption.
Used
- �� Elimination
Application:
- �� Retain only statements consistent with Einstein's photon model.
Final Logic:
- �� Statements 1 and 2 are correct.
- One Photon → One Electron
10 Match List I with List II for electron emission energies
| List I | List II |
|---|---|
| 1. Maximum kinetic energy | a. Energy absorbed < φ₀ |
| 2. Lower kinetic energy | b. Least tightly bound electrons |
| 3. Zero kinetic energy | c. Tightly bound electrons |
| 4. Cannot escape | d. Incident frequency equals threshold |
�� Least bound electrons have Kmax. �� Tightly bound electrons emerge with less energy. �� Threshold frequency gives zero kinetic energy.
Correct matching: List I — List II 1. Maximum kinetic energy — b. Least tightly bound electrons 2. Lower kinetic energy — c. Tightly bound electrons 3. Zero kinetic energy — d. Incident frequency equals threshold 4. Cannot escape — a. Energy absorbed < φ₀ → Therefore Option D is correct.
- �� Options A, B and C contain incorrect energy interpretations.
Used
- �� Option Grouping
Application:
- �� Match each emission condition with the corresponding physical situation.
Final Logic:
- �� Only Option D provides all correct pairings.
- Threshold → Zero K.E.
11 If the threshold frequency for caesium is 5.16 × 10¹⁴ Hz, what will be its work function?
(h = 6.63 × 10⁻³⁴ J s, 1 eV = 1.6 × 10⁻¹⁹ J)
�� Work function: φ₀ = hν₀. �� Convert joules into eV. �� Direct substitution.
- Using: φ₀ = hν₀ = (6.63 × 10⁻³⁴)(5.16 × 10¹⁴) = 3.42 × 10⁻¹⁹ J Converting to eV: φ₀ = (3.42 × 10⁻¹⁹)/(1.6 × 10⁻¹⁹) = 2.14 eV → Therefore option A is correct.
- �� Option B → Value in joules incorrectly treated as eV.
- �� Option C → Calculation error.
- �� Option D → Incorrect conversion.
Used
- �� Substitution
Application:
- �� Apply φ₀ = hν₀ and convert units.
Final Logic:
- �� φ₀ = 2.14 eV.
- Work Function = hν₀
12 Minimum emission condition statements
1. Requires ν > ν₀.
2. Dictates that photoelectric emission cannot occur if hν < φ₀.
3. Shows that threshold frequency is exactly the same for all metals.
4. Ensures Kmax is positive for emission.
�� Frequency must exceed threshold. �� Photon energy must exceed work function. �� Different metals have different threshold frequencies.
- Statement 1 is correct because emission requires ν > ν₀. → Statement 2 is correct because if hν < φ₀, electrons cannot escape. → Statement 4 is correct because for ν > ν₀: Kmax = hν − φ₀ > 0 → Statement 3 is incorrect since threshold frequency depends on the metal.
- �� Statement 3 → Different metals possess different work functions and threshold frequencies.
Used
- �� Elimination
Application:
- �� Remove the statement contradicting material dependence.
Final Logic:
- �� Statements 1, 2 and 4 are correct.
- Above ν₀ → Positive K.E.
13 Incorrect statement about Millikan's slope measurements
�� Slope equals h/e. �� h and e are universal constants. �� Slope is independent of metal.
- Einstein's equation: V₀ = (h/e)ν − φ₀/e → The slope is h/e and therefore depends only on universal constants. → It is independent of the photosensitive material used. → Hence option B is correct.
- �� Option A → Correct experimental result.
- �� Option C → Correct method used by Millikan.
- �� Option D → Correct conclusion from the experiment.
Used
- �� Elimination
Application:
- �� Identify which statement contradicts Einstein's equation.
Final Logic:
- �� Slope depends on h/e, not on the metal.
- Slope = Universal Constant
14 The experimental verification of the photoelectric equation by Millikan
�� Millikan performed precise experiments. �� Wide frequency range was used. �� Results supported Einstein's equation.
- Millikan carried out highly accurate measurements using different frequencies and photosensitive metals. → The resulting V₀–ν graph verified Einstein's photoelectric equation and provided an accurate value of Planck's constant. → Therefore, option B is correct.
- �� Option A → He initially attempted to test and challenge Einstein's proposal.
- �� Option C → Measured h agreed closely with Planck's value.
- �� Option D → The experiment supported the particle nature of light.
Used
- �� Elimination
Application:
- �� Select the experimentally verified statement.
Final Logic:
- �� Millikan used precise measurements across frequencies.
- Millikan Measured, Einstein Verified
15 Let an electric field be E and the charge of a photon be q. Since photons are electrically neutral, their electrostatic force in the field will be
�� Photon charge is zero. �� Electric force = qE. �� Neutral particles experience no electrostatic force.
- Electrostatic force is: F = qE → For a photon: q = 0 Therefore: F = 0 × E = 0 → Hence option B is correct.
- �� Option A → Applies only to charged particles.
- �� Option B → Speed of light is unrelated to electrostatic force.
- �� Option C → Planck's constant is unrelated to electric force.
Used
- �� Substitution
Application:
- �� Substitute q = 0 into F = qE.
Final Logic:
- �� Neutral photons experience zero electrostatic force.
- Photon Charge = 0
16 For a fixed frequency, an increase in intensity results in a _______ in the number of photons per second, but _______ in the energy of each photon.
�� Intensity controls photon flux. �� Frequency controls photon energy. �� Photon energy remains constant.
- Photon energy is: E = hν → Since frequency is fixed, energy per photon remains unchanged. → Increasing intensity only increases the number of photons arriving per second. → Therefore option B is correct.
- �� Option A → Opposite trend.
- �� Option C → Photon energy does not increase.
- �� Option D → Photon number increases with intensity.
Used
- �� Elimination
Application:
- �� Distinguish intensity effects from frequency effects.
Final Logic:
- �� More photons, same photon energy.
- Intensity → Count, Frequency → Energy
17 Correct statements about the momentum of light
1. The momentum of a photon is given by p = h/λ.
2. All photons of a particular wavelength have the exact same momentum.
3. Photon momentum is directly proportional to intensity.
4. Momentum confirms a particle-like nature of light.
�� Photon momentum depends on wavelength. �� Same wavelength implies same momentum. �� Momentum supports particle behavior.
- Statement 1 is correct: p = h/λ → Statement 2 is correct because photons of identical wavelength possess identical momentum. → Statement 4 is correct because momentum transfer demonstrates particle nature. → Statement 3 is incorrect because photon momentum depends on wavelength, not intensity.
- �� Statement 3 → Intensity changes photon number, not momentum per photon.
Used
- �� Elimination
Application:
- �� Remove the statement confusing intensity with momentum.
Final Logic:
- �� Statements 1, 2 and 4 are correct.
- Momentum = h/λ
18 Match List I with List II regarding radiation interaction
| List I | List II |
|---|---|
| 1. Wavelength λ | a. Wave picture |
| 2. Group velocity of matter wave | b. Velocity of the particle |
| 3. Compton effect | c. Scattering of X-rays from electrons |
| 4. Eye-lens gathering light | d. Momentum p = h/λ |
�� λ relates to momentum. �� Group velocity equals particle velocity. �� Compton effect involves X-ray scattering.
Correct matching: List I — List II 1. Wavelength λ — d. Momentum p = h/λ 2. Group velocity of matter wave — b. Velocity of the particle 3. Compton effect — c. Scattering of X-rays from electrons 4. Eye-lens gathering light — a. Wave picture → Therefore, Option C is correct.
- �� Options A, B and D contain incorrect conceptual pairings.
Used
- �� Option Grouping
Application:
- �� Match each phenomenon with its defining concept.
Final Logic:
- �� Only Option A gives all correct matches.
- Compton → X-ray Scattering
19 In analyzing a photon-electron collision process, it is essential to note that
�� Energy is conserved. �� Momentum is conserved. �� Radiation also carries momentum.
- In photon-electron interactions such as Compton scattering, both total energy and total momentum remain conserved. → These conservation laws are fundamental to all isolated systems. → Therefore option B is correct.
- �� Option A → Photon number need not be conserved.
- �� Option C → Not a general rule.
- �� Option D → Radiation possesses momentum.
Used
- �� Elimination
Application:
- �� Apply universal conservation laws.
Final Logic:
- �� Both energy and momentum are conserved.
- Collision = Energy + Momentum Conserved
20 Non-conservation of photon number statements
1. A photon may be entirely absorbed by an electron.
2. The total number of photons before and after a collision may completely differ.
3. A new photon may be created during emission or collision.
4. Photons possess rest mass which must be rigorously conserved.
�� Photon number is not conserved. �� Photons may be absorbed or created. �� Photons have zero rest mass.
- Statement 1 is correct because photons can be completely absorbed in processes such as the photoelectric effect. → Statement 2 is correct because photon number may change during interactions. → Statement 3 is correct because photons can be emitted or created in physical processes. → Statement 4 is incorrect because photons possess zero rest mass.
- �� Statement 4 → Photons do not have rest mass.
Used
- �� Elimination
Application:
- �� Remove the statement contradicting photon properties.
Final Logic:
- �� Statements 1, 2 and 3 are correct.
- Photon Count Changes, Rest Mass Zero
