4 Absorption of UV in the atmosphere

• Nitrogen (N₂), oxygen (O₂) molecules and atomic oxygen absorb photons with wavelengths shorter than 240 nm (high-energy UV-C and shorter).
• The formation and destruction of ozone (O₃) absorb photons in the ultraviolet region with wavelengths from 240 nm to 310 nm (the rest of UV-C and most of UV-B).
• In this way the ozone present in the stratosphere protects us from these high-energy photons. Only part of UV-B and most of UV-A reach the surface.

Problem. Calculate the energy of one photon and of one mole of photons for wavelengths of 240 nm and 310 nm (h = 6.63 × 10⁻³⁴ J·s, c = 3.0 × 10⁸ m/s, N_A = 6.02 × 10²³). Compare with the bond energy of O₂ (498 kJ/mol).

Solution. E = hc/λ.

• λ = 240 nm: E = (6.63 × 10⁻³⁴ × 3.0 × 10⁸)/(240 × 10⁻⁹) = 8.29 × 10⁻¹⁹ J per photon; per mole = 8.29 × 10⁻¹⁹ × 6.02 × 10²³ = 4.99 × 10⁵ J = 499 kJ/mol.
• λ = 310 nm: E = 1.989 × 10⁻²⁵/3.10 × 10⁻⁷ = 6.42 × 10⁻¹⁹ J; per mole = 386 kJ/mol. The O=O bond needs 498 kJ/mol, so only photons with energy ≥ 498 kJ/mol, that is wavelength ≤ 240 nm, can break an O₂ molecule. A 310 nm photon (386 kJ/mol) is too weak to split O₂ but strong enough to split ozone (whose bond is much weaker, about 100–150 kJ/mol). This explains the book's two numbers, 240 nm and 310 nm.