Step 1: Recall how plume shape depends on the vertical temperature (lapse rate) profile. The shape a smoke plume takes as it disperses from a stack is governed directly by the atmospheric stability at and around stack height.
Step 2: Match strong instability (P). Under strong instability (a superadiabatic lapse rate, typical of a clear, sunny afternoon), large-scale turbulent eddies throw the plume rapidly up and down, producing a wavy, undulating shape called a looping plume. This corresponds to (iv).
Step 3: Match neutral stability (Q). Under neutral stability (lapse rate close to the dry adiabatic rate, often on cloudy/windy days), the plume spreads roughly equally in the vertical and horizontal directions, forming a cone shape, called a coning plume; this corresponds to (iii).
Step 4: Match surface inversion (R). A surface-based inversion means the air is very stable from the ground up through and above stack height, strongly suppressing vertical mixing. The plume can then only spread sideways along a thin horizontal layer, producing a flat, ribbon-like fanning plume; this corresponds to (i).
Step 5: Match aloft (elevated) inversion (S). When the inversion lies above the stack (with unstable/neutral air below the inversion and below the stack), the plume mixes downward rapidly once the surface layer becomes unstable, bringing high pollutant concentrations to ground level; this phenomenon is called fumigation, corresponding to (ii).
Step 6: Assemble and conclude. The correct matching is (P)-(iv), (Q)-(iii), (R)-(i), (S)-(ii), which is option (B). The remaining options mismatch at least one condition, for example option (A) wrongly assigns fanning to strong instability, which actually produces a looping plume.