The Chapman Cycle: How Sunlight Builds and Breaks the Ozone Layer

Four reactions, two of them slow

Chapman's genius was to split the chemistry into a fast inner loop and a slow outer loop. The slow steps create and destroy ozone in a net sense; the fast steps just shuffle it back and forth. Here is the whole scheme, balanced:

• Step 1 — Initiation: O₂ + hν → O + O. A molecule of dioxygen absorbs a high-energy ultraviolet photon (wavelength λ < 242 nm, in the UV-C) and snaps apart. This costs the full O=O bond energy of about 498 kJ/mol, which is why only the most energetic solar photons can do it. Rate coefficient J₁ ≈ 3 × 10⁻¹² s⁻¹ — a slow, rare event.
• Step 2 — Ozone formation: O + O₂ + M → O₃ + M. A lone oxygen atom collides with O₂, and a third body M (usually N₂ or O₂) carries off the excess energy so the newborn ozone doesn't immediately fly apart. Rate k₂ ≈ 1.2 × 10⁻³³ cm⁶ molecule⁻² s⁻¹. This is fast — an O atom lives only seconds before becoming O₃.
• Step 3 — Ozone photolysis: O₃ + hν → O + O₂. Ozone absorbs UV-B and visible photons and breaks, regenerating an O atom. J₃ ≈ 5 × 10⁻⁴ s⁻¹ — thousands of times faster than step 1.
• Step 4 — Termination: O + O₃ → 2 O₂. An oxygen atom meets an ozone molecule and both are annihilated into two O₂. Rate k₄ ≈ 8 × 10⁻¹⁵ cm³ molecule⁻¹ s⁻¹ — slow, because O atoms are scarce.

Notice that steps 2 and 3 do not change the total oxygen accounting: step 3 makes an O atom, step 2 spends it. Only steps 1 and 4 alter the net amount of ozone-plus-atomic-oxygen.

Odd oxygen: the accounting trick that makes it simple

The key to understanding the cycle is to stop tracking O and O₃ separately and instead track their sum, called odd oxygen: Oₓ = O + O₃. The word 'odd' refers to species carrying an odd number of oxygen atoms.

Under this bookkeeping, steps 2 and 3 vanish from the ledger — they merely convert one form of odd oxygen into the other. What's left is startlingly clean:

• Odd oxygen is created only by step 1 (O₂ splitting makes 2 O atoms = +2 Oₓ).
• Odd oxygen is destroyed only by step 4 (O + O₃ → 2 O₂ removes 2 Oₓ).

Because production (step 1) and loss (step 4) are both slow, the lifetime of the Oₓ family is weeks to months, even though an individual O atom lives seconds and an individual O₃ molecule is photolyzed within an hour. Ozone is being destroyed and remade constantly, but the reservoir it belongs to turns over glacially. That separation of timescales is why the ozone layer is stable: it can lose ozone locally in an afternoon and refill it by dawn, while the total column stays nearly constant for weeks.

Why the layer sits at 25 km and nowhere else

The ozone maximum is not an accident of geography — it falls out of the physics as a competition between two ingredients that vary oppositely with altitude:

• UV photons (needed for step 1) are abundant high up but get absorbed as they penetrate downward. Their supply decreases with decreasing altitude.
• Air density — the O₂ and the third body M needed for step 2 — increases exponentially with decreasing altitude.

High in the mesosphere there is plenty of UV to split O₂, but the air is too thin for the three-body reaction (step 2) to efficiently form ozone. Down in the troposphere the air is dense, but almost no λ < 242 nm photons survive to that depth. The product of 'enough UV' and 'enough density' peaks in the middle stratosphere, near 20–30 km. That is the Chapman layer, and it is why every planet with an O₂ atmosphere and a UV star will build an ozone shield at a predictable pressure level. The peak mixing ratio reaches roughly 12 ppm, corresponding to about 5 × 10¹² molecules cm⁻³.

The layer that heats itself — and shields the biosphere

Every photon ozone swallows in step 3 deposits its energy as heat. Ozone absorbs strongly across the Hartley band (200–310 nm) and the weaker Chappuis bands (~450–850 nm), and this absorption is what warms the stratosphere and creates the temperature inversion that defines it — air that gets warmer with height, from about −60 °C at the tropopause to near 0 °C at the stratopause. That inversion suppresses vertical mixing, which is why aircraft cruise there in smooth air.

Biologically, the payoff is enormous. Splitting O₂ (step 1) mops up the deadliest UV-C, and photolyzing O₃ (step 3) mops up most of the UV-B (280–315 nm) that damages DNA. The Hartley band absorption cross-section of ozone is so large that even a 3 mm-thick equivalent layer cuts biologically weighted UV by orders of magnitude. Without the Chapman cycle continuously regenerating that ozone, terrestrial life as we know it could not exist on exposed land.

Where Chapman's model breaks: it makes too much ozone

Chapman's four reactions are correct — but incomplete. When you plug the measured rate constants and solar fluxes into the pure-oxygen scheme, the model overpredicts the observed ozone abundance by roughly a factor of 2. Something else is destroying ozone that Chapman never included: catalytic cycles run by trace free radicals.

These catalysts, written generically as X, attack ozone without being consumed, so a single molecule can destroy tens of thousands of O₃ before it is removed. The general balanced cycle is:

• X + O₃ → XO + O₂
• XO + O → X + O₂
• Net: O + O₃ → 2 O₂ (identical to Chapman step 4, but catalyzed)

The important catalysts, by altitude:

• HOₓ (X = OH·, HO₂·) — dominant in the lower and upper stratosphere; sourced from H₂O and CH₄.
• NOₓ (X = NO, ·NO₂) — dominant in the mid-stratosphere; sourced from N₂O rising up from the surface.
• ClOₓ / BrOₓ (X = Cl·, Br·) — the anthropogenic villains from CFCs and halons, responsible for the Antarctic ozone hole.

So the real steady-state ozone concentration is set by Chapman production balanced against Chapman loss plus catalytic loss. Chapman explains the shape and location of the layer; the catalysts explain its true thickness and its vulnerability.

Null cycles, day–night breathing, and the diurnal swing

Within the Chapman scheme, the pair 'step 3 then step 2' (O₃ + hν → O + O₂, then O + O₂ + M → O₃ + M) forms a null cycle: it interconverts ozone and atomic oxygen many times without changing the total odd oxygen at all. Ozone is torn apart and rebuilt over and over, purely converting sunlight into heat. Most photolysis events do exactly this — they are 'wasted' from an ozone-budget standpoint but essential for stratospheric heating.

Because step 1 and step 3 both need sunlight, the cycle breathes with the day. At night, photolysis (steps 1 and 3) shuts off. Atomic oxygen, having nothing to make it, rapidly reacts away via step 2, so by nightfall almost all odd oxygen is stored as O₃. At sunrise, photolysis resumes and the O/O₃ ratio jumps back up. The total Oₓ barely changes over a single day — consistent with its weeks-to-months lifetime — but the partitioning between O and O₃ swings dramatically. This diurnal choreography is measurable and is a standard test of stratospheric chemistry models.

Why the Chapman cycle still matters

Nearly a century after Chapman, his four reactions remain the backbone of every stratospheric chemistry model. You cannot understand ozone depletion, the recovery under the Montreal Protocol, or the ozone signatures astronomers hunt for on exoplanets without first understanding the Chapman baseline — the ozone an atmosphere would have from oxygen and UV alone.

• For the ozone hole: Chapman sets the 'undepleted' reference against which the ClOₓ-driven losses of 200+ DU each Antarctic spring are measured.
• For climate: the stratospheric heating that ozone provides shapes the general circulation; getting the Chapman heating right is a prerequisite for climate models.
• For astrobiology: ozone is used as a proxy for O₂ on distant worlds, but the O₂–O₃ relationship is nonlinear precisely because of Chapman photochemistry — so quantifying alien oxygen means running Chapman's cycle under a different star's spectrum.

The lesson is a durable one in atmospheric science: a simple, correct core mechanism, plus a small set of trace-catalyst corrections, explains a planetary-scale phenomenon that keeps the land habitable.

The four Chapman reactions: what each step does, its driver, and its timescale.

Step	Balanced reaction	Driver	Role / timescale
1 · Initiation	O₂ + hν → O + O	UV-C, λ < 242 nm	Makes odd oxygen (slow, minutes–days)
2 · O₃ formation	O + O₂ + M → O₃ + M	3-body collision	Forms ozone (seconds)
3 · O₃ photolysis	O₃ + hν → O + O₂	UV-B/Chappuis, <850 nm	Recycles ozone (<1 hr, null)
4 · Termination	O + O₃ → 2 O₂	Bimolecular	Destroys odd oxygen (slow)
Net cycle 1+4	3 O₂ ⇌ 2 O₃ (via UV)	Solar UV flux	Sets steady-state O₃