Final answer:
The wave nature of matter causes quantization in bound systems such as atoms and molecules. Confined particles have allowed wavelengths that fit into the small space they occupy, leading to discrete energy levels. This wave nature prevents the collapse of matter and gives atoms their sizes.
Step-by-step explanation:
The wave nature of matter causes quantization in bound systems such as the atom. When a particle is confined or bound to a small space, its allowed wavelengths are those which fit into that space. For example, in the particle in a box model, a particle is free to move in a small space surrounded by impenetrable barriers.
This wave nature of matter and the quantization of energy levels in bound systems prevent the collapse of matter and give atoms their sizes. Only those states where matter interferes constructively exist, or are 'allowed', resulting in discrete energy levels.
Examples of bound systems in which the wave nature of matter and quantization are observed include atoms, molecules, and blackbody radiators. In larger systems, quantization becomes less evident as there are more possibilities for the tiny particle waves to fit into the available space.