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The paper considers broadcasting protocols in radio networks with known topology that are efficient in both time and energy. The radio network is modelled as an undirected graph G = (V, E) where |V| = n. It is assumed that during execution of the communication task every node in V is allowed to transmit at most once. Under this assumption it is shown that any radio broadcast protocol requires D + Ω(√n - D) transmission rounds, where D is the diameter of G. This lower bound is complemented with an efficient construction of a deterministic protocol that accomplishes broadcasting in D + O(√n log n) rounds. Moreover, if we allow each node to transmit at most k times, the lower bound D + Ω((n - D)1/(2k)) on the number of transmission rounds holds. We also provide a randomised protocol that accomplishes broadcasting in D + O(kn1/(k-2) log2 n) rounds. The paper concludes with a discussion of several other strategies for energy efficient radio broadcasting and a number of open problems in the area.