Unveiling Temperature of the Cosmic Microwave Background Radiation Via Plank's Formula

From the late 19th century to the early 20th century, blackbody radiation theory lies at the intersection of quantum mechanics and thermodynamics, with its formulation revealing the quantum nature of energy. It resolves the contraction of ultraviolet catastrophe and establishes the functional relationship between the radiation spectrum and temperature. This paper systematically deduces Planck's blackbody radiation law and its inferences, and uses the blackbody radiation formula to invert the cosmic microwave background radiation. Combining theoretical derivation and the extraction of references and observational data, data fitting is achieved through the inversion of multi-spectrum blackbody spectral distribution. The applicability of Wien's displacement law was verified at the theoretical level, and the cosmic microwave background radiation was derived. The blackbody radiation formula and the cosmic microwave background radiation provide benchmarks for cosmological models, supporting the calculation of various parameters and critical temperatures. In the future, perhaps more energy release mechanisms of the early universe can be explored.