  We report the charge-changing cross sections ($\sigma_{\text{cc}}$) of 24
$p$-shell nuclides on both hydrogen and carbon at about 900$A$ MeV, of which
$^{8,9}$Li, $^{10\textendash12}$Be, $^{10,14,15}$B, $^{14,15,17\textendash22}$N
and $^{16}$O on hydrogen and $^{8,9}$Li on carbon are for the first time.
Benefiting from the data set,we found a new and robust relationship between the
scaling factor of the Glauber model calculations and the separation energies of
the nuclei of interest on both targets.This allows us to deduce proton radii
($R_p$) for the first time from the cross sections on hydrogen. Nearly
identical $R_p$ values are deduced from both target data for the neutron-rich
carbon isotopes, however, the $R_p$ from the hydrogen target is systematically
smaller in the neutron-rich nitrogen isotopes.This calls for further
experimental and theoretical investigations.
