The quantization of an electron's charge and its ability to exhibit interference in experiments like Young's double-slit experiment are both consequences of the wave-particle duality of quantum mechanics.
In the context of Young's double-slit experiment, when electrons are fired one by one toward a barrier with two slits, they behave as both particles and waves. Each electron can pass through both slits simultaneously and interfere with itself, resulting in an interference pattern on a screen placed behind the barrier.
The key point to understand is that the quantization of charge refers to the fact that the charge of an electron is always observed to be a multiple of the elementary charge, denoted as "e." The elementary charge is the fundamental unit of electric charge and is equal to approximately 1.6 x 10^(-19) coulombs.
Interference, on the other hand, arises from the wave-like nature of particles, including electrons. The wave function associated with the electron describes its probability amplitude distribution, which determines the likelihood of finding the electron at different positions.
In the double-slit experiment, the wave function of an electron is split into two components as it passes through the slits. These two components interfere with each other, resulting in regions of constructive and destructive interference on the screen. The interference pattern arises due to the wave-like nature of the electron, and it is a characteristic behavior observed in experiments with particles exhibiting wave-particle duality.
The quantization of charge does not directly affect the interference pattern observed in the experiment. The quantization of charge simply means that the charge of an electron is always found to be a multiple of the elementary charge. The interference pattern, however, arises due to the wave-like behavior of the electron, described by its wave function.
So, in Young's double-slit experiment, the interference pattern arises from the wave nature of the electron, while the quantization of charge is a separate property observed in all experiments involving electrons. Both aspects are consequences of the fundamental principles of quantum mechanics.