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In cognitive radio networks (CRNs), effective and efficient channel exploitation is imperative for unlicensed secondary users to seize available network resources and improve resource utilization. In this paper, we propose a simple channel sensing order for secondary users in multi-channel CRNs without a priori knowledge of primary user activities. By sensing the channels according to the descending order of their achievable rates with optimal stopping, we show that the proposed channel exploitation approach is efficient yet effective in elevating throughput and resource utilization. Simulation results show that our proposed channel exploitation approach outperforms its counterparts by up to 18% in a single-secondary user pair scenario. In addition, we investigate the probability of packet transmission collision in a multi-secondary user pair scenario, and show that the probability of collision decreases as the number of channels increases and/or the number of secondary user pairs decreases. It is observed that the total throughput and resource utilization increase with the number of secondary user pairs due to increased transmission opportunities and multi-user diversity. Our results also demonstrate that resource utilization can be further improved via the proposed channel exploitation approach when the number of secondary user pairs approaches the number of channels.