https://doi.org/10.1351/goldbook.09907
Number indicative of column performance, calculated from the ratios of measures of adjusted retention and peak width: \[\eqalign{& N_{\rm{eff}} = \left(\frac{V_{\rm{R}}^{\prime}}{\sigma} \right)^{2} = \left(\frac{t_{\rm{R}}^{\prime}}{\sigma} \right)^{2} \cr & N_{\rm{eff}} = 16 \left(\frac{V_{\rm{R}}^{\prime}}{w_{\rm{b}}} \right)^{2} = 16 \left(\frac{t_{\rm{R}}^{\prime}}{w_{\rm{b}}} \right)^{2} \cr & N_{\rm{eff}} \approx 5.545 \left(\frac{V_{\rm{R}}^{\prime}}{w_{\rm{h}}} \right)^{2} \approx 5.545 \left(\frac{t_{\rm{R}}^{\prime}}{w_{\rm{h}}} \right)^{2}}\]
Notes:
- \(V_{\rm{R}}^{\prime}\): adjusted retention volume; \(t_{\rm{R}}^{\prime}\): total retention time; \(\sigma\): standard deviation of the Gaussian peak; \(w_{\rm{b}}\): peak width at base; \(w_{\rm{h}}\): peak width at half height; \(\rm{8 \ln 2} ≈ 5.545\).
- These expressions assume a Gaussian (symmetrical) peak.
- Units for the quantities being divided must be consistent so that their ratio is dimensionless: i.e. if the numerator is a time, then peak width must also be expressed in terms of time
- The plate number is related to the effective plate number and retention factor (\(k\)) \(N = N_{\rm{eff}}{\left(\frac{{k + 1}}{k} \right)^2}\)