31. Which of the following is the correct statement:
Resolution Proportional 1/2 Theoretical Plates Chromatography
Correct Answer: Option A
Resolution in chromatography is proportional to the square root of the number of theoretical plates, making option (A) correct. This relationship stems from the standard resolution equation used in HPLC and GC analysis.
Detailed Option Analysis
A. Resolution ∝ √N (Square Root)
The resolution Rs formula is Rs = (√N)/4 × ((α-1)/α) × (k2/(k1+1)), where N is the number of theoretical plates. Thus, Rs ∝ √N when selectivity (α) and retention (k) are constant.
B. Resolution ∝ 1/√N (Inversely Proportional)
Incorrect: This reverses the direct proportionality; higher N improves resolution by reducing peak broadening, not worsening it.
C. Resolution ∝ N2 (Square)
Incorrect: Resolution scales with √N, not N2; squaring would overestimate improvement from column efficiency.
D. Resolution ∝ N (Linear)
Incorrect: Linear proportionality (Rs ∝ N) ignores the square root dependence derived from Gaussian peak variance (σ ∝ 1/√N).
Factor Comparison Table
| Factor | Effect on Resolution | Optimization Strategy |
|---|---|---|
| √N (Efficiency) | Moderate gain[web:14] | Longer columns, smaller particles |
| α (Selectivity) | Strongest impact | Mobile phase changes |
| k (Retention) | Optimal at 2–10[web:16] | Gradient elution |
Exam Relevance for GATE Life Sciences
This PYQ tests chromatography fundamentals for instrument-based purification/separation topics. Understanding √N scaling distinguishes it from common misconceptions about linear or squared relationships.
Key Formula to Remember: Rs = (√N)/4 × ((α-1)/α) × (k/(1+k))
1 Comment
Vanshika Sharma
February 3, 2026Opt A is correct