CUET UG Physics Booster Test 2- Nuclear Forces and Stability
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QUESTION 1 OF 20
Incorrect statement about the strong nuclear binding force,
QUESTION 2 OF 20
Electrostatic force behaviors inside the nucleus statements,
1. Repulsion exists strongly between positively charged protons.
2. It dominates over the strong nuclear force at all distances.
3. It falls rapidly to zero beyond a few femtometres.
4. It acts universally between charges, unlike the nuclear force.
QUESTION 3 OF 20
The distance at which the attractive and repulsive forces between two nucleons perfectly balance to yield minimum potential energy is
QUESTION 4 OF 20
If a pair of nucleons is forced to a separation distance of 0.5 fm, what is the nature of the force and the minimal distance r₀ for this system?
QUESTION 5 OF 20
Match List I with List II concerning force characteristics
| List I | List II |
|---|---|
| 1. Strong nuclear force range | a. Practically infinite |
| 2. Gravitational force range | b. A few femtometres |
| 3. Force behavior for distance > a few fm | c. Saturation of binding energy |
| 4. Consequence of short-ranged force | d. Rapid fall to zero |
QUESTION 6 OF 20
The nuclear force is effective exclusively at the __________ scale, while macroscopic interactions are generally driven by the __________ scale forces like gravity.
QUESTION 7 OF 20
Because the nuclear force is highly short-ranged, a nucleon in a sufficiently large nucleus
QUESTION 8 OF 20
Nucleons residing on the surface of a large nucleus
QUESTION 9 OF 20
Correct statements regarding specific nucleon interactions
1. The force between two protons is approximately the same as between two neutrons.
2. The force between a proton and a neutron is vastly different from p-p interactions.
3. Nuclear force heavily depends on the presence of the elementary charge e.
4. n-n interaction is governed entirely by Coulomb's law.
QUESTION 10 OF 20
Incorrect statement regarding the charge independence of the nuclear force
QUESTION 11 OF 20
Which of the following effectively describes the relative sequence of force strengths between two protons separated by 1 fm inside a nucleus?
QUESTION 12 OF 20
In order to maintain structural integrity and not instantly fly apart, an atomic nucleus requires that
QUESTION 13 OF 20
Mathematical modeling of nuclear forces statements
1. It strictly follows a simple inverse-square relationship.
2. It possesses no uniquely simple mathematical form.
3. It differs structurally from Newton's law of gravitation.
4. It can be perfectly modelled using purely Coulombic equations.
QUESTION 14 OF 20
Match List I with List II for the nuclear potential energy curve regions
| List I | List II |
|---|---|
| 1. Nucleon separation > 0.8 fm | a. Minimum potential energy reached |
| 2. Nucleon separation < 0.8 fm | b. Indicates a strongly repulsive force |
| 3. Nucleon separation = 0.8 fm | c. Indicates an attractive force |
| 4. Gradient of potential curve for r < r₀ | d. Strongly repulsive region |
QUESTION 15 OF 20
Regarding the required parameters for stability in light atomic nuclei
QUESTION 16 OF 20
As nuclei become progressively heavier, the necessary neutron to proton ratio required to overcome Coulomb repulsion and maintain stability shifts closer to:
QUESTION 17 OF 20
Correct statements indicating nuclear instability
1. Nuclei featuring an excess of neutrons relative to the stable ratio are generally unstable.
2. Nuclei holding an excess of protons relative to the stable ratio are generally unstable.
3. Deviating widely from the stability ratio inherently prevents any form of decay.
4. Unstable nuclei exist entirely independently of the neutron-proton ratio.
QUESTION 18 OF 20
Radioactivity serves as a fundamental sign of nuclear __________, fundamentally triggered when the nucleus possesses an __________ of distinct nucleons.
QUESTION 19 OF 20
Incorrect statement regarding stable nuclear species distribution
QUESTION 20 OF 20
Artificial production and observation of unstable isotopes statements
1. They are synthesized by bombarding stable targets with alpha particles or neutrons.
2. They constitute the vast majority of the known pool of isotopes.
3. They can be independently identified via astronomical observations.
4. They automatically shift to a 3:2 ratio immediately upon creation.
Test Complete!
Answer Review
1 Incorrect statement about the strong nuclear binding force,
�� Strong force acts inside the nucleus. �� Electrons are governed by electromagnetic force. �� Nuclear binding energy is of MeV scale.
The strong nuclear force acts between nucleons and binds protons and neutrons within the nucleus. Electron motion in atomic orbitals is governed by electromagnetic attraction between electrons and the nucleus, not by the strong force. Therefore, option C is correct.
- �� Option A → Correct because strong force binds nucleons.
- �� Option B → Correct because nuclear binding energies are typically a few MeV per nucleon.
- �� Option D → Correct because strong force must overcome Coulomb repulsion.
Used
- Odd One Out
Application:
- Identify the statement describing atomic rather than nuclear behavior.
Final Logic:
- Electron motion is governed by electromagnetic force, not strong force.
Electrons → EM Force
2 Electrostatic force behaviors inside the nucleus statements,
1. Repulsion exists strongly between positively charged protons.
2. It dominates over the strong nuclear force at all distances.
3. It falls rapidly to zero beyond a few femtometres.
4. It acts universally between charges, unlike the nuclear force.
�� Coulomb force acts between charges. �� Proton-proton repulsion exists. �� Coulomb force is long-ranged.
Statement 1 is correct because positively charged protons repel each other. Statement 2 is incorrect because strong nuclear force dominates at nuclear distances. Statement 3 is incorrect because Coulomb force does not fall rapidly to zero; it is long-ranged. Statement 4 is correct because Coulomb interaction acts universally between electric charges. Therefore, statements 1 and 4 are correct.
- �� Option B → Includes statements 2 and 3, both incorrect.
- �� Option C → Includes statement 2, which is incorrect.
- �� Option D → Includes statement 3, which is incorrect.
Used
- Elimination
Application:
- Compare long-range Coulomb force with short-range nuclear force.
Final Logic:
- Only statements 1 and 4 are valid.
Coulomb = Charge Everywhere
3 The distance at which the attractive and repulsive forces between two nucleons perfectly balance to yield minimum potential energy is
�� Potential energy minimum corresponds to stable separation. �� Attractive and repulsive forces balance. �� Occurs near 0.8 fm.
At approximately 0.8 fm, the attractive nuclear force and short-range repulsive force balance each other. This corresponds to the minimum of the nucleon potential-energy curve and the most stable separation. Therefore, option A is correct.
- �� Option B → Larger than the equilibrium separation.
- �� Option C → Outside the region of strongest nuclear attraction.
- �� Option D → Far beyond nuclear-force range.
Used
- Memory-Based Recall
Application:
- Recall the standard nucleon potential-energy graph.
Final Logic:
- Minimum potential energy occurs near 0.8 fm.
r₀ = 0.8 fm
4 If a pair of nucleons is forced to a separation distance of 0.5 fm, what is the nature of the force and the minimal distance r₀ for this system?
�� 0.5 fm lies inside the repulsive core. �� Equilibrium distance is 0.8 fm. �� Strong repulsion prevents collapse.
At separations below about 0.8 fm, nucleons experience a strong repulsive force. The equilibrium separation corresponding to minimum potential energy remains approximately 0.8 fm. Therefore, option D is correct.
- �� Option A → Both force nature and distance are incorrect.
- �� Option B → Force is not attractive at 0.5 fm.
- �� Option C → Equilibrium distance is not 1.2 fm.
Used
- Contextual/Tonal Matching
Application:
- Use the nucleon force-versus-distance graph.
Final Logic:
- 0.5 fm → Repulsive region; r₀ → 0.8 fm.
Below 0.8 → Push
5 Match List I with List II concerning force characteristics
| List I | List II |
|---|---|
| 1. Strong nuclear force range | a. Practically infinite |
| 2. Gravitational force range | b. A few femtometres |
| 3. Force behavior for distance > a few fm | c. Saturation of binding energy |
| 4. Consequence of short-ranged force | d. Rapid fall to zero |
�� Nuclear force is short-ranged. �� Gravity is infinite-ranged. �� Saturation arises from limited interaction range.
1 → b : Strong nuclear force acts over a few femtometres. 2 → a : Gravitational force has effectively infinite range. 3 → d : Nuclear force rapidly falls to zero beyond a few femtometres. 4 → c : Short-range interaction leads to saturation of binding energy. Thus, option A is correct.
- �� Option B → Nuclear and gravitational ranges are interchanged.
- �� Option C → Multiple incorrect matches.
- �� Option D → Force behavior beyond a few fm is incorrectly matched.
Used
- Option Grouping
Application:
- Match each force property with its defining characteristic.
Final Logic:
- Short range → few fm → rapid fall → saturation.
Few fm → Saturation
6 The nuclear force is effective exclusively at the __________ scale, while macroscopic interactions are generally driven by the __________ scale forces like gravity.
�� Nuclear force acts over femtometres. �� Gravity has infinite range. �� Nuclear effects are microscopic.
The strong nuclear force is effective over distances of a few femtometres. Gravity, which governs many macroscopic phenomena, has an effectively infinite range. Therefore, option B is correct.
- �� Option A → Scales are incorrect.
- �� Option C → Does not represent nuclear-force range.
- �� Option D → Not specific physical scales.
Used
- Dimensional/Unit Analysis
Application:
- Compare nuclear and gravitational interaction ranges.
Final Logic:
- Nuclear → fm, Gravity → infinite range.
Strong = fm, Gravity = Infinite
7 Because the nuclear force is highly short-ranged, a nucleon in a sufficiently large nucleus
�� Nuclear force is short-ranged. �� Only nearby nucleons interact strongly. �� Leads to saturation.
A nucleon interacts significantly only with neighbouring nucleons lying within the short range of the nuclear force. Distant nucleons contribute negligibly. Therefore, option A is correct.
- �� Option B → Binding energy is not shared equally among all nucleons.
- �� Option C → Distant nucleons exert negligible influence.
- �� Option D → Binding energy does not vary as A².
Used
- Elimination
Application:
- Apply the saturation property of nuclear force.
Final Logic:
- Short range restricts interactions to nearby nucleons.
Near Neighbours Matter
8 Nucleons residing on the surface of a large nucleus
�� Surface nucleons have fewer neighbours. �� Interior nucleons are more strongly bound. �� Surface effect lowers average binding energy.
A surface nucleon lacks neighbouring nucleons on one side of the nucleus. Consequently, it interacts with fewer nucleons than an interior nucleon. Therefore, option B is correct.
- �� Option A → Maximum neighbours occur for interior nucleons.
- �� Option C → Binding energy changes gradually.
- �� Option D → Surface nucleons do not dominate mass.
Used
- Elimination
Application:
- Compare interior and surface nucleons.
Final Logic:
- Surface nucleons have fewer neighbouring interactions.
Surface = Fewer Friends
9 Correct statements regarding specific nucleon interactions
1. The force between two protons is approximately the same as between two neutrons.
2. The force between a proton and a neutron is vastly different from p-p interactions.
3. Nuclear force heavily depends on the presence of the elementary charge e.
4. n-n interaction is governed entirely by Coulomb's law.
�� Nuclear force is charge independent. �� p-p and n-n interactions are similar. �� Coulomb law does not govern n-n interaction.
Statement 1 is correct because nuclear force between p-p and n-n pairs is approximately equal. Statement 2 is incorrect because p-n interactions are not vastly different. Statement 3 is incorrect because nuclear force is nearly independent of charge. Statement 4 is incorrect because neutrons have no electric charge and interact through nuclear force. Therefore, only statement 1 is correct.
- �� Option B → Includes statement 2, which is incorrect.
- �� Option C → Statements 2 and 3 are incorrect.
- �� Option D → Includes statement 4, which is incorrect.
Used
- Elimination
Application:
- Use the principle of charge independence.
Final Logic:
- Only statement 1 remains valid.
p-p ≈ n-n
10 Incorrect statement regarding the charge independence of the nuclear force
�� Nuclear force is independent of charge. �� p-p and n-n forces are nearly equal. �� p-n attraction is not due to charge difference.
The nuclear force arises from the strong interaction and is largely independent of electric charge. The attraction between a proton and a neutron is not caused by their differing charges. Hence, option C is the incorrect statement.
- �� Option A → Correct evidence for charge independence.
- �� Option B → Correct description of nuclear force.
- �� Option D → Correct experimental observation.
Used
- Odd One Out
Application:
- Identify the statement that incorrectly attributes nuclear force to charge.
Final Logic:
- Strong interaction, not charge difference, produces nuclear attraction.
Strong ≠ Charge
11 Which of the following effectively describes the relative sequence of force strengths between two protons separated by 1 fm inside a nucleus?
�� Strong nuclear force dominates at nuclear distances. �� Coulomb force is weaker than the strong force. �� Gravity is negligible.
At a separation of about 1 fm, the strong nuclear force is the dominant interaction between nucleons. Coulomb repulsion between protons is significant but weaker. Gravitational attraction is extremely small compared with both. Therefore, the correct order is: Nuclear Force > Coulomb Force > Gravitational Force
- �� Option B → Coulomb force is not stronger than the strong force at nuclear distances.
- �� Option C → Gravity is the weakest interaction, not the strongest.
- �� Option D → Coulomb force is much stronger than gravity.
Used
- Option Grouping
Application:
- Compare the relative magnitudes of the three forces.
Final Logic:
- Strong > Coulomb > Gravity.
Strong Wins, Gravity Loses
12 In order to maintain structural integrity and not instantly fly apart, an atomic nucleus requires that
�� Protons repel each other. �� Strong force binds nucleons. �� Stable nuclei require strong-force dominance.
The positively charged protons inside a nucleus repel each other through Coulomb force. Stability is achieved only because the attractive strong nuclear force is stronger than the repulsive Coulomb force over nuclear distances. Therefore, option B is correct.
- �� Option A → Electrons do not neutralize proton repulsion inside the nucleus.
- �� Option C → Gravity is far too weak.
- �� Option D → Protons do not lose charge periodically.
Used
- Elimination
Application:
- Identify the force responsible for nuclear stability.
Final Logic:
- Strong force must exceed Coulomb repulsion.
Strong Holds, Coulomb Pushes
13 Mathematical modeling of nuclear forces statements
1. It strictly follows a simple inverse-square relationship.
2. It possesses no uniquely simple mathematical form.
3. It differs structurally from Newton's law of gravitation.
4. It can be perfectly modelled using purely Coulombic equations.
�� Nuclear force is complex. �� No simple universal equation exists. �� It differs from gravitational and Coulomb forces.
Statement 1 is incorrect because nuclear force does not follow an inverse-square law. Statement 2 is correct because no uniquely simple mathematical expression describes nuclear force. Statement 3 is correct because its behavior differs significantly from Newtonian gravitation. Statement 4 is incorrect because Coulomb equations cannot fully model nuclear interactions. Therefore, statements 2 and 3 are correct.
- �� Option A → Includes statement 4, which is incorrect.
- �� Option B → Statements 1 and 4 are incorrect.
- �� Option C → Includes statement 1, which is incorrect.
Used
- Elimination
Application:
- Compare nuclear-force behavior with known force laws.
Final Logic:
- Only statements 2 and 3 correctly describe nuclear-force modeling.
Strong Force ≠ Inverse Square
14 Match List I with List II for the nuclear potential energy curve regions
| List I | List II |
|---|---|
| 1. Nucleon separation > 0.8 fm | a. Minimum potential energy reached |
| 2. Nucleon separation < 0.8 fm | b. Indicates a strongly repulsive force |
| 3. Nucleon separation = 0.8 fm | c. Indicates an attractive force |
| 4. Gradient of potential curve for r < r₀ | d. Strongly repulsive region |
�� r > 0.8 fm gives attraction. �� r < 0.8 fm gives repulsion. �� r = 0.8 fm corresponds to minimum potential energy.
1 → c : Beyond 0.8 fm, the nuclear force is attractive. 2 → d : Below 0.8 fm lies the strongly repulsive region. 3 → a : At 0.8 fm, potential energy is minimum. 4 → b : The gradient for r < r₀ corresponds to a strongly repulsive force. Therefore, option A is correct.
- �� Option B → Attraction and repulsion regions are reversed.
- �� Option C → Minimum-energy position is incorrectly matched.
- �� Option D → Multiple curve features are mismatched.
Used
- Option Grouping
Application:
- Associate each distance region with the corresponding potential-energy behavior.
Final Logic:
- Above r₀ → attraction, below r₀ → repulsion, at r₀ → minimum energy.
Above r₀ Pull, Below r₀ Push
15 Regarding the required parameters for stability in light atomic nuclei
�� Light nuclei are stable near N = Z. �� Neutrons reduce proton repulsion. �� N/Z ≈ 1 is preferred.
For light nuclei, maximum stability is achieved when the neutron-to-proton ratio is approximately 1:1. This provides sufficient nuclear attraction while maintaining balance within the nucleus. Therefore, option C is correct.
- �� Option A → More suitable for heavier nuclei.
- �� Option B → Neutrons are essential for stability.
- �� Option D → Excess protons increase instability.
Used
- Memory-Based Recall
Application:
- Recall the stability condition for light nuclei.
Final Logic:
- Light nuclei require N ≈ Z.
Light → 1:1
16 As nuclei become progressively heavier, the necessary neutron to proton ratio required to overcome Coulomb repulsion and maintain stability shifts closer to:
�� Heavy nuclei contain many protons. �� Extra neutrons improve stability. �� N/Z ratio increases with mass number.
As the number of protons increases, Coulomb repulsion becomes stronger. Additional neutrons provide extra nuclear attraction without adding electrical repulsion. Thus the stability ratio shifts toward approximately 3:2. Therefore, option C is correct.
- �� Option A → Appropriate mainly for light nuclei.
- �� Option B → Too large for most stable heavy nuclei.
- �� Option D → Smaller than the typical heavy-nucleus value.
Used
- Memory-Based Recall
Application:
- Recall the trend of the stability curve.
Final Logic:
- Heavy nuclei require more neutrons than protons.
Heavy → 3:2
17 Correct statements indicating nuclear instability
1. Nuclei featuring an excess of neutrons relative to the stable ratio are generally unstable.
2. Nuclei holding an excess of protons relative to the stable ratio are generally unstable.
3. Deviating widely from the stability ratio inherently prevents any form of decay.
4. Unstable nuclei exist entirely independently of the neutron-proton ratio.
�� Stability depends strongly on N/Z ratio. �� Excess neutrons can cause instability. �� Excess protons can also cause instability.
Statement 1 is correct because neutron-rich nuclei often undergo beta decay. Statement 2 is correct because proton-rich nuclei are generally unstable. Statement 3 is incorrect because deviation from stability promotes decay rather than preventing it. Statement 4 is incorrect because neutron-proton ratio is a major factor governing stability. Therefore, statements 1 and 2 are correct.
- �� Option B → Both statements are incorrect.
- �� Option C → Includes statement 3, which is incorrect.
- �� Option D → Includes statement 4, which is incorrect.
Used
- Elimination
Application:
- Check each statement using the stability-band concept.
Final Logic:
- Both neutron excess and proton excess can cause instability.
Too Many N or P → Decay
18 Radioactivity serves as a fundamental sign of nuclear __________, fundamentally triggered when the nucleus possesses an __________ of distinct nucleons.
�� Radioactivity indicates instability. �� Nucleon imbalance causes decay. �� Unstable nuclei emit radiation.
Radioactivity is a direct indication of nuclear instability. Nuclei possessing an excess of neutrons or protons relative to the stable ratio tend to undergo radioactive decay. Therefore, option B is correct.
- �� Option A → Stability does not produce radioactivity.
- �� Option C → Expansion and absence are unrelated.
- �� Option D → Radioactivity is not equivalent to fusion.
Used
- Contextual/Tonal Matching
Application:
- Associate radioactivity with unstable nuclei.
Final Logic:
- Instability caused by nucleon excess leads to decay.
Radioactivity = Instability
19 Incorrect statement regarding stable nuclear species distribution
�� Most isotopes are radioactive. �� Stable isotopes are relatively few. �� Stability depends on N/Z ratio.
Only a small fraction of known isotopes are stable. Approximately 10% are stable, while the majority are radioactive. Therefore the claim that nearly 90% are stable is incorrect. Hence, option A is correct.
- �� Option B → Correct statement regarding stable isotope abundance.
- �� Option C → Correct description of nuclear stability.
- �� Option D → Correct because most isotopes are unstable.
Used
- Odd One Out
Application:
- Identify the statement that contradicts known isotope statistics.
Final Logic:
- Stable isotopes are the minority, not the majority.
Stable ≈ 10%
20 Artificial production and observation of unstable isotopes statements
1. They are synthesized by bombarding stable targets with alpha particles or neutrons.
2. They constitute the vast majority of the known pool of isotopes.
3. They can be independently identified via astronomical observations.
4. They automatically shift to a 3:2 ratio immediately upon creation.
�� Radioisotopes can be artificially produced. �� Most known isotopes are unstable. �� Unstable isotopes can be detected astronomically.
Statement 1 is correct because unstable isotopes are commonly synthesized by bombardment reactions. Statement 2 is correct because radioactive isotopes form the majority of known isotopes. Statement 3 is correct because isotopes can be identified through astronomical observations and spectroscopic analysis. Statement 4 is incorrect because nuclei do not instantly adjust to a 3:2 ratio upon formation. Therefore, statements 1, 2 and 3 are correct.
- �� Option A → Includes statement 4, which is incorrect.
- �� Option C → Includes statement 4, which is incorrect.
- �� Option D → Omits statements 2 and 3 and includes statement 4.
Used
- Elimination
Application:
- Verify each statement using radioisotope production and detection facts.
Final Logic:
- Only statements 1, 2 and 3 are correct.
Bombard → Radioisotope
