Resolution vs. efficiency — Chromatographic resolution (R_s) scales with which function of the number of theoretical plates (N)?

Introduction / Context:
Resolution expresses how well two peaks are separated. The classical resolution equation shows that resolution increases with the square root of efficiency, meaning large gains in plate number give diminishing returns in R_s.

Given Data / Assumptions:

• N reflects column efficiency (more plates, narrower peaks).
• Resolution equation (simplified): R_s ∝ (√N / 4) * (k' / (1 + k')) * (α − 1)/α.
• α is selectivity; k' is retention factor.

Concept / Approach:
Because R_s increases with √N, doubling resolution requires quadrupling N. Thus, adjusting selectivity or k' often yields bigger improvements than simply increasing efficiency.

Step-by-Step Solution:

Verification / Alternative check:
Empirical method development shows that switching stationary phases (changing α) often improves R_s more than modest increases in efficiency.

Why Other Options Are Wrong:

Common Pitfalls:
Expecting linear R_s gains from efficiency; remember the square-root dependence.

Final Answer:
Proportional to the square root of N.