Abstract The opportunistic spectrum access (OSA) has emerged as promising approach to increase the efficiency in spectrum sharing. The important feature of the OSA is to enable the unlicensed users or secondary users (SUs) to search for unused spectrum vacated by idle licensed user or primary user (PU). In this paper, we consider the maximization of the number of frames sent by the SUs during the idle period (white space) of the PU, while avoiding the infringement into the privileges of the PU. We set up this problem in terms of an optimal stopping problem. Explicit expression for the optimal number of frames that can be sent by the SUs in a white space is derived. Performance analysis for channel utilization and channel idle time is presented. Finally, the analytical results for optimal number of frames sent by SU in white space are numerically illustrated.