Why can't an atom's electrons ever be located between orbits?

At the core of quantum mechanics is the concept that electrons (and other particles) exhibit both wave-like and particle-like properties. This is described by the de Broglie wavelength, which is given by the equation: \[\lambda = \frac{h}{p}\] where \(\lambda\) is the wavelength, \(h\) is the Planck's constant (\(6.63\times10^{-34} \text{J s}\)), and \(p\) is the momentum of the particle. The wave-particle duality of electrons is central to understanding why they cannot exist between orbits in an atom.

Energy quantization is the idea that electrons in atoms can only occupy specific, discrete energy levels, which are called orbits or energy shells. These orbits are related to the wave nature of electrons. According to wave-particle duality, electrons in an atom can be represented as standing waves. For an electron to form a stable standing wave around the nucleus of an atom, its wave must have an integer number of wavelengths (\(n\)) to form a closed loop. This requirement is known as the quantization condition: \[2\pi r = n\lambda\] The allowed energy levels of an electron in an atom depend on the quantization condition. Therefore, only certain energy levels are allowed while other energy levels are not, leading to the quantization of energy levels in the atom.

Electrons in an atom are limited to specific quantized energy orbits due to their wave-like nature and the quantization condition. They cannot exist in energy states between these quantized levels. When electrons move between these quantized orbits, they do so by "quantum leaps" - making instantaneous transitions between orbits without occupying any of the energy levels in between. Consequently, electrons cannot be located between these quantized orbits. In summary, electrons cannot be found between orbits in an atom due to the following reasons: 1. The wave-particle duality of electrons and their wave-like nature 2. The quantization condition that leads to specific, discrete energy levels in the atom 3. Quantum leaps that allow electrons to transition between orbits without occupying energy levels in between