The possibility of axion detection by observing axion induced atomic excitations as suggested by Sikivie is discussed. The atom is cooled at low temperature and it is chosen to posses three levels. The first is the ground state, the second is completely empty chosen so that the energy difference between the two is close to the axion mass. Under the spin induced axion-electron interaction an electron is excited from the first to the second level. The presence of such an electron there can be confirmed by exciting it further via radiation of a suitably chosen photon energy to the appropriately selected third level, which is also empty, and lies at a higher excitation energy. From the observation of its subsequent de-excitation one infers the presence of the axion. The system is in a magnetic field so that the energies involved can be suitably adjusted. Since the axion is absorbed by the atom the cross section exhibits resonance behavior. Using an axion-electron coupling indicated by the limit obtained by the Borexino experiment, reasonable axion absorption rates have been obtained for various atomic targets.