Atomic theory or the nature of matter is a principal concept in science and science education. This has, however, been complicated by the difficulty students have in learning the concept and the subsequent construction of many alternative models. To understand better the conceptual barriers to learning atomic structure, this study explores the troublesome nature of this fundamental scientific concept. In order to illustrate the distinction of student understanding by threshold barriers, this study chose three particularly high-achieving students from an original interview sample of 20 students who were selected from an introductory college chemistry course. The pre-course and post-course interview responses were examined and compared in detail. This study considers the concepts of "probability" and "energy quantization" to both describe the structure of the threshold of understanding students' need to negotiate in their construction of the target model of atomic structure. In this respect, this study suggests atomic structure as a possible threshold concept for further study in science. Identifying the nature and structure of the threshold of understanding confronting students, and analyzing the troublesomeness of atomic structure, provides valuable information for understanding student learning difficulties, and insight into how they may be addressed. (Contains 3 tables and 7 figures.)