Final answer:
Wein's displacement law states that cooler objects emit radiation at longer wavelengths compared to hotter objects, which emit at shorter wavelengths. This is observed when a heated metal changes color, and is used in astrophysics to determine the temperatures of stars.
Step-by-step explanation:
According to Wein's displacement law, cooler objects radiate energy at longer wavelengths than hotter ones. This principle is important in understanding electromagnetic radiation across various objects in the universe, including stars. The law mathematically expresses that the product of the absolute temperature (T) of a black body and the wavelength (λ) at which it emits the most power is a constant. Hence, as the temperature of a body increases, it radiates more power at all wavelengths and the peak emission shifts to shorter wavelengths, which have a higher frequency and energy. For example, if you observe the color of a metal being heated, as it gets hotter, it changes color from red to orange to yellow, showcasing the shift to shorter wavelengths.
Given the significance of Wein's displacement law, we can conclude that Betelgeuse is cooler than Rigel, based on their radiation emission. Betelgeuse, being cooler, will emit its peak energy at a longer wavelength compared to Rigel, which is hotter and therefore emits at a shorter wavelength. This theory has practical applications in fields such as astrophysics and radio astronomy, where the law helps researchers infer the temperatures of stars and other celestial objects by examining their spectra.