What is reason after 80 km from ground surface in heterosphere the composition of air and its ratio changes but not in homosphere?

Question

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1. Restating the question in plain language

The student is asking:

Why does the composition of the atmosphere (the relative amounts of N₂, O₂, Ar, etc.) stay essentially constant up to about 80 km, but above that height the proportions begin to change?
Is the 80 km “boundary” a theoretical construct, a result of measurements, or both?

In short: What physical processes make the lower 80 km of the atmosphere well‑mixed, and why do they stop being effective higher up?

2. Step‑by‑step explanation

2.1 Define the two regions

Region	Approx. altitude	Common name	Main characteristic
Homosphere	0 – ~80 km	Homosphere	The major constituents (N₂, O₂, Ar, CO₂) are mixed so thoroughly that their volume mixing ratios are essentially constant with height.
Heterosphere	> ~80 km	Heterosphere	The mixing ratios start to vary with altitude; lighter gases become relatively more abundant with height.

The transition altitude is not a hard wall but a transition layer (roughly 70–100 km) where the dominant transport mechanism changes.

2.2 How gases are mixed in the lower atmosphere

Two physical processes keep the gases well mixed:

Process	What it does	Typical strength in the homosphere
Turbulent (eddy) diffusion	Random, chaotic motions of air parcels (e.g., caused by weather, convection, gravity waves) transport molecules vertically.	Eddy diffusivity (K_{\text{eddy}}) ≈ 10–10³ m² s⁻¹ in the troposphere, decreasing with height but still > molecular diffusion below ~80 km.
Molecular (Brownian) diffusion	Random motion of individual molecules colliding with each other.	Diffusivity (D) ≈ 0.1–1 m² s⁻¹ for N₂, O₂ at sea level; increases with decreasing pressure but is much smaller than eddy diffusion in the homosphere.

Key point: As long as eddy diffusion dominates over molecular diffusion, any parcel of air that is displaced vertically quickly becomes mixed back to the background composition. The result is a uniform mixing ratio for the major gases.

2.3 When does eddy diffusion stop dominating?

The competition between the two diffusion mechanisms can be quantified by comparing their coefficients:

[ \frac{K_{\text{eddy}}}{D} \gg 1 \quad \Longrightarrow \text{well‑mixed (homosphere)}\[4pt] \frac{K_{\text{eddy}}}{D} \lesssim 1 \quad \Longrightarrow \text{diffusive separation (heterosphere)} ]

Eddy diffusivity drops with altitude because atmospheric density and the sources of turbulence (convection, weather) become weaker. Empirically, (K_{\text{eddy}}) falls roughly as (K_{\text{eddy}} \propto \rho^{-0.5}) (where (\rho) is air density).
Molecular diffusivity increases with decreasing pressure (roughly (D \propto 1/\rho)) because collisions are less frequent, allowing molecules to travel farther between collisions.

The two curves intersect near 70–90 km. Using typical empirical profiles (e.g., the NRLMSISE‑00 model), the crossover altitude is ≈ 80 km.

2.4 What happens above the crossover?

When molecular diffusion dominates, each species behaves independently under the influence of gravity. The vertical distribution of a constituent i follows the barometric (hydrostatic) formula with its own scale height:

[ n_i(z) = n_i(z_0)\,\exp!\Big[-\frac{z - z_0}{H_i}\Big], \qquad H_i = \frac{k_B T}{m_i g}, ]

where

(n_i) = number density of species i
(k_B) = Boltzmann constant
(T) = temperature (≈ 200 K in the mesosphere/thermosphere)
(m_i) = molecular mass of species i
(g) = acceleration due to gravity (≈ 9.8 m s⁻²)

Because (H_i) depends on the mass, lighter gases (e.g., H, He) have larger scale heights and therefore their relative concentration increases with altitude, while heavier gases (N₂, O₂) fall off more rapidly. This creates the heterosphere composition gradient.

2.5 Why is the 80 km value used in textbooks?

Observational evidence – Measurements from sounding rockets, satellite drag data, and mass spectrometers (e.g., the Atmosphere Explorer missions) show a clear change in mixing ratios around 70–100 km.
Modeling convention – Atmospheric models (e.g., US Standard Atmosphere, NRLMSISE‑00) adopt a transition altitude near 80 km because that is where the modeled eddy diffusion coefficient falls below the molecular diffusion coefficient for the major species.
Practical simplicity – Using a single number (80 km) gives a convenient “rule of thumb” for the homosphere/heterosphere boundary, even though the real transition is a gradual crossover.

Thus the 80 km figure is both empirically observed and theoretically justified, but it should be understood as an approximate, not a strict, dividing line.

2.6 Summary of the physical picture

Altitude	Dominant transport	Resulting composition
0 – ~70 km	Turbulent (eddy) diffusion (\gg) molecular diffusion	Uniform mixing ratios → homosphere
~70 – ~100 km	Eddy and molecular diffusion comparable (transition layer)	Gradual onset of separation
> ~100 km	Molecular diffusion (\gg) eddy diffusion	Species separate by mass → heterosphere

3. Final answer

Below ~80 km the atmosphere is called the homosphere because vigorous turbulent mixing (eddy diffusion) overwhelms molecular diffusion, keeping the volume mixing ratios of N₂, O₂, Ar, CO₂, etc., essentially constant with height.
Above ~80 km turbulent mixing becomes weak; molecular diffusion becomes dominant. Each gas then follows its own exponential decline with a scale height that depends on its molecular mass, so lighter gases become relatively more abundant. This region is the heterosphere.
The ≈ 80 km boundary is a practical, observationally supported approximation that marks where the eddy‑diffusion coefficient drops to the same order as the molecular‑diffusion coefficient for the main atmospheric constituents.

4. Common mistakes

Mistake	Why it’s wrong	Correct approach
Thinking the 80 km line is a physical “wall.”	The atmosphere changes continuously; there is no abrupt discontinuity.	Treat the 70–100 km region as a gradual transition where the two diffusion processes become comparable.
Attributing the change solely to temperature.	Temperature does affect scale heights, but the dominant factor for the composition change is the switch from turbulent to molecular diffusion.	Emphasize the relative magnitudes of eddy vs. molecular diffusion coefficients.
Assuming that all gases separate immediately above 80 km.	Separation proceeds according to each species’ molecular weight; heavy gases still dominate up to several hundred km before becoming negligible.	Use the barometric formula with species‑specific scale heights to see the gradual nature of separation.
Neglecting the role of external sources (e.g., solar UV, meteoric input).	While photochemistry and meteoric ablation affect trace species, the overall change in the major constituent ratios is driven by diffusion.	Mention that for trace species, photochemistry can dominate, but the homosphere/heterosphere distinction concerns the bulk gases.
Using a single value of eddy diffusivity for all altitudes.	Eddy diffusivity varies by many orders of magnitude with height.	Refer to empirical profiles (e.g., (K_{\text{eddy}} \approx 10^2) m² s⁻¹ at 50 km, falling to < 1 m² s⁻¹ near 90 km).

Keeping these points in mind will help avoid misconceptions when discussing atmospheric layering and composition.

Original question: What is reason after 80 km from ground surface in heterosphere the composition of air and its ratio changes but not in homosphere? on Physics Stack Exchange, licensed CC BY-SA.