The radio antipodal number of a graph G is the smallest integer c such that there exists an assignment f : V (G) → {1, 2, . . . , c} satisfying |f(u) − f(v)| ≥ D − d(u, v) for every two distinct vertices u and v of G, where D is the diameter of G. In this note we determine the exact value of the antipodal number of the path, thus answering the conjecture given in [G. Chartrand, D. Erwin and P. Zhang, Math. Bohem. 127 (2002), 57– 69]. We also show the connections between this colouring and radio labelings.