Question

For what sizes of particles and velocities must one consider quantum effects?

Answer 1

The De Broglie postulate says that the wavelength of a particle is h/mv, where "h" is Plank's constant, "m" is the mass, and "v" is the velocity. Plank's constant is extremely small, so in order for the wavelength to not get wiped out, the product of m and v must be correspondingly small. Thus, quantum effects are relevant for particles that are either very small, or moving very slowly.