Hyperfine spectra of 48-51K (Z = 19) isotopes were measured at ISOLDE (CERN) for the first time, providing nuclear structure information when filling the ν2p3/2 orbit up to N = 32. The experiment was performed at the high-resolution collinear laser spectroscopy set-up (COLLAPS) with an improved highly efficient optical detection system. The analysis yielded the nuclear spin, magnetic moments and differences in mean square charge radii for isotopes between N = 19 and N = 32. The determination of the nuclear spin and magnetic moments of the neutron-rich isotopes, together with the isomeric shift in 38K were the main topics of this thesis. The measured ground-state spins of 49K (I = 1/2) and 51K (I = 3/2) shed light on the evolution of the 1/2...