Final answer:
The energy, radius and velocity of an electron are quantized according to de Broglie's wave theory, which explains the existence of discrete orbits in atoms due to the requirement of standing waves and constructive interference within permitted orbits.
Step-by-step explanation:
When an electron in an atom is treated as a de Broglie wave, what is quantized includes: The energy of the electron, the radius of the orbit, and the velocity of the electrons. The wave nature of matter, as proposed by de Broglie, suggests that electrons can exist only in orbits where they interfere constructively with themselves, leading to quantization. This constructive interference implies that not all orbits are permissible, but only those where the electron's de Broglie wavelength allows for standing waves on a quantized scale.
Therefore, all of these aspects (energy, radius of the orbit, and velocity of the electrons) are quantized. Bohr's model suggested quantization of energy and radii, while de Broglie's wave theory provided the rationale for WHY these quantities are discretely valued, through the concept of standing waves and constructive interference in orbitals.