In order to provide a database for modeling hypersonic entry in a partially ionized gas under non-equilibrium conditions, the electron-impact excitation cross sections of atoms are calculated using a quantum mechanical perturbation theory. Unlike the variational method, which has the limitation of treating only about 30 target states at the present time, the perturbation method allows the calculation of electron collisions with the full set of atomic states. The energy levels covered in the present calculations involve 684 states of N, 552 states of O, and 915 states of C, retrieved from the level lists in the HyperRad code. A few limited variational R-matrix results and experimental data are used to benchmark the present perturbation calculations. Electron-impact cross sections and rate coefficients for all dipole-allowed transitions (16239 transitions for N, 11072 for O, and 22546 for C) have been calculated. In addition, both the dipole-allowed and exchange transition cross sections and rate coefficients for N atoms using the NIST level list have also been computed. The newly computed state-to-state rate coefficients are used to study two test cases: (1) the internal excitation and ionization processes of nitrogen atoms in an isothermal and isochoric heat bath; and (2) the evolution of thermal and chemical non-equilibrium processes behind a strong shock for a flow consisting of nitrogen molecules, atoms, ions, and electrons.