Final answer:
The statement is true—electrons within an atom have quantized energy levels and cannot exist between these discrete levels. This is a fundamental concept in quantum mechanics and is crucial in understanding the behavior of electrons in atoms.
Step-by-step explanation:
Energy Levels in an Atom
The statement that energy levels cannot be in between discrete levels is true. In the concept of quantized energy, electrons within an atom can only possess certain allowed discrete energy values, and any values that exist between these discrete levels are not possible. This quantization is a fundamental principle in quantum mechanics, which suggests that just like you cannot stand between the steps of a staircase, electrons cannot exist in between the energy levels or electron shells.
Bohr's model of the hydrogen atom, although not completely accurate in representing the full complexity of atomic structure, shows that electrons must occupy specific energy levels. When we consider particles bound within a potential well, such as electrons in an atom, these particles are also restricted to certain discrete energy levels. This also applies to particles in a one-dimensional box, where their energy values are quantized and a zero kinetic energy is not allowed, meaning the particle cannot be completely at rest.
It's also important to note that energy quantization is dependent on boundary conditions; for a particle that is freely wandering and not confined, the allowed energies would be continuous. But within the confines of an atom, electrons can only reside in these discrete, quantified states, each correlated with a certain energy level.