Conditions:

One thing which seems to be important for resolution under a certain set of conditions is the length of the column. A single way to improve the resolution is to employ a longer column. This will mean that with a longer column, we will have more theoretical plates. The separation of two peaks (t_R)_Y  - (t_R)_X is directly proportional to the distance the two species migrate. Instead of, the width of a peak increases with the square root of the distance. Therefore, through increasing the length of a column the two bands will separate faster than they broaden and the resolution will improve. The two important drawbacks in making the column too long are requirement of high pressure of carrier gas and unusually long time for elution. In case we are not able to obtain a satisfactory separation by using a good column of reasonable length giving proper attention to operating parameters like temperature and flow rate of carrier gas, the reasonable approach is to change the stationary liquid phase. This can be viewed as, if the logical attempts to achieve resolution by narrowing the solute bands fail, we must move the peaks farther apart. For making the peaks apart that we have to modify K values.

In the above context, you are advised where the term selectivity factor/ separation factor was introduced and the following expressions were given.

α = K_Y/K_X =(t_R)_Y-t_M/((t_R)_X-t_M ≈ (t_R)_Y/(t_R)_X ...

You may remember that the separation factor is the ratio of distribution constants of the two solutes X and Y and is usually the same as the ratio of retention times of the two solutes. It can be seen that α and R are not the same thing. The ratio of retention times, measured at the peaks of elution bands does not itself represent the effectiveness of separation because it does not tell anything about the width of the peak. It seems logical that there will be a relation between R and α if the number of theoretical plates in the column is taken into account, that is

R = N ½ (α - 1)α/4