A column or TLC plate is rated by how narrow its peaks (or spots) are relative to how far they have travelled. The plate count N = 16(tR/W)² treats the column as a cascade of equilibrium stages; a higher N means more equilibrium steps redistributing the analyte between phases, which produces a narrower band. A 25 cm reverse-phase HPLC column at 5 µm particle size delivers N around 25,000 to 50,000 for a well-retained peak. A gravity silica column delivers 500 to 2,000. A TLC plate around 5,000. A Whatman paper strip 200 to 500. The numbers explain why each format does the job it does.
Plate height H = L / N gives the average length per equilibrium stage. Smaller H means a more efficient column. The Van Deemter equation H = A + B/u + Cu describes how H depends on linear flow velocity u, with three terms representing eddy diffusion, longitudinal diffusion and resistance to mass transfer. The minimum of H against u is the optimum operating velocity. Too slow a flow and the band broadens by longitudinal diffusion; too fast and it broadens by mass-transfer lag; the sweet spot is the flow where Van Deemter sits at its minimum, typically 1 ml/min on a 4.6 mm i.d. column.
Resolution Rs = 2(tR2 − tR1) / (W1 + W2) decides whether two adjacent peaks are usable for quantitation. Rs of 1.5 or higher is baseline separation; each peak can be integrated independently. Rs of 1.0 is a 4 % overlap, acceptable for qualitative work but bad for quantitation. Rs below 0.8 means the two peaks cannot be reliably split. The three levers for improving Rs are: increase plate count (longer column, smaller particles, slower flow at Van Deemter's minimum); change the retention factor difference (different mobile-phase polarity, pH change for ionisable analytes); or increase selectivity α by switching stationary-phase chemistry. On TLC the same logic runs by changing mobile-phase composition, lengthening development distance, or switching from standard plates to HPTLC.