The Planck Constant h from a Half-Wave Dipole Antenna Radiation Model

This study explores the physical origin of the Planck constant h using an electromagnetic radiation model of hydrogen. Electron–proton nutation is treated as a half-wave electric-dipole antenna. The model derives seven field modes and, after integrating the damped radiation energy over a nutation period, obtains an energy–frequency coefficient close to the Planck constant. The Planck-constant-like coefficient depends only on three fundamental constants: the elementary charge e, the speed of light c , and the vacuum permittivity. In this model, the Planck constant originates from electron–proton dipole radiation, whose power 10^-4_W is much higher than the blackbody radiation power of hydrogen 10^-10_W . The excited dipole radiates in the maximum-energy half-wave mode. Only about one seventh of the energy propagates into the far field, while the remaining fraction is absorbed by non-excited hydrogen molecules and contributes to the local temperature . These molecules then emit thermal radiation governed by T, with an effective antenna length on the scale of the electron orbital radius r ~10^-4 lamda. The large radiation-energy difference implies that a small fraction of excited molecules can provide sufficient energy to establish the average local temperature and thereby produce blackbody radiation. Our previous work[5] estimated the excitation probability as 10^-8, consistent with the high-power half-wave radiation mode proposed here.