  Investigations of isotope shifts of atomic spectral lines provide insights
into nuclear properties. Deviations from the linear dependence of the isotope
shifts of two atomic transitions on nuclear parameters, leading to a
nonlinearity of the so-called King plot, are actively studied as a possible way
of searching for the new physics. In the present work we calculate the
King-plot nonlinearities originating from the Standard-Model atomic theory. The
calculation is performed both analytically, for a model example applicable for
an arbitrary atom, and numerically, for one-electron ions. It is demonstrated
that the Standard-Model predictions of the King-plot nonlinearities are
hypersensitive to experimental errors of nuclear charge radii. This effect
significantly complicates identifications of possible King-plot nonlinearities
originating from the new physics.
