The names given to the orbital shells (s, p, d, f, etc.) are derived from historical conventions and terminology in quantum mechanics. These names originated from the spectroscopic notation used to describe the spectral lines observed in atomic spectra.
In the late 19th and early 20th centuries, scientists observed the emission and absorption spectra of elements and noticed distinct patterns of spectral lines. These lines were categorized into different series, labeled as the Balmer, Lyman, Paschen, Brackett, and Pfund series, among others. Each series represented transitions of electrons between different energy levels.
The spectral lines within these series were further categorized based on their characteristics, such as intensity and wavelength. The letter designations (s, p, d, f) were used to label different groups of lines within each series. For example, the sharp lines were labeled as "s," principal lines as "p," diffuse lines as "d," and fundamental lines as "f."
Eventually, scientists realized that these line categories corresponded to different types of orbitals within the electron shells. The s orbitals have a spherical shape, p orbitals have a dumbbell shape with three orientations (px, py, pz), d orbitals have more complex shapes with five orientations, and f orbitals have even more complex shapes with seven orientations.
Although the precise reason for the specific letter designations (s, p, d, f) is historical, they have been widely adopted and continue to be used to describe the different types of orbitals within an atom.