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The goal of this paper is to develop a unified approach to radiation conditions for the entire class of null-solutions of the Helmholtz operator which are Clifford algebra-valued. The latter is an algebraic context which permits the simultaneous consideration of scalar-valued and vector-valued functions, as well as differential forms of any mixed degree. In such a setting, we provide a multitude of novel radiation conditions which naturally contain the classical Sommerfeld and Silver-Muller radiation conditions in the case of null-solutions for the scalar Helmholtz operator and the Maxwell system respectively, and which also encompass as a particular case the radiation condition introduced by McIntosh and Mitrea for perturbed Dirac operators. Bibliography: 52 titles. Illustrations: 1 figure., UDC 517.9 The behavior at infinity is a fundamental aspect in dealing with scattering phenomena. When studying the propagation of a time-harmonic acoustic wave u, governed by the Helmholtz operator [...]