Study of the nuclear structure of nuclides used for medical diagnosis using positron emission tomography (PET) is presented in this work. These nuclides are ¹¹C, ¹³N, ¹⁵O and ¹⁸F, which are unstable by emitting β⁺ particles. They have half-lives of several minutes, which make them suitable radionuclides for PET. These radionuclides are produced through nuclear reactions using a cyclotron.  Studying the nuclear structure of these light nuclides is performed through the shell model. The full space of the p-shell model is used for the p-shell nuclei, and the full space of the sd-shell model for the sd-shell nucleus. The study includes calculations of magnetic moments and quadrupole electric moments. Calculations of form factors are presented to give predictions for future experimental studies. Protons and neutrons’ effective charges are used to include core-polarization effects. The single-particle states used in the calculations are those of the harmonic oscillator potential. Excellent agreement is obtained between the calculated observables and the available experimental data.