The time evolution of entanglement and disentanglement between a Λ-type three-l evel atom and a single-mode field initially in the number state in an ideal cavi ty are investigated by considering von Neumann entropy of the optical field. Res ults indicate that entanglement of the system displays periodicity; the maximal degree of entanglement depends on the initial atomic state, the initial photon n umber and the ratio of detuning to the coupling constant, while the number of ti mes for maximal entanglement and disentanglement in a period is independent of t he initial photon number. The initial relative phase between the two lower state s have effects on the time evolution of field entropy, while the initial relativ e phases between the excited state and the ground states of the atom does not.