In this paper we consider a cognitive radio network in a heterogeneous multi-channel scenario where channels are different in terms of achievable bit rates. Upon arrival licensed users (PUs) will occupy first the channels with higher achievable rates. As a result, secondary users (SUs) will see a set of channels which are different not only in their physical capacities but also in the activity profile of PUs. Consequently, from the point of view of the effective throughput that SUs can obtain in each channel there exists a trade-off between the rate they can obtain in a certain channel and the amount of time they can use it. We develop a model that allows to solve this trade-off by computing the maximum effective throughput that SUs can achieve in each channel.