CUET UG Physics Booster Test 2- Nuclear Reactions and Radioactivity
📌 Answers are locked once submitted — results and explanations appear at the end.
QUESTION 1 OF 20
In the sequence of Becquerel's accident, the initial compound used and the radiation behaviour observed were respectively:
QUESTION 2 OF 20
Photographic blackening statements in Becquerel's experiment:
1. The package was separated from the plate by a piece of silver.
2. The compound had to be constantly illuminated by visible light during the plate's exposure.
3. The emission could penetrate black paper.
4. The observation proved radioactivity is a nuclear phenomenon.
QUESTION 3 OF 20
If hypothetical elements emit purely negatively charged particles representing a count of x and y electrons from two separate radioactive samples, the total charge emitted mathematically matches:
QUESTION 4 OF 20
Correct statements about beta decay:
1. Positrons are particles with the same mass as electrons.
2. Positrons possess a charge exactly opposite to that of an electron.
3. Beta decay involves the emission of a helium nucleus.
4. It occurs to help radioactive fragments achieve stable end products.
QUESTION 5 OF 20
Incorrect statement about gamma decay
QUESTION 6 OF 20
What is the energy of a 200 keV gamma photon expressed in Joules? (Given 1 eV = 1.6 × 10⁻¹⁹ J)
QUESTION 7 OF 20
In the nuclear reaction where Uranium-235 is bombarded with a neutron,
QUESTION 8 OF 20
The total gain in binding energy during the fission of a heavy nucleus (A = 240) into two fragments (A = 120)
QUESTION 9 OF 20
Match the aspects of intermediate mass fragments (List I) with their specific details (List II) from U-235 fission.
| List I | List II |
|---|---|
| 1. Disintegration energy | a. Increases to about 8.5 MeV |
| 2. Fragment stability | b. Ba-144 and Kr-89 |
| 3. Fragment elements (example) | c. Highly radioactive initially |
| 4. Binding energy per nucleon | d. Appears first as kinetic energy |
QUESTION 10 OF 20
In a hypothetical calculation tracking negative charges emitted by beta decay in successive fragment stabilizations, if x electrons and y electrons are emitted from two fragment chains respectively, what is the mathematical expression for their combined emitted charge?
QUESTION 11 OF 20
Incorrect statement about the joining of light nuclei
QUESTION 12 OF 20
Solar energy source statements:
1. The interior of the sun has a temperature of 1.5 × 10⁷ K.
2. The estimated temperature required for average energy particles to overcome the Coulomb barrier is 3 × 10⁹ K.
3. Fusion in the sun involves protons with energies much below the average energy.
4. The fuel is hydrogen in its core.
QUESTION 13 OF 20
The Coulomb barrier height
QUESTION 14 OF 20
Calculate the kinetic energy K required to overcome a Coulomb barrier if T = 3 × 10⁹ K. (Use (3/2)kT = K, k = 1.38 × 10⁻²³ J/K, 1 eV = 1.6 × 10⁻¹⁹ J)
QUESTION 15 OF 20
In the multi-step proton-proton cycle, the combination of e⁺ and e⁻ produces _____, while the combination of four hydrogen atoms ultimately releases _____ of energy.
QUESTION 16 OF 20
The depletion of hydrogen in the core and the subsequent start of helium burning respectively cause:
QUESTION 17 OF 20
Correct statements about plasma in controlled reactors:
1. Plasma is a mixture of positive ions and electrons.
2. It must be heated to temperatures in the range of 10⁸ K.
3. It must be confined using magnetic or alternative techniques because physical containers would melt.
4. It is used to generate steady power.
QUESTION 18 OF 20
Match the energy process (List I) with its location/application (List II)
| List I | List II |
|---|---|
| 1. Uncontrolled nuclear fission | a. Stars (e.g., Sun) |
| 2. Natural thermonuclear fusion | b. Nuclear reactors (current electricity) |
| 3. Controlled nuclear fission | c. Atom bomb |
| 4. Controlled thermonuclear fusion | d. Future unlimited power devices |
QUESTION 19 OF 20
Incorrect statement regarding energy scales
QUESTION 20 OF 20
When analyzing the output of 1 kg of uranium compared to 1 kg of coal,
Test Complete!
Answer Review
1 In the sequence of Becquerel's accident, the initial compound used and the radiation behaviour observed were respectively:
�� Becquerel studied uranium compounds. �� Radiation penetrated black paper. �� The discovery was accidental.
Becquerel used uranium-potassium sulphate while studying phosphorescent compounds. The emitted radiation penetrated opaque barriers such as black paper and exposed photographic plates. Therefore, option A is correct.
- �� Option B → Reflection from silver was not observed.
- �� Option C → Helium gas was not used in the experiment.
- �� Option D → Gold foil scattering relates to Rutherford's experiment.
Used
- Contextual/Tonal Matching
Application:
- Identify the correct historical experiment and observation.
Final Logic:
- Becquerel's uranium compound emitted penetrating radiation.
Uranium + Black Plate
2 Photographic blackening statements in Becquerel's experiment:
1. The package was separated from the plate by a piece of silver.
2. The compound had to be constantly illuminated by visible light during the plate's exposure.
3. The emission could penetrate black paper.
4. The observation proved radioactivity is a nuclear phenomenon.
�� Silver and black paper were present. �� Radiation penetrated the covering. �� The nuclear nature was not established by this experiment alone.
Statement 1 is correct because a silver piece separated the package from the plate. Statement 2 is incorrect because continuous illumination was not required. Statement 3 is correct because the emitted radiation penetrated black paper. Statement 4 is incorrect because Becquerel's observation alone did not establish radioactivity as a nuclear phenomenon. Therefore, statements 1 and 3 are correct.
- �� Option B → Includes statement 2, which is incorrect.
- �� Option C → Includes statements 2 and 4, both incorrect.
- �� Option D → Includes statement 4, which is incorrect.
Used
- Elimination
Application:
- Verify each statement using Becquerel's experimental observations.
Final Logic:
- Only statements 1 and 3 directly describe the experiment.
Silver + Black Paper
3 If hypothetical elements emit purely negatively charged particles representing a count of x and y electrons from two separate radioactive samples, the total charge emitted mathematically matches:
�� Each electron has charge -e. �� Total electrons = x + y. �� Charges add algebraically.
The total number of emitted electrons is (x + y). Since each electron carries a charge of -e, the combined charge is: -(x + y)e Therefore, option D is correct.
- �� Option A → Incorrect algebraic expression.
- �� Option B → Sign is incorrect.
- �� Option C → Incorrect total electron count.
Used
- Substitution
Application:
- Multiply total electrons by charge per electron.
Final Logic:
- Charge = Number of electrons × (-e).
Electron = Negative
4 Correct statements about beta decay:
1. Positrons are particles with the same mass as electrons.
2. Positrons possess a charge exactly opposite to that of an electron.
3. Beta decay involves the emission of a helium nucleus.
4. It occurs to help radioactive fragments achieve stable end products.
�� Positrons are anti-electrons. �� Mass is the same as electron mass. �� Beta decay promotes stability.
Statement 1 is correct because positrons have the same mass as electrons. Statement 2 is correct because positrons carry a positive charge. Statement 3 is incorrect because helium nuclei are emitted in alpha decay. Statement 4 is correct because beta decay helps unstable nuclei move toward stability. Therefore, statements 1, 2 and 4 are correct.
- �� Option B → Includes statement 3, which is incorrect.
- �� Option C → Includes statement 3, which is incorrect.
- �� Option D → Includes statement 3, which is incorrect.
Used
- Elimination
Application:
- Distinguish beta decay from alpha decay.
Final Logic:
- Beta decay emits electrons or positrons, not helium nuclei.
β = e⁻ or e⁺
5 Incorrect statement about gamma decay
�� Gamma rays are photons. �� Gamma emission changes energy state only. �� Atomic number remains unchanged.
Gamma decay emits electromagnetic radiation without changing the atomic number or mass number of the nucleus. A decrease of atomic number by 2 occurs in alpha decay, not gamma decay. Therefore, option C is correct.
- �� Option A → Correct description of gamma rays.
- �� Option B → Correct energy range.
- �� Option D → Gamma rays are electromagnetic radiation.
Used
- Odd One Out
Application:
- Identify the statement that incorrectly attributes alpha-decay properties to gamma decay.
Final Logic:
- Gamma emission does not alter atomic number.
γ = Energy Only
6 What is the energy of a 200 keV gamma photon expressed in Joules? (Given 1 eV = 1.6 × 10⁻¹⁹ J)
�� Convert keV into eV. �� Multiply by 1.6 × 10⁻¹⁹ J. �� Use unit conversion carefully.
200 keV = 200 × 10³ eV = 2 × 10⁵ eV Energy: = (2 × 10⁵)(1.6 × 10⁻¹⁹) = 3.2 × 10⁻¹⁴ J Therefore, option A is correct.
- �� Option B → Equivalent to only 2 eV.
- �� Option C → Five times larger than the correct value.
- �� Option D → Corresponds to 2 keV.
Used
- Dimensional/Unit Analysis
Application:
- Convert keV → eV → Joules.
Final Logic:
- 200 keV = 3.2 × 10⁻¹⁴ J.
200 × 1.6 = 320
7 In the nuclear reaction where Uranium-235 is bombarded with a neutron,
�� U-235 undergoes fission. �� Mass defect produces energy. �� Intermediate-mass fragments are formed.
After absorbing a neutron, U-235 forms U-236 and splits into two medium-mass fragments. The mass defect is converted into kinetic energy, radiation and heat. Therefore, option C is correct.
- �� Option A → Exact mass equality does not hold because of mass defect.
- �� Option B → Additional neutrons are emitted.
- �� Option D → Fragments generally have higher binding energy per nucleon.
Used
- Elimination
Application:
- Apply the basic mechanism of nuclear fission.
Final Logic:
- Mass defect → Energy release.
U-236 → Split + Energy
8 The total gain in binding energy during the fission of a heavy nucleus (A = 240) into two fragments (A = 120)
�� Gain per nucleon ≈ 0.9 MeV. �� Total nucleons = 240. �� Energy released ≈ 216 MeV.
Gain in binding energy per nucleon: = 8.5 − 7.6 = 0.9 MeV Total energy released: = 240 × 0.9 = 216 MeV Therefore, option B is correct.
- �� Option A → Uses total binding energy rather than gain.
- �� Option C → Fission is exothermic.
- �� Option D → Energy is nuclear, not chemical.
Used
- Substitution
Application:
- Multiply gain per nucleon by total nucleons.
Final Logic:
- 0.9 × 240 = 216 MeV.
0.9 × 240 = 216
9 Match the aspects of intermediate mass fragments (List I) with their specific details (List II) from U-235 fission.
| List I | List II |
|---|---|
| 1. Disintegration energy | a. Increases to about 8.5 MeV |
| 2. Fragment stability | b. Ba-144 and Kr-89 |
| 3. Fragment elements (example) | c. Highly radioactive initially |
| 4. Binding energy per nucleon | d. Appears first as kinetic energy |
�� Fission energy first appears as kinetic energy. �� Fragments are radioactive. �� Binding energy per nucleon increases.
1 → d : Disintegration energy initially appears as kinetic energy. 2 → c : Fission fragments are highly radioactive. 3 → b : Ba-144 and Kr-89 are example fragments. 4 → a : Binding energy per nucleon rises to about 8.5 MeV. Therefore, option A is correct.
- �� Option B → Disintegration energy and binding energy are interchanged.
- �� Option C → Multiple mismatches occur.
- �� Option D → Fragment stability and binding energy are incorrectly matched.
Used
- Option Grouping
Application:
- Match fragment properties with their corresponding descriptions.
Final Logic:
- Energy → Kinetic, Fragments → Radioactive, Examples → Ba/Kr, E/A → 8.5 MeV.
Energy → Motion First
10 In a hypothetical calculation tracking negative charges emitted by beta decay in successive fragment stabilizations, if x electrons and y electrons are emitted from two fragment chains respectively, what is the mathematical expression for their combined emitted charge?
�� Each electron carries charge -e. �� Charges add algebraically. �� Total electrons = x + y.
If x and y electrons are emitted, the total number of emitted electrons is (x + y). Since each electron has charge -e, the total emitted charge is: -(x + y)e Therefore, option A is correct.
- �� Option B → Sign is incorrect.
- �� Option C → Incorrect algebraic total.
- �� Option D → Incorrect expression.
Used
- Substitution
Application:
- Multiply total emitted electrons by charge per electron.
Final Logic:
- Charge = (x + y)(-e).
Electron = Minus
11 Incorrect statement about the joining of light nuclei
�� Fusion of light nuclei releases energy. �� Binding energy per nucleon increases. �� Fusion powers stars.
Fusion of light nuclei forms a more tightly bound nucleus with a higher binding energy per nucleon. The increase in binding energy corresponds to a release of energy, making fusion an exothermic process rather than an endothermic one. Therefore, option C is correct.
- �� Option A → Consistent with the light-nuclei region of the binding-energy curve.
- �� Option B → Correct reason for energy release in fusion.
- �� Option D → Fusion is the energy source of stars.
Used
- Odd One Out
Application:
- Identify the statement that contradicts the energy-releasing nature of fusion.
Final Logic:
- Fusion of light nuclei is exothermic, not endothermic.
Fusion = Join + Energy
12 Solar energy source statements:
1. The interior of the sun has a temperature of 1.5 × 10⁷ K.
2. The estimated temperature required for average energy particles to overcome the Coulomb barrier is 3 × 10⁹ K.
3. Fusion in the sun involves protons with energies much below the average energy.
4. The fuel is hydrogen in its core.
�� Solar core temperature is about 1.5 × 10⁷ K. �� Hydrogen is the primary fuel. �� Fusion occurs through quantum tunnelling.
Statement 1 is correct because the Sun's core temperature is approximately 1.5 × 10⁷ K. Statement 2 is correct as a classical estimate for overcoming the Coulomb barrier; however, it is not a statement describing the actual solar fusion process. Statement 3 is correct because solar fusion occurs at energies much lower than the classical barrier due to quantum tunnelling. Statement 4 is correct because hydrogen is the principal fuel in the solar core. Since the question concerns the solar energy source, the correct set is statements 1, 3 and 4. Therefore, the provided answer (A) is incorrect. The correct answer is B. (1), (3), (4).
- �� Option A → Includes statement 2 and omits statement 3.
- �� Option C → Omits statements 1 and 4.
- �� Option D → Includes statement 2, which does not describe the actual solar fusion mechanism.
Used
- Elimination
Application:
- Separate classical Coulomb-barrier estimates from the actual solar-fusion process.
Final Logic:
- Solar fusion occurs at 1.5 × 10⁷ K through tunnelling using hydrogen fuel.
Sun = H + Tunnelling
13 The Coulomb barrier height
�� Like charges repel. �� Fusion requires overcoming repulsion. �� This repulsion is the Coulomb barrier.
The Coulomb barrier arises from electrostatic repulsion between positively charged nuclei. For fusion to occur, nuclei must approach close enough for the strong nuclear force to dominate. Therefore, option B is correct.
- �� Option A → The barrier is due to Coulomb repulsion, not strong-force attraction.
- �� Option C → Neutrons are uncharged and do not face a Coulomb barrier.
- �� Option D → The barrier for proton-proton interactions is not approximately 1.02 MeV.
Used
- Contextual/Tonal Matching
Application:
- Associate the barrier with electrostatic repulsion.
Final Logic:
- Coulomb barrier = Repulsive electrostatic barrier.
Coulomb = Charge Repulsion
14 Calculate the kinetic energy K required to overcome a Coulomb barrier if T = 3 × 10⁹ K. (Use (3/2)kT = K, k = 1.38 × 10⁻²³ J/K, 1 eV = 1.6 × 10⁻¹⁹ J)
�� Use K = (3/2)kT. �� Convert joules into eV. �� Express result in keV.
K = (3/2)(1.38 × 10⁻²³)(3 × 10⁹) = 6.21 × 10⁻¹⁴ J Converting to eV: K = (6.21 × 10⁻¹⁴)/(1.6 × 10⁻¹⁹) ≈ 3.88 × 10⁵ eV ≈ 388 keV ≈ 400 keV Therefore, option A is correct.
- �� Option B → Much larger than calculated value.
- �� Option C → Approximately three times larger than the result.
- �� Option D → Far above the calculated energy.
Used
- Substitution
Application:
- Directly substitute values into K = (3/2)kT.
Final Logic:
- 3 × 10⁹ K corresponds to about 400 keV.
3 Billion K → 400 keV
15 In the multi-step proton-proton cycle, the combination of e⁺ and e⁻ produces _____, while the combination of four hydrogen atoms ultimately releases _____ of energy.
�� Positron-electron annihilation produces photons. �� Four protons ultimately form helium. �� Total energy released is about 26.7 MeV.
When a positron encounters an electron, annihilation occurs and gamma photons are emitted. The overall proton-proton chain converts four hydrogen nuclei into one helium nucleus, releasing approximately 26.7 MeV. Therefore, option B is correct.
- �� Option A → Electron-positron annihilation does not produce neutrons.
- �� Option C → Tritons are not the annihilation products.
- �� Option D → Alpha particles are formed later, not by e⁺e⁻ annihilation.
Used
- Memory-Based Recall
Application:
- Recall the proton-proton chain and annihilation process.
Final Logic:
- e⁺ + e⁻ → γ ; 4H → He + 26.7 MeV.
4H → He + 26.7 MeV
16 The depletion of hydrogen in the core and the subsequent start of helium burning respectively cause:
�� Hydrogen depletion contracts the core. �� Core temperature rises. �� Helium fusion forms carbon.
When hydrogen is exhausted, the core contracts under gravity. The increasing temperature eventually initiates helium burning, producing carbon nuclei. Therefore, option A is correct.
- �� Option B → Iron is not formed directly from helium burning.
- �� Option C → Helium undergoes fusion, not fission.
- �� Option D → Beta decay is not the dominant process.
Used
- Contextual/Tonal Matching
Application:
- Follow the sequence of stellar evolution.
Final Logic:
- Hydrogen exhaustion → Core contraction → Helium fusion → Carbon.
H Ends → Core Shrinks → C Forms
17 Correct statements about plasma in controlled reactors:
1. Plasma is a mixture of positive ions and electrons.
2. It must be heated to temperatures in the range of 10⁸ K.
3. It must be confined using magnetic or alternative techniques because physical containers would melt.
4. It is used to generate steady power.
�� Plasma contains ions and electrons. �� Fusion requires extremely high temperatures. �� Magnetic confinement is necessary.
Statement 1 is correct because plasma consists of free ions and electrons. Statement 2 is correct because temperatures around 10⁸ K are required. Statement 3 is correct because no physical container can withstand such temperatures. Statement 4 is correct because controlled fusion aims to provide continuous power generation. Therefore, all four statements are correct.
- �� Option B → Omits statement 2.
- �� Option C → Omits statements 1 and 4.
- �� Option D → Omits statement 3.
Used
- Elimination
Application:
- Verify each statement using fusion-reactor principles.
Final Logic:
- All four statements accurately describe fusion plasma.
Plasma = Ions + Electrons
18 Match the energy process (List I) with its location/application (List II)
| List I | List II |
|---|---|
| 1. Uncontrolled nuclear fission | a. Stars (e.g., Sun) |
| 2. Natural thermonuclear fusion | b. Nuclear reactors (current electricity) |
| 3. Controlled nuclear fission | c. Atom bomb |
| 4. Controlled thermonuclear fusion | d. Future unlimited power devices |
�� Atom bombs use uncontrolled fission. �� Stars use natural fusion. �� Reactors use controlled fission.
1 → c : Atom bombs involve uncontrolled fission. 2 → a : Stars are powered by natural fusion. 3 → b : Nuclear power plants use controlled fission. 4 → d : Controlled fusion is expected to provide future large-scale power. Therefore, option A is correct.
- �� Option B → Applications are mismatched.
- �� Option C → Fusion and fission locations are interchanged.
- �� Option D → Multiple incorrect pairings.
Used
- Option Grouping
Application:
- Associate each energy process with its real-world application.
Final Logic:
- Bomb → Fission, Sun → Fusion, Reactor → Controlled Fission.
Bomb-Sun-Reactor-Future
19 Incorrect statement regarding energy scales
�� Nuclear reactions release far more energy. �� Chemical energies are in eV. �� Nuclear energies are in MeV.
Nuclear reactions release approximately a million times more energy than chemical reactions for the same quantity of matter. Therefore, the statement claiming they produce a million times less energy is incorrect. Hence, option B is correct.
- �� Option A → Correct energy scale for chemistry.
- �� Option C → Correct energy scale for nuclear processes.
- �� Option D → Correct description of mass-energy conversion.
Used
- Extreme Word Filter
Application:
- Look for the statement reversing the known energy comparison.
Final Logic:
- Nuclear energy ≫ Chemical energy.
MeV > eV
20 When analyzing the output of 1 kg of uranium compared to 1 kg of coal,
�� Uranium releases about 10¹⁴ J/kg. �� Coal releases about 10⁷ J/kg. �� Nuclear mass defects are much larger.
The energy from uranium fission is approximately: 10¹⁴ J / 10⁷ J = 10⁷ times greater than that obtained from burning coal. This difference arises from nuclear mass defects, which are vastly larger than chemical mass defects. Therefore, option B is correct.
- �� Option A → Uranium energy originates from nuclear binding energy, not chemical energy.
- �� Option C → Coal releases about 10⁷ J, not 10¹⁴ J.
- �� Option D → Nuclear and chemical mass defects are vastly different.
Used
- Substitution
Application:
- Compare the given energy values directly.
Final Logic:
- 10¹⁴ ÷ 10⁷ = 10⁷.
Uranium = 10⁷ × Coal
