= Solution
Activation as a <cloud condensation nucleus> depends primarily on dry particle size, soluble composition and hygroscopicity, together with wetting and surface-tension effects. In <Köhler theory>, droplet curvature raises the equilibrium <vapor pressure>, while dissolved solute lowers <water> activity. Each particle therefore has a <critical supersaturation>; larger or more hygroscopic particles generally activate at a lower value. A size distribution cannot be replaced by an undifferentiated total <aerosol> count.<A single parameter representation of hygroscopic growth and cloud condensation nucleus activity by M. D. Petters and S. M. Kreidenweis>[Atmospheric Chemistry and Physics 7 (2007), pp. 1961–1971, dry diameter, hygroscopicity parameter and <critical supersaturation>]{ref}
Actual droplet number also depends on the supersaturation attained in the <cloud> updraught. Adding particles increases competition for condensing <water vapor> and can lower the peak supersaturation, leaving some particles unactivated. Updraught speed, <entrainment> and the <aerosol> size distribution therefore make the number of activated droplets a nonlinear function of the available nuclei. \b[Suitable nuclei need sufficiently low activation thresholds, and additional <aerosol> does not guarantee one additional droplet per particle.]
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