Microscopic Origin of Planck’s Blackbody Radiation: Continuous Spectrum from Discrete Electron Orbital Frequencies in Iron via Thermal Modulation

Planck’s blackbody radiation theory relies on the oscillator frequency $f$, yet its microscopic origin remains elusive. This study proposes that the discrete orbital frequencies $f_{n}$ of iron (Fe) electrons, spanning 1s to 4s shells ($6.55 \times 10^{14}$ Hz to $8.88 \times 10^{17}$ Hz), serve as the physical basis for these oscillators. Using a Bohr model with effective nuclear charge, we calculate $f_{n}$ and their harmonics, demonstrating through Fourier transform analysis that thermal modulation at 3000 K ($\sigma_f \approx 6.24 \times 10^{13}$ Hz) and superposition of $10^{24}$ electrons transform these discrete frequencies into a continuous spectrum ($10^{14}$–$10^{18}$ Hz), matching Planck’s experimental range at 3000 K ($f_{\text{max}} \approx 1.76 \times 10^{14}$ Hz). Compared to lattice vibrations ($f_D \sim 10^{12}$ Hz), electron transitions ($f_X \sim 10^{18}$ Hz), and plasma oscillations ($f_p \sim 10^{14}$ Hz), our model offers broader frequency coverage and a mechanism for continuity, rooting Planck’s oscillators in iron’s electronic structure. This bridges quantum discreteness with macroscopic radiation, suggesting future validation via spectroscopy and extension to other metals.