The surface energy quantifies the disruption of intermolecular bond that occurs when a surface is created. The paper discusses critical size dc of mono-dispersed nanometer particle by analyzing the change of interfacial surface energy. The traditional theory neglects that the mono-dispersed nanometer particle has quantum standing wave in its internal structure with a size below critical dc. During the preparation of mono-dispersed nanometer powder, the large surface energy is formed ont only by cutting surface bond but also by forming quantum standing wave that opposites to interfacial edge unsaturated bond on the nanometer partcile surface atom. The preparation process of nanometer material needs more energy than the size surpass dc material. The new theory can explain why the melting point of nanometer powder decreases and other phenomina of nanometer material.