# Plate Theory and Extensions - Effective Plate Number > Page 64

where (y) | is the retention distance |

and (x) | is the peak width. |

Now, the
number of *effective plates* (N_{E}),
by definition, is given by

(56)

where (y_{o})
is the retention distance of an unretained solute (the position of the dead
point).

Now from the plate theory,

Thus,

By dividing
through by (v_{m} ), and noting that ,

Consequently, (57)

Equation (57)
shows the relationship between efficiency and 'effective plates'. The number of
'effective plates' in a column is not an arbitrary measure, but is directly related to efficiency as derived from
the plate theory. Equation (57)shows that, as (k') becomes large, (n) and (N_{E}) converge to the same value.