Why do hotter objects emit radiation at shorter peak wavelengths?

The observation that hotter objects emit radiation at shorter peak wavelengths is described by Wien’s displacement law, which states that the wavelength of peak emission is inversely proportional to the absolute temperature of the object.12

While this law provides the empirical relationship, Max Planck provided the theoretical explanation for why this occurs by addressing the limitations of classical physics. Classical models, such as the Rayleigh-Jeans law, incorrectly predicted that energy emission would increase infinitely at higher frequencies—a discrepancy known as the ultraviolet catastrophe.

Planck resolved this by proposing that energy is not continuous but is instead emitted in discrete "chunks" or quanta defined by the equation $E=h\nu$, where $h$ is Planck’s constant and $\nu$ is the frequency. At a given temperature, there is limited thermal energy available to produce high-frequency (short-wavelength) quanta. As the temperature increases, more thermal energy becomes available, allowing for the emission of higher-frequency, shorter-wavelength radiation, thereby shifting the peak of the spectrum.34