We consider the classical dynamics of alkali atoms in microwave fields. The atom is described by a simplified one-dimensional integrable model that includes two atom-dependent parameters, σ and C. Chirikov's overlap criterion is applied for determining the conditions needed to produce chaotic motion (ionization) when the atom is placed in a periodically varying electric field. In order to test the ionization conditions we analyse the behaviour of single classical trajectories for several values of the field strength by numerically integrating the Hamilton's equations. The results validate Chirikov's predictions for low resonances and show that the ionization process depends on the field's phase γ. However, by changing γ we can get physically equivalent trajectories if we also choose the right initial conditions for the Hamilton equations. The dynamical process along a classical trajectory is characterized by suitable quantities and some crucial properties are exploited for predicting ionization far before the ionization time is reached.