The atomic dynamics in liquid alkali metals at the melting point has been studied with the help of an equation of motion in terms of the velocity autocorrelation function. An atom is considered to be moving in a mean-time-dependent field, in a series of steps much smaller than the average interatomic spacing (small-step diffusion approximation). The theoretical formulation presented here is a special case of our generalized formulation for simple monatomic liquids [Phys. Rev. E. 70, 51201 (2004)]. It gives a good account of the single-particle motion in liquid Li, Na, K, Rb, and Cs. The calculated self-diffusion coefficients are found to be in excellent agreement with the experiments. The formulation is also used to investigate the collective excitations arising due to density fluctuations. The dispersion curves for the collective excitations for Li, Na, and K show a decent overall agreement with the inelastic neutron scattering and inelastic x-ray scattering results. The effect of quantum-mechanical correction has been observed for Li, Na, and K. It suggests a significant improvement over the classical results. Since the applicability of the small-step diffusion approximation is limited to weak electron-ion coupling at high electron densities, the present formulation gives satisfactory dispersion curves for Rb and Cs in a small intermediate $q$ range. It has been observed that an abrupt change in the dynamical properties occurs at the position of potassium in accordance with the change in atomic number density.