A stable nucleus (light with A < 10) has

1. Atomic Structure: The Composition of the Nucleus (basic)

At the heart of every atom lies a incredibly tiny, dense, and positively charged core known as the atomic nucleus. While the entire atom determines how elements interact chemically, the nucleus is where the mass and the identity of the element are stored. As defined in Environment and Ecology by Majid Hussain, Major Crops and Cropping Patterns in India, p.100, the nucleus is the central portion of the atom containing protons and neutrons (collectively called nucleons).

The composition of a nucleus is a delicate balancing act. Protons carry a positive charge and, naturally, they try to repel each other due to the Coulomb force (electrostatic repulsion). To keep the nucleus from flying apart, neutrons act as a sort of "nuclear glue." They provide an attractive Strong Nuclear Force that binds the nucleons together without adding further electrical repulsion. For light nuclei—specifically those with an atomic number (Z) less than 20—stability is generally reached when the number of neutrons (N) is roughly equal to the number of protons (Z). This means the N/Z ratio is approximately 1.

Particle	Charge	Role in Nucleus
Proton	Positive (+1)	Determines the element's identity (Atomic Number).
Neutron	Neutral (0)	Provides stability by adding attractive nuclear force.

Common stable light isotopes like Helium-4 (2 protons, 2 neutrons), Carbon-12 (6 protons, 6 neutrons), and Oxygen-16 (8 protons, 8 neutrons) all follow this 1:1 ratio. If this balance is significantly disturbed—for instance, if there are too many or too few neutrons—the nucleus becomes unstable or radioactive, seeking a more stable configuration through decay. Interestingly, in extreme cosmic conditions like a supernova, protons and electrons can be forced to combine, resulting in neutron stars, which are composed almost entirely of neutrons and are incredibly dense Physical Geography by PMF IAS, The Universe, The Big Bang Theory, Galaxies & Stellar Evolution, p.14.

Sources: Environment and Ecology by Majid Hussain, Major Crops and Cropping Patterns in India, p.100; Physical Geography by PMF IAS, The Universe, The Big Bang Theory, Galaxies & Stellar Evolution, p.14; Science, Class VIII NCERT, Particulate Nature of Matter, p.115

2. Atomic Number (Z) and Mass Number (A) (basic)

To understand the heart of an atom, we must look at its nucleus — the small, positively charged central core containing protons and neutrons Environment and Ecology, Major Crops and Cropping Patterns in India, p.100. Two fundamental numbers define every atom: the Atomic Number (Z) and the Mass Number (A). The Atomic Number (Z) represents the number of protons in the nucleus. This is the atom's unique identity; for instance, any atom with 6 protons is Carbon, no matter what Science, Carbon and its Compounds, p.66. The Mass Number (A), on the other hand, is the sum of protons and neutrons. Since electrons have negligible mass, nearly all of an atom's weight is concentrated in these two particles, often referred to collectively as nucleons.

The relationship is expressed by the simple formula: A = Z + N (where N is the number of neutrons). While Z determines the chemical identity, the balance between protons and neutrons determines nuclear stability. For "light nuclei" — those with an atomic number (Z) less than 20 — nature prefers a perfect balance. In these elements, the number of neutrons is usually equal to the number of protons, meaning the N/Z ratio is 1. This symmetry allows the strong nuclear force to effectively glue the nucleus together, overcoming the electromagnetic repulsion that makes positive protons want to fly apart.

Feature	Atomic Number (Z)	Mass Number (A)
Definition	Number of Protons	Protons + Neutrons
Role	Determines Chemical Identity	Determines Nuclear Mass/Stability
Example (Carbon)	Z = 6	A = 12 (typically)

As atoms grow heavier (Z > 20), this 1:1 ratio begins to fail. Because protons are all positively charged, they repel each other with increasing intensity as their numbers grow. To keep a heavy nucleus from shattering, "extra" neutrons are required to act as additional nuclear glue. However, for the light elements we encounter most in basic chemistry — like Helium (2p, 2n), Carbon (6p, 6n), and Oxygen (8p, 8n) — the rule of thumb remains: N ≈ Z.

Sources: Environment and Ecology, Major Crops and Cropping Patterns in India, p.100; Science, Carbon and its Compounds, p.66

3. The Strong Nuclear Force vs. Coulomb Repulsion (intermediate)

To understand why an atom's nucleus stays together, we must look at a fascinating 'tug-of-war' between two fundamental forces. On one side, we have Coulomb Repulsion (the electrostatic force). Because protons are all positively charged, they naturally exert a repulsive force on one another. We see the power of these electrostatic forces in chemistry, where they hold ions like sodium and chloride together in a lattice Science, class X (NCERT 2025 ed.), Metals and Non-metals, p.47. However, inside the nucleus, this force tries to push the protons apart, threatening to blow the atom into pieces. To counter this, Nature employs the Strong Nuclear Force. This is an incredibly powerful attractive force that acts between all nucleons—protons and neutrons alike. Its defining characteristic is that it is short-range. While it is much stronger than the Coulomb force at very close distances, its strength drops to zero once particles move slightly apart. This is a common theme in physics; even in basic matter, interparticle attractions decrease drastically with just a slight increase in distance Science, Class VIII, NCERT(Revised ed 2025), Particulate Nature of Matter, p.101. In light nuclei (where the atomic number Z is less than 20), stability is usually reached when the number of neutrons (N) and protons (Z) are equal (an N/Z ratio of 1). Because the nucleus is small, every nucleon is close to its neighbors, allowing the strong force to easily dominate the repulsion. However, as the nucleus grows larger, the long-range Coulomb repulsion from all the protons combined starts to challenge the short-range strong force. To stay stable, heavier atoms must pack in extra neutrons. These neutrons act as 'nuclear glue,' adding more strong-force attraction without adding any additional repulsive electric charge.

Feature	Strong Nuclear Force	Coulomb Repulsion
Nature	Purely attractive (in the nucleus)	Repulsive (between protons)
Range	Very short (only adjacent nucleons)	Long-range (acts across the whole nucleus)
Actants	Protons and Neutrons	Only Protons

Sources: Science, class X (NCERT 2025 ed.), Metals and Non-metals, p.47; Science, Class VIII, NCERT(Revised ed 2025), Particulate Nature of Matter, p.101

4. Isotopes and Their Role in Nature (intermediate)

To understand isotopes, we must first look at the identity of an atom. Every atom of an element has a fixed number of protons, known as the atomic number (Z). However, the number of neutrons in the nucleus can vary. Isotopes are atoms of the same element that possess the same number of protons but a different number of neutrons (N). This means they share the same chemical personality—for instance, all isotopes of carbon have a valency of four and exhibit the same ability to form strong covalent bonds and long chains, a property called catenation (Science, Class X (NCERT 2025 ed.), Carbon and its Compounds, p.62). While their chemistry is identical, their nuclear stability is vastly different.

Nuclear stability is determined by the delicate balance between two opposing forces: the strong nuclear force (which acts like 'glue' between nucleons) and the electrostatic repulsion (the 'push' between positively charged protons). For light nuclei (elements with Z < 20), stability is usually achieved when the number of protons and neutrons is roughly equal, giving an N/Z ratio of approximately 1. Examples include Helium-4 (2p, 2n), Carbon-12 (6p, 6n), and Oxygen-16 (8p, 8n). In these light atoms, the strong nuclear force easily overcomes the relatively weak repulsion between the few protons present.

As we move to heavier elements, the story changes. Because electrostatic repulsion grows more rapidly than the nuclear force as more protons are added, heavier nuclei require a higher proportion of neutrons to act as a buffer and provide additional binding energy. This shifts the stability belt, where stable isotopes of heavy elements might have an N/Z ratio closer to 1.5. If an isotope falls outside this stable ratio—having either too many or too few neutrons—it becomes unstable and undergoes radioactive decay. Understanding these isotopes is critical for practical applications, such as in nuclear power plants like the one at Tarapur, which harness the energy released from nuclear transitions (Environment and Ecology, Majid Hussain, Distribution of World Natural Resources, p.24).

Sources: Science, Class X (NCERT 2025 ed.), Carbon and its Compounds, p.62; Environment and Ecology, Majid Hussain, Distribution of World Natural Resources, p.24

5. Radioactivity and the Decay Process (intermediate)

At the heart of nuclear physics lies a delicate balancing act. A nucleus is held together by the strong nuclear force, which must overcome the Coulomb repulsion (the natural tendency of positively charged protons to push each other away). For lighter elements, specifically those with an atomic number (Z) less than 20, stability is typically achieved when the number of neutrons (N) and protons (Z) are roughly equal, creating an N/Z ratio of 1. As we move to heavier elements, the electrostatic repulsion between protons grows significantly; to keep the nucleus from flying apart, more neutrons are required to provide additional 'nuclear glue' without adding extra charge. This is why heavier stable nuclei have an N/Z ratio closer to 1.5. When this balance is not met, the nucleus becomes unstable and undergoes radioactivity. This is defined as the spontaneous emission of particles or energy as an unstable atomic nucleus disintegrates to reach a more stable state Environment, Shankar IAS Academy (10th ed.), Environmental Pollution, p.82. This process typically releases three types of radiation:

• Alpha (α) particles: Essentially helium nuclei (two protons and two neutrons).
• Beta (β) particles: High-speed electrons (or positrons).
• Gamma (γ) rays: High-energy, short-wave electromagnetic radiation Environment, Shankar IAS Academy (10th ed.), Environmental Pollution, p.82.

The rate at which these substances decay is measured by their half-life—the time it takes for exactly half of the radioactive atoms in a sample to transform into a different state Environment, Shankar IAS Academy (10th ed.), Environmental Pollution, p.83. This decay is not just a laboratory curiosity; it is a massive energy source for our planet. In fact, the disintegration of radioactive substances like Uranium and Thorium in the Earth's crust and mantle provides more than half of the Earth's total internal heat Physical Geography by PMF IAS, Earth's Interior, p.58.

Sources: Environment, Shankar IAS Academy (10th ed.), Environmental Pollution, p.82-83; Physical Geography by PMF IAS, Earth's Interior, p.58

6. The N/Z Ratio and the Stability Belt (exam-level)

To understand nuclear stability, we must look at the nucleus as a delicate balancing act between two opposing forces. On one hand, we have the Electrostatic (Coulomb) Force, which causes positively charged protons to repel each other. On the other hand, we have the Strong Nuclear Force, a powerful but short-range attraction that acts between all nucleons (protons and neutrons) to hold them together. Environment and Ecology, Major Crops and Cropping Patterns in India, p.100 defines this nucleus as the small, positive central portion of the atom.

The N/Z ratio (the number of Neutrons divided by the number of Protons) is the primary indicator of whether a nucleus will be stable or radioactive. For light nuclei (where the atomic number Z is less than 20), stability is typically reached when the number of protons and neutrons is equal, resulting in an N/Z ratio of 1. Examples include Helium (⁴He), Carbon (¹²C), and Oxygen (¹⁶O). In these small clusters, the strong nuclear force easily overcomes the relatively weak repulsion between a few protons. Physical Geography by PMF IAS, The Universe, p.2 reminds us that these basic elements like Hydrogen and Helium were the first to form in the early universe.

However, as atoms get heavier and the number of protons increases, the electrostatic repulsion grows much faster than the strong nuclear force can keep up with. To maintain stability, the nucleus needs "extra" neutrons. These neutrons act as a sort of nuclear glue; they increase the total strong nuclear force without adding any additional repulsive electrical charge. Consequently, for heavy nuclei, the N/Z ratio must increase, eventually reaching approximately 1.5 for the heaviest stable elements like Bismuth (Z = 83).

When we plot the number of neutrons (N) against the number of protons (Z) for all known stable isotopes, they fall within a narrow region called the Stability Belt (or Band of Stability). Nuclei that fall outside this belt—either because they have too many neutrons or too many protons—are unstable and will undergo radioactive decay to move back toward the belt of stability.

Sources: Environment and Ecology, Major Crops and Cropping Patterns in India, p.100; Physical Geography by PMF IAS, The Universe, The Big Bang Theory, Galaxies & Stellar Evolution, p.2

7. Stability Requirements for Light Nuclei (exam-level)

To understand why some atoms are stable while others are radioactive, we must look at the tug-of-war occurring inside the nucleus. Every nucleus contains protons and neutrons. Protons, being positively charged, naturally repel each other through Coulomb (electrostatic) repulsion. To prevent the nucleus from flying apart, the Strong Nuclear Force acts like a powerful but short-range "glue" that binds these particles together. In the realm of light nuclei—generally those with an atomic number (Z) less than 20—the requirements for stability are quite specific and symmetrical.

For these lighter elements, stability is achieved when the number of neutrons (N) is approximately equal to the number of protons (Z), resulting in an N/Z ratio of 1. Because the total number of protons is small in light atoms, the repulsive electrostatic force is relatively weak. Therefore, a 1:1 ratio of neutrons to protons provides just enough nuclear "glue" to maintain a perfect balance. We see this clearly in the "primordial elements" like Helium-4 (2p, 2n), Carbon-12 (6p, 6n), and Oxygen-16 (8p, 8n), which were among the first to coalesce in the early universe Physical Geography by PMF IAS, The Universe, The Big Bang Theory, Galaxies & Stellar Evolution, p.2.

However, as we move beyond the lightest elements (A > 10), the balance begins to shift. While the rule of N ≈ Z holds firm up to Calcium (Z = 20), any significant deviation usually leads to instability. If a light nucleus has too many or too few neutrons, it becomes unstable and undergoes radioactive disintegration, emitting particles such as alpha or beta radiation to reach a more stable state Environment, Shankar IAS Academy, Environmental Pollution, p.82. Common stable light isotopes follow a predictable pattern:

• Helium-4: 2 Protons, 2 Neutrons (N/Z = 1.0)
• Nitrogen-14: 7 Protons, 7 Neutrons (N/Z = 1.0)
• Neon-20: 10 Protons, 10 Neutrons (N/Z = 1.0)

It is important to note that very small exceptions exist, such as Hydrogen-1 (which has no neutrons and is stable because there is no proton-proton repulsion) and Helium-3. But for the vast majority of light elements you will encounter in chemistry and physics, the 1:1 ratio is the golden rule for a peaceful, non-radioactive nucleus Science, Class VIII NCERT, Nature of Matter, p.123.

Sources: Physical Geography by PMF IAS, The Universe, The Big Bang Theory, Galaxies & Stellar Evolution, p.2; Environment, Shankar IAS Academy, Environmental Pollution, p.82; Science, Class VIII NCERT, Nature of Matter: Elements, Compounds, and Mixtures, p.123

8. Solving the Original PYQ (exam-level)

To master this question, you must synthesize two fundamental concepts: Coulomb Repulsion and the Strong Nuclear Force. In your recent lessons, you learned that protons, being positively charged, naturally repel each other. However, the nucleus stays together because of the Strong Nuclear Force, which acts between all nucleons (protons and neutrons). For light nuclei (A < 10), the number of protons is small, meaning the repulsive force is relatively weak. In this scenario, the most stable and energy-efficient configuration is achieved when there is a balanced N/Z ratio of 1, where the number of neutrons and protons is equal.

Walking through the reasoning, the constraint A < 10 is your primary clue. Think of the Stability Belt graph you studied: at the very beginning of the curve, stable isotopes like Helium-4 (2p, 2n) and Carbon-12 (6p, 6n) sit perfectly on the 1:1 line. Because the electromagnetic repulsion is manageable in these small clusters, nature does not require "excess" neutrons to act as spacers. Therefore, you can confidently conclude that Option (A): exactly the same number of neutrons and protons is the correct physical requirement for stability in this specific range.

UPSC often includes Option (B) as a clever trap. While it is true that heavy nuclei require more neutrons than protons to remain stable (due to massive electrostatic repulsion), this rule does not apply to the "light" nuclei specified in the question. Options (C) and (D) are extreme distractors; a nucleus without protons would not be a chemical element, and a nucleus without neutrons (with the sole exception of Hydrogen-1) lacks the necessary Nuclear Glue to bind multiple protons together. Always check the atomic mass range provided in the stem to avoid falling for these generalizations. You can find further clarification on this trend in NCERT Physics Class 12, Chapter 13: Nuclei.