why are the orbitals of the hydrogen atom described as probability maps? Why are the edges of the hydrogen orbitals sometimes drawn to appear "fuzzy"?
Truth be known, they are drawn to be fuzzy because we really don't know EXACTLY where they are. It is best if we describe the probability of an electron being within that range. In fact, the whole idea of orbits and sub-orbits (orbitals) is a carry over from the old days of Bohr, Sommerfeld, Rydberg, Balmer, etc. Wave mechanics comes the closest we have today to describing an atom and students (and many professors) simply don't have the math background to engage in a discussion using wave mechanics. So we rely on the picture method instead.
The orbitals of the hydrogen atom are described as probability maps because they represent the regions in space where an electron is most likely to be found. According to the principles of quantum mechanics, electrons do not have well-defined paths or trajectories, but rather exist as a wave of probabilities.
The edges of the hydrogen orbitals are sometimes drawn to appear "fuzzy" in order to illustrate the uncertainty associated with finding an electron at a specific location. In reality, the electron's position is not fixed or defined, but rather exists as a spread-out cloud around the nucleus. The fuzzy edges represent the decreasing probability of finding an electron as you move further away from the nucleus. These drawings help visualize the concept that electrons are both particles and waves, and they exist in a state of superposition, occupying multiple positions simultaneously until they are observed.
The orbitals of the hydrogen atom are described as probability maps because they represent the areas around the nucleus where an electron is most likely to be found. These maps show the probability distribution of finding an electron at a particular location in space.
The fuzzy edges or blurred appearance of hydrogen orbitals in visual representations arise due to the inherent uncertainty of electron position in quantum mechanics. According to Heisenberg's Uncertainty Principle, it is impossible to simultaneously know the exact position and momentum of an electron. Therefore, instead of discrete paths or defined boundaries, orbitals are represented as regions extending into space where the probability of finding an electron is relatively higher.
In quantum mechanics, the wave-like behavior of electrons is described by mathematical functions called wavefunctions. The square of the wavefunction, known as the probability density, gives the probability of finding an electron in a particular region of space. The contours or isosurfaces of constant probability density are then used to represent the orbitals, with higher probability densities represented by closer contours.
It is important to note that the fuzzy edges do not signify an actual physical boundary where the electron ends, but rather represent a decreasing probability of finding the electron. The electron can exist anywhere within the orbital, but the probability becomes progressively lower as you move away from the densest parts of the orbital towards the fuzzy edges.