  We report on the measurement of optical isotope shifts for
$^{38,39,42,44,46\text{-}51}$K relative to $^{47}$K from which changes in the
nuclear mean square charge radii across the N=28 shell closure are deduced. The
investigation was carried out by bunched-beam collinear laser spectroscopy at
the CERN-ISOLDE radioactive ion-beam facility. Mean square charge radii are now
known from $^{37}$K to $^{51}$K, covering all $\nu f_{7/2}$-shell as well as
all $\nu p_{3/2}$-shell nuclei. These measurements, in conjunction with those
of Ca, Cr, Mn and Fe, provide a first insight into the $Z$ dependence of the
evolution of nuclear size above the shell closure at N=28.
