The point at which materials begin to exhibit quantum effects is not determined by their size alone but rather by the characteristics of the system under consideration. Quantum effects become significant when the properties of particles or objects are governed by the laws of quantum mechanics, which occur at atomic and subatomic scales.
In general, as systems become smaller and approach the nanoscale, quantum effects become more pronounced. This is because at such scales, the behavior of particles is no longer accurately described by classical physics, but instead requires quantum mechanical principles to be properly understood.
For example, in nanoscale materials, properties like electronic behavior, energy levels, and transport phenomena can exhibit quantum effects. Quantum confinement is one such effect that arises when the dimensions of a material are comparable to the de Broglie wavelength of the particles involved (such as electrons or photons). This confinement leads to discrete energy levels and altered physical properties compared to their bulk counterparts.
However, it's important to note that the specific size at which quantum effects become dominant can vary depending on the material and the particular phenomenon being considered. Different materials and systems have different characteristic length scales at which quantum effects become prominent.