The Baer construction of the prime radical is a well-known concept in ring theory. It shows that the prime radical of an arbitrary ring is the union of the chain of ideals of the ring, constructed by transfinite induction, which starts with the zero ideal and ends with the prime radical. This construction is a fundamental tool in the study of prime ideals and their properties. In this research activity, we aim to investigate the termination of the Baer construction, which is a crucial aspect of understanding the prime radical and its behavior in various rings. We will explore the conditions under which the Baer construction terminates and the implications of this termination on the prime radical and its properties.