Final answer:
An electron's energy within an atom being quantized means that the electron can only have certain set energy levels, with quantum numbers used to characterize these states.
Step-by-step explanation:
When we say that an electron's energy within an atom is quantized, it means that the electron can only occupy specific energy levels that are discrete and fixed. Electrons can't possess energy values that are in-between these quantized states. They can jump from one energy level to another but can't exist at a state between these levels. These energy levels can be defined by quantum numbers, which are integers that characterize an electron's state in an atom.
The concept of quantization is fundamental to quantum mechanics and was a key development from the classical understanding of energy. Such quantization was first proposed by Niels Bohr in his model of the hydrogen atom, and is important for understanding phenomena such as the emission and absorption spectrum of elements. For example, when an electron transitions between these quantized energy states, the energy emitted or absorbed will correspond to the difference in energy between these states, often observed as spectra lines.