If four balloons A, B, C and D are filled with hydrogen, oxygen, helium and nitrogen gases respectively and left in air, which balloon reaches to the highest distance from the Earth?

1. Atomic Mass and Molecular Weight of Gases (basic)

To understand how gases behave in our atmosphere, we must first look at their smallest building blocks: atoms and molecules. An atom is the basic unit of matter, but many elements—like Hydrogen (H) or Oxygen (O)—cannot exist independently in nature because they are chemically unstable on their own. Instead, they bond together to form molecules Science, Class VIII (NCERT 2025), Particulate Nature of Matter, p.115. For instance, two nitrogen atoms share three pairs of electrons to form a stable triple-bonded molecule, N₂ Science, Class X (NCERT 2025), Carbon and its Compounds, p.60.

Molecular Weight (or Molecular Mass) is simply the sum of the atomic masses of all atoms present in a molecule. If we know the atomic mass of an element, we can calculate the weight of the gas. This is a critical "identity card" for a gas because as molecular mass increases, we see a clear gradation in physical properties like melting points, boiling points, and density Science, Class X (NCERT 2025), Carbon and its Compounds, p.67.

In our atmosphere, different gases have vastly different molecular weights. This weight determines where they "hang out." Heavier gases like Nitrogen and Oxygen tend to stay toward the bottom of the atmosphere, while lighter gases like Hydrogen and Helium are found in much smaller, trace amounts and are easily displaced Physical Geography by PMF IAS, Earths Atmosphere, p.271.

Gas Name	Chemical Formula	Approx. Molecular Weight (g/mol)
Hydrogen	H₂	2 (1 + 1)
Helium	He	4
Nitrogen	N₂	28 (14 + 14)
Oxygen	O₂	32 (16 + 16)

Sources: Science, Class VIII (NCERT 2025), Particulate Nature of Matter, p.115; Science, Class X (NCERT 2025), Carbon and its Compounds, p.60; Science, Class X (NCERT 2025), Carbon and its Compounds, p.67; Physical Geography by PMF IAS, Earths Atmosphere, p.271

2. Density and its Relationship with Molar Mass (basic)

To understand why certain objects or gases rise while others sink, we must first master Density. At its simplest, density is the measure of how much mass is packed into a given volume (Density = Mass / Volume). In the realm of chemistry, the density of a gas is fundamentally linked to its Molar Mass (the mass of one mole of its molecules). If you have two containers of the same size and at the same temperature/pressure, the one containing molecules with a higher molar mass will be denser. For example, Oxygen (O₂) has a molar mass of approximately 32 g/mol, making it significantly denser than Hydrogen (H₂), which has a molar mass of only about 2 g/mol Science, Class VIII NCERT (2025), Chapter 8, p.123. Environmental factors also shift these values. Temperature acts as a primary driver of density changes: as a substance is heated, its particles move apart and spread out. This increase in volume—without any change in mass—causes the density to decrease Science, Class VIII NCERT (2025), Chapter 9, p.147. This principle explains why hot air rises and how hot air balloons function. Conversely, Pressure has the opposite effect on gases; increasing pressure squeezes particles closer together, reducing volume and thus increasing density Science, Class VIII NCERT (2025), Chapter 9, p.148. In our atmosphere, gravity acts as a sorting mechanism based on these principles. In the upper atmosphere (the heterosphere), gases are distributed in distinct layers according to their weight. The lightest elements, Hydrogen and Helium, are found at the outermost margins, while heavier elements like Nitrogen and Oxygen are pulled toward the Earth's surface Environment and Ecology, Majid Hussain, Basic Concepts, p.6. This is why a balloon filled with Hydrogen experiences the greatest lifting force—it is the "lightest" gas available, creating the largest density deficit compared to the surrounding air.

Comparing Common Gases

Gas Molecule	Approx. Molar Mass	Relative Density	Atmospheric Behavior
Hydrogen (H₂)	2 g/mol	Lowest	Highly buoyant; rises to the exosphere.
Helium (He)	4 g/mol	Very Low	Buoyant; used in weather balloons.
Nitrogen (N₂)	28 g/mol	Moderate	Primary component of the lower atmosphere.
Oxygen (O₂)	32 g/mol	Higher	Stays concentrated near the Earth's surface.

Sources: Science, Class VIII NCERT (2025), Nature of Matter: Elements, Compounds, and Mixtures, p.123; Science, Class VIII NCERT (2025), The Amazing World of Solutes, Solvents, and Solutions, p.147-148; Environment and Ecology, Majid Hussain (3rd ed.), Basic Concepts of Environment and Ecology, p.6

3. Archimedes' Principle and Buoyancy in Air (intermediate)

To understand why certain objects soar while others stay grounded, we must first recognize that air is a fluid, just like water. According to Archimedes' Principle, any object immersed in a fluid experiences an upward force called buoyancy. This force is exactly equal to the weight of the fluid that the object displaces. While we often observe this in swimming pools, the same physics applies to the 'ocean' of air surrounding us. As noted in Science, Class VIII. NCERT(Revised ed 2025), Exploring Forces, p.76, when an object is in a fluid, gravity pulls it down, but buoyancy pushes it up. If the buoyant force is greater than the object's weight, it rises.

The 'lifting power' of a balloon depends on the density difference between the gas inside and the air outside. Since density is mass per unit volume, a gas with a lower molecular weight will generally be less dense than the surrounding atmosphere at the same temperature and pressure. For instance, the air we breathe is mostly Nitrogen (N₂ ~ 28 g/mol) and Oxygen (O₂ ~ 32 g/mol). If we fill a balloon with a lighter gas like Hydrogen (H₂ ~ 2 g/mol) or Helium (He ~ 4 g/mol), the weight of the gas inside is much less than the weight of the air the balloon displaces. This creates a net upward force. This is why, as explained in Physical Geography by PMF IAS, Pressure Systems and Wind System, p.306, the surrounding atmosphere exerts a buoyant force on low-pressure or less dense 'cells' of air, causing them to rise.

The following table illustrates how different gases compare in their potential to generate lift:

Gas Type	Approx. Molecular Weight	Behavior in Normal Air
Hydrogen (H₂)	2 g/mol	Highest lifting capacity; rises rapidly.
Helium (He)	4 g/mol	High lifting capacity; safe and non-flammable.
Air (N₂ + O₂)	~29 g/mol	Neutral; does not rise unless heated.
Carbon Dioxide (CO₂)	44 g/mol	Denser than air; the balloon will sink.

Sources: Science, Class VIII. NCERT(Revised ed 2025), Exploring Forces, p.76; Physical Geography by PMF IAS, Pressure Systems and Wind System, p.306

4. Composition and Layers of Earth's Atmosphere (intermediate)

Think of Earth's atmosphere not just as "air," but as a massive, multi-layered chemical reservoir held in place by gravity. This reservoir is primarily composed of Nitrogen (78.08%) and Oxygen (20.95%), which are often called permanent gases because their proportions remain constant in the lower atmosphere Physical Geography by PMF IAS, Earths Atmosphere, p.271. However, the atmosphere is far from uniform. As we move upward, the laws of chemistry and physics—specifically gravity and molecular weight—begin to sort these gases. Heavier molecules like Nitrogen (N₂) and Oxygen (O₂) tend to cluster near the Earth's surface, while the lightest gases, such as Hydrogen and Helium, migrate toward the outer edges Environment and Ecology, Majid Hussain, BASIC CONCEPTS OF ENVIRONMENT AND ECOLOGY, p.6.

This vertical arrangement leads to a distinct change in composition at higher altitudes. While we breathe easily at sea level, Oxygen becomes negligible by the time you reach about 120 km. Similarly, heavier molecules like Carbon Dioxide (CO₂) and water vapor are almost non-existent beyond 90 km Physical Geography by PMF IAS, Earths Atmosphere, p.272. Above 80 km, we enter a region called the Heterosphere. Unlike the lower atmosphere where gases are well-mixed, the Heterosphere is "gravity-sorted," with layers of gases arranged by their atomic weights.

Gas Type	Approx. Volume (%)	Behavioral Characteristic
Nitrogen (N₂)	78.08%	Heavier gas; stays in the lower layers.
Oxygen (O₂)	20.95%	Vital for life; drops off significantly above 120 km.
Argon (Ar)	0.93%	An inert noble gas; the third most abundant.
Hydrogen (H₂)	Trace (0.00005%)	Lightest gas; found at the fringe of space (Exosphere).

In the outermost layer, the Exosphere (above 480 km), the atmosphere is so rarified that it is nearly a vacuum. Here, light gases like Hydrogen and Helium are weakly held by gravity. Occasionally, these molecules gain enough thermal energy or get a "push" from the solar wind to reach escape velocity, leaking out into space forever—a process known as atmospheric escape Physical Geography by PMF IAS, Earths Atmosphere, p.280.

Sources: Physical Geography by PMF IAS, Earths Atmosphere, p.271; Environment and Ecology, Majid Hussain, BASIC CONCEPTS OF ENVIRONMENT AND ECOLOGY, p.6; Physical Geography by PMF IAS, Earths Atmosphere, p.272; Physical Geography by PMF IAS, Earths Atmosphere, p.280

5. Properties of Noble Gases vs. Reactive Gases (intermediate)

To understand why certain gases behave the way they do in our atmosphere, we must look at their electronic stability. In the world of chemistry, atoms strive to achieve a "complete" outer shell of electrons, similar to the noble gases like helium (He), neon (Ne), or argon (Ar). Because helium already has two electrons in its only shell (the K-shell), it is perfectly stable and does not naturally react with other elements Science, class X (NCERT 2025 ed.), Carbon and its Compounds, p.60. In contrast, reactive gases like hydrogen (H₂) or oxygen (O₂) have incomplete shells. To find stability, they form covalent bonds, often pairing up with themselves to form diatomic molecules Science, class X (NCERT 2025 ed.), Carbon and its Compounds, p.60.

This difference in chemical nature has massive real-world consequences. While hydrogen is the lightest gas in the universe, it is also highly reactive and flammable because it is constantly seeking to bond. Helium, though slightly heavier than hydrogen, is an inert noble gas, making it much safer for human use in balloons or airships. Beyond their chemistry, their physical weight determines where they live. In our atmosphere, gravity sorts gases by density: heavier gases like nitrogen (N₂) and oxygen (O₂) stay close to the surface, while the lightest gases—hydrogen and helium—rise to the very edge of space in a region called the heterosphere Environment and Ecology, Majid Hussain (Access publishing 3rd ed.), BASIC CONCEPTS OF ENVIRONMENT AND ECOLOGY, p.6.

Interestingly, because these light gases are so small and energetic, they can reach "escape velocity." This means they can literally break free from Earth's gravity and vanish into the vacuum of space, a process known as atmospheric escape. We are only able to keep much of our atmosphere intact because Earth's magnetic field shields it from the solar wind, which would otherwise strip these light gases away much faster Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.), Earths Atmosphere, p.280.

Property	Reactive Gases (e.g., Hydrogen)	Noble Gases (e.g., Helium)
Chemical Stability	Unstable alone; forms bonds to fill shells.	Inherently stable; full outer shells.
Bonding	Usually diatomic (H₂, O₂, Cl₂).	Monatomic (exists as single atoms).
Atmospheric Position	H₂ rises to the exosphere due to low weight.	He rises to the exosphere due to low weight.

Sources: Science, class X (NCERT 2025 ed.), Carbon and its Compounds, p.60; Environment and Ecology, Majid Hussain (Access publishing 3rd ed.), BASIC CONCEPTS OF ENVIRONMENT AND ECOLOGY, p.6; Physical Geography by PMF IAS, Manjunath Thamminidi, PMF IAS (1st ed.), Earths Atmosphere, p.280

6. Lifting Power and Maximum Altitude (exam-level)

To understand why certain objects soar while others stay grounded, we must look at the principle of buoyancy. A gas-filled balloon rises because the total weight of the balloon (including the gas inside) is less than the weight of the air it displaces. This 'upward push' is driven by density differences. At a fundamental level, the density of a gas is largely determined by its molecular weight. Hydrogen (H₂), with a molecular weight of approximately 2 g/mol, is the lightest gas in the universe. Helium (He), while also very light at approximately 4 g/mol, is twice as heavy as hydrogen. Because hydrogen is the least dense, it provides the maximum lifting power per unit of volume compared to any other gas. In contrast, the bulk of our atmosphere consists of 'heavier' gases like Nitrogen (N₂) and Oxygen (O₂). These gases tend to remain concentrated at the bottom of the atmosphere due to their higher molecular weights Physical Geography by PMF IAS, Earths Atmosphere, p.271. When we fill a balloon with a very light gas like hydrogen or helium, the surrounding denser air exerts an upward buoyant force, much like a cork popping to the surface of water. However, this ascent isn't infinite. As a balloon rises, the atmospheric pressure and density around it decrease Science, Class VIII . NCERT, Pressure, Winds, Storms, and Cyclones, p.84. The maximum altitude of a balloon is reached at the point of equilibrium—where the density of the thinning outside air exactly matches the average density of the balloon. Since a hydrogen-filled balloon starts with the lowest internal density, it can continue to displace 'enough' air to keep rising long after a helium or hot-air balloon has reached its limit. This is why hydrogen balloons are capable of reaching the highest altitudes among all gas-filled variants.

Gas	Approx. Molecular Weight	Atmospheric Role / Lifting Ability
Hydrogen (H₂)	2 g/mol	Highest lifting power; reaches maximum altitude.
Helium (He)	4 g/mol	High lifting power; safer (non-flammable) but heavier than H₂.
Nitrogen (N₂)	28 g/mol	Main constituent of air; stays at lower altitudes Physical Geography by PMF IAS, Earths Atmosphere, p.271.

Sources: Physical Geography by PMF IAS, Earths Atmosphere, p.271; Science, Class VIII . NCERT(Revised ed 2025), Pressure, Winds, Storms, and Cyclones, p.84

7. Solving the Original PYQ (exam-level)

To solve this question, we must synthesize two core concepts you have just mastered: Archimedes' Principle and the Molecular Weight of gases. In our atmosphere, a balloon acts as a displaced volume of fluid; for it to rise, the upward buoyant force must exceed the weight of the balloon and its contents. This force is maximized when the density gradient between the internal gas and the surrounding air is at its peak. As discussed in Physical Geography by PMF IAS, the atmosphere is primarily composed of Nitrogen (~28 g/mol) and Oxygen (~32 g/mol), which sets the "heavy" baseline against which we measure the lift of lighter alternatives.

Walking through the logic, we compare the molecular weights: Hydrogen (H2) is the lightest at ~2 g/mol, followed by Helium (He) at ~4 g/mol. While both are lighter than air and will rise, Hydrogen’s lower density results in the greatest net upward force per unit volume. According to Science, Class VIII, NCERT, the effect of density on buoyancy determines how high an object can displace its surroundings. Therefore, Balloon A, filled with Hydrogen, provides the maximum lifting force and will reach the highest distance from the Earth.

UPSC often includes "traps" like Option C (Helium) because it is the gas most commonly used in real-world weather balloons due to its safety (non-flammability). However, the question asks which actually reaches the highest distance, requiring a pure physics comparison where Hydrogen wins. Options B (Oxygen) and D (Nitrogen) are incorrect because their densities are nearly identical to the surrounding air, meaning they would experience negligible buoyancy and remain at lower altitudes. Always focus on the fundamental scientific property—in this case, the lowest molecular mass—rather than common industrial usage.