Abstract

The electron is found at discrete energy levels within the atom, transition between these levels is considered to involve a `jump' rather than via a continuous motion. If we simulate the transition in the H atom as a series of individual steps, with each step the frequency of the electron, we can map a semi-continuous transition (from n=1 to n=2 requires about 1887860 steps, transition period a function of the photon wavelength). Plotting the electron from n=1 to ionization traces a hyperbolic spiral, the significance being that at specific spiral angles, the angle components cancel returning an integer value for the radius (360°=4r, 360+120°=9r, 360+180°=16r, 360+216°=25r ... 720°). If we set initial radius r = Bohr radius, then we can use the spiral perimeter to calculate the transition frequencies at these angles. As these spiral angles correlate the energy level Bohr radii directly with pi, we may ask if quantization of the atom has a geometrical origin. Furthermore, the closer the vicinity of the electron to the proton, the greater the divergence from the idealized value suggesting the electron maybe causing a distortion within the proton internal structure.