The quantization of the electron energy inside an atom explains much of the behavior of atoms such as why atoms emit only discrete frequencies of light. An electron in a low orbit of an atom will absorb a photon causing the electron to jump to a higher orbit and then emits a photon jumping back to the lower orbit.
The quantization of space-time has its bases in two of Max Planck’ natural units that are based on five universal physical constants: Gravitational constant, Reduced Planck constant, Speed of light in a vacuum, Coulomb constant, and Boltzmann's constant The two with physical significance are Planck Length and Planck Time are the smallest possible measurements of space-time according our current understanding of the laws of Physics because of the uncertainty principle when a plied to these scales. This suggests that time and space themselves are Quantized. The smallest measurement of length that has any meaning with in the laws of physics as we understand them today is called Planck Length and it has a value of 1.616 252 × 10−35 m. The amount of time it takes a photon to cross a Planck Length. It is the smallest measurement of time that has any meaning with in the laws of physics as we understand them today is called Planck Time with a value of 5.391 24 × 10−44 s.
Quantization requires physical quantities like position, energy and momentum to have discrete values explaining much of what goes on in side atom and based on our current understanding of the laws of physics it suggest that time and space are quantized.