The neutron, proton, electron and alpha particle are moving with equal kinetic energies. How can the particles be arranged in the increasing order of their velocities?

1. Atomic Structure: The Subatomic Building Blocks (basic)

To understand the complex world of nuclear physics, we must start with the atom's architecture. Every atom is a miniature solar system: a dense, central nucleus containing protons (positively charged) and neutrons (electrically neutral), surrounded by a cloud of electrons (negatively charged). Historically, about 300,000 years after the Big Bang, the universe cooled enough for these electrons to combine with protons and neutrons, forming the very first atoms of Hydrogen and Helium Physical Geography by PMF IAS, The Universe, p.2. While the nucleus holds almost all the atom's mass, the electrons determine its chemical personality by occupying different 'shells' and sometimes being shared between atoms to form stable bonds Science class X (NCERT 2025 ed.), Carbon and its Compounds, p.59. Understanding the relative mass of these particles is crucial for physics. A proton and a neutron have very similar masses (approx. 1 atomic mass unit or amu), though a neutron is slightly heavier. In contrast, an electron is a lightweight, with a mass only about 1/1836th of a proton. When we talk about an alpha particle, we are referring to a helium nucleus—a composite particle made of two protons and two neutrons—making it roughly four times heavier than a single proton. The nucleus of a simple atom like Sodium, for instance, remains a stable core of 11 protons even if the atom loses an electron to become a cation Science class X (NCERT 2025 ed.), Metals and Non-metals, p.46. In the realm of dynamics, the mass of these particles dictates how they move when given energy. If different particles are moving with the same Kinetic Energy (KE), their velocities will differ significantly based on the formula KE = ½mv². From this, we can derive that velocity (v) is inversely proportional to the square root of the mass (v ∝ 1/√m). This means that for a fixed amount of energy, the heaviest particle will be the slowest, and the lightest particle will be the fastest.

Particle	Approx. Mass (amu)	Relative Velocity (at equal KE)
Alpha Particle	4.00	Slowest
Neutron	1.008	Slow
Proton	1.007	Fast
Electron	0.00054	Fastest

Sources: Physical Geography by PMF IAS, The Universe, The Big Bang Theory, Galaxies & Stellar Evolution, p.2; Science class X (NCERT 2025 ed.), Metals and Non-metals, p.46; Science class X (NCERT 2025 ed.), Carbon and its Compounds, p.59

2. Mass and Charge: The Relative Scale of Particles (basic)

To master atomic physics, we must first understand the 'weight' and 'power' of the tiny actors involved. Matter is composed of subatomic particles like electrons, protons, and neutrons Physical Geography by PMF IAS, The Universe, The Big Bang Theory, Galaxies & Stellar Evolution, p.1. These particles differ drastically in mass and charge, which determines how they behave when they move. The proton and neutron are the heavyweights of the atom, residing in the nucleus. While they have nearly equal mass (~1 atomic mass unit or amu), the neutron is slightly heavier. In contrast, the electron is a featherweight, with a mass approximately 1/1836th of a proton. Finally, we have the Alpha particle (α), which is essentially a Helium nucleus consisting of two protons and two neutrons, making it the heaviest of this group (approx. 4 amu).

The relationship between a particle's mass and its speed is governed by Kinetic Energy (KE), defined by the formula: KE = ½mv². If we give an alpha particle, a neutron, a proton, and an electron the exact same amount of energy, they will not move at the same speed. Because velocity (v) is inversely proportional to the square root of mass (v ∝ 1/√m), the heaviest particle will be the slowest, and the lightest will be the fastest.

This scale of mass and charge is why a nucleus with six protons can effectively hold onto its electrons in a carbon atom Science, Class X (NCERT 2025 ed.), Carbon and its Compounds, p.59. Even when an atom becomes an ion by losing or gaining electrons, the massive nucleus remains the stable anchor Science, Class X (NCERT 2025 ed.), Metals and Non-metals, p.46.

Particle	Relative Mass (approx.)	Relative Charge	Velocity (at equal KE)
Alpha (α)	4 amu	+2	Slowest
Neutron	1.008 amu	0	Slow
Proton	1.007 amu	+1	Fast
Electron	1/1836 amu	-1	Fastest

Sources: Physical Geography by PMF IAS, The Universe, The Big Bang Theory, Galaxies & Stellar Evolution, p.1; Science, Class X (NCERT 2025 ed.), Carbon and its Compounds, p.59; Science, Class X (NCERT 2025 ed.), Metals and Non-metals, p.46

3. Alpha Particles: Nature and Composition (intermediate)

In our journey through atomic physics, we encounter radioactivity—the spontaneous process where unstable atomic nuclei (like Uranium or Thorium) disintegrate to achieve stability by emitting particles or energy. Environment, Shankar IAS Academy (10th Ed), Environmental Pollution, p.82. Among these emissions, the Alpha particle (α) is the heaviest and most distinct. You can think of an alpha particle as a Helium nucleus: it consists of two protons and two neutrons tightly bound together, carrying a net positive charge of +2. Because it lacks electrons, it is essentially a ⁴He²⁺ ion.

To understand how these particles behave in motion, we must look at the relationship between mass and velocity. All matter is composed of small particles, and their movement depends heavily on their energy and mass. Science, Class VIII NCERT, Particulate Nature of Matter, p.113. In physics, the Kinetic Energy (KE) of a particle is expressed as KE = ½mv². If we compare different subatomic particles—alpha particles, protons, neutrons, and electrons—at the same kinetic energy, their velocities will differ significantly based on their masses.

The mass hierarchy is a critical concept for your UPSC preparation. The Alpha particle is the heaviest (~4 amu), followed by the neutron (~1.008 amu), then the proton (~1.007 amu), and finally the electron, which is the lightest (~1/1836 amu). Physical Geography by PMF IAS, The Universe, The Big Bang Theory, Galaxies & Stellar Evolution, p.2. Using the formula v = √(2KE/m), we see that velocity is inversely proportional to the square root of the mass (v ∝ 1/√m). Therefore, for a fixed amount of energy, the "heavier" the particle, the slower it travels.

Particle	Composition	Approximate Mass	Relative Velocity (at same KE)
Alpha (α)	2 Protons + 2 Neutrons	4 amu	Lowest (Slowest)
Neutron	1 Neutron	1 amu	Low
Proton	1 Proton	1 amu	Moderate
Electron (β)	1 Electron	1/1836 amu	Highest (Fastest)

Sources: Environment, Shankar IAS Academy (10th Ed), Environmental Pollution, p.82; Science, Class VIII NCERT, Particulate Nature of Matter, p.113; Physical Geography by PMF IAS, The Universe, The Big Bang Theory, Galaxies & Stellar Evolution, p.2

4. Radioactivity: Comparing Emissions (intermediate)

When we compare radioactive emissions, we are essentially looking at a race between different subatomic "bullets." To understand how they behave, we must look at their mass and charge. These two factors determine how fast a particle moves, how deep it penetrates, and how much damage it causes to living tissue.

Let's start with the relationship between mass and velocity. If we assume different particles are emitted with the same Kinetic Energy (KE), we can use the fundamental formula KE = ½mv². From this, we see that velocity (v) is inversely proportional to the square root of the mass (v ∝ 1/√m). In simpler terms: the heavier the particle, the slower it moves. Among the common emissions:

• Alpha particles are the heaviest (approx. 4 amu), making them the slowest.
• Neutrons (~1.008 amu) and Protons (~1.007 amu) are much lighter than Alpha particles but significantly heavier than electrons.
• Electrons (Beta particles) are the featherweights (~1/1836 amu), meaning they travel at much higher velocities for the same energy level.

This physical size also dictates Penetrating Power vs. Ionizing Power. There is usually an inverse relationship between the two. Alpha particles, being bulky and highly charged, are like "bowling balls"—they crash into atoms immediately, causing high ionization (damage) but are stopped easily by a sheet of paper or human skin Environment, Shankar IAS Academy, Environmental Pollution, p.82. Conversely, Gamma rays are weightless electromagnetic waves. Because they lack mass and charge, they can penetrate deep into materials, including human organs, and require thick lead or massive concrete to be blocked Environment, Shankar IAS Academy, Environmental Pollution, p.82.

Emission Type	Mass	Velocity (at equal KE)	Penetration Power
Alpha	Highest	Lowest	Low (stopped by paper)
Beta (Electron)	Lowest	Highest	Moderate (stopped by glass/metal)
Gamma Ray	Zero	Speed of Light	Highest (stopped by lead/concrete)

In the upper atmosphere, specifically the Ionosphere, these high-energy radiations (Gamma, X-rays, and UV) constantly bombard atoms, stripping away electrons to create a flux of ions Environment and Ecology, Majid Hussain, BASIC CONCEPTS OF ENVIRONMENT AND ECOLOGY, p.8. This process of "ionization" is what makes radiation dangerous to biological life, as it can break macromolecules like DNA, leading to immediate tissue death or long-term genetic mutations Environment, Shankar IAS Academy, Environmental Pollution, p.83.

Sources: Environment, Shankar IAS Academy, Environmental Pollution, p.82; Environment, Shankar IAS Academy, Environmental Pollution, p.83; Environment and Ecology, Majid Hussain, BASIC CONCEPTS OF ENVIRONMENT AND ECOLOGY, p.8

5. Work and Energy: The Kinetic Energy Formula (basic)

Concept: Work and Energy: The Kinetic Energy Formula

6. Solving the Original PYQ (exam-level)

Now that you have mastered the fundamental properties of subatomic particles and the laws of motion, this question serves as the perfect bridge between Chemistry and Physics. The core concept here is the relationship defined by the Kinetic Energy formula (KE = ½mv²). When kinetic energy is constant across different particles, the velocity becomes inversely proportional to the square root of the mass (v ∝ 1/√m). To solve this, you simply need to combine your knowledge of particle hierarchy with this mathematical principle: the heavier the particle, the slower it must move to maintain the same energy level.

Let’s walk through the mass hierarchy to determine the correct sequence. The Alpha particle, essentially a helium nucleus containing two protons and two neutrons, is the heaviest at approximately 4 amu. Next are the nucleons; recall that a neutron is slightly heavier than a proton. Finally, the electron is the lightest by a massive margin (approx. 1/1836 amu). Applying our inverse rule, the heaviest particle (Alpha) is the slowest, followed by the neutron, then the proton, and finally the lightest (Electron) as the fastest. This logical progression confirms that (A) Alpha particle-neutron-proton-electron is the correct increasing order of velocities.

UPSC designed the other options as conceptual traps to test your precision. A common pitfall is the neutron-proton swap seen in options like (C) and (D); because their masses are so close, students often forget that the neutron is marginally more massive and thus slower. Other distractors rely on students failing to recognize that an Alpha particle is a composite structure, assuming instead it might be lighter than a proton. Success in these questions, as noted in NCERT Class 11 Physics, depends on your ability to rank masses accurately before applying the physics proportionality.