In this paper, we consider a cognitive radio network with energy harvesting secondary users and orthogonal channels for the primary users. Secondary users have finite capacity batteries to store harvested energy for future use. Secondary users can use the primary users' channel and transmit their data if the channel is not occupied by the primary user. We define an instantaneous reward for the secondary users which is equal to the throughput if the channel is available. Otherwise, we assign a negative reward to the secondary user as a penalty. We formulate the long term average reward maximization problem for each secondary user. We extend the fixed fraction policy in  to our setup and show that it yields near optimal performance. We derive an upper bound on the long term average reward, as well as additive and multiplicative lower bounds. We observe that, for energy arrivals that are frequent and when secondary users have several channel options to choose from, the secondary users are better off spending all available energy immediately, i.e., a greedy policy is a better choice whereas the fixed fraction policy is better when the energy arrivals are scarce.