Understanding students' prior beliefs in nuclear physics is a first step towards improving nuclear physics instruction. This paper describes the development of a diagnostic survey in nuclear physics covering the areas of radioactive decay, binding energy, properties of the nuclear force and nuclear reactions, that was administered to students at two institutions in a pre- and post-test design. The pre-test was given in a free-text entry format, with responses being used to develop a multiple-choice version that was given as a post-test. We performed statistical tests to evaluate the reliability and discriminatory power. Students' reasoning comments and rated certainties in their responses were used to determine students' misconceptions. We give details of misconceptions in the areas of radioactive decay, binding energy and nuclear density, and discuss possible underlying reasons for these misconceptions.