According to Wien's law, what is the relationship between peak wavelength and temperature?

Wien's law states that the peak wavelength of radiation emitted by a black body is inversely proportional to its absolute temperature. This can be expressed mathematically as ( \lambda_{max} T = b ), where ( \lambda_{max} ) is the peak wavelength, ( T ) is the absolute temperature in Kelvin, and ( b ) is a constant (approximately ( 2898 , \mu m \cdot K )).

This means that as the temperature of a black body increases, the peak wavelength of the emitted radiation decreases. Conversely, if the temperature decreases, the peak wavelength increases. Therefore, the relationship expressed in the correct answer, which indicates that the product of the peak wavelength and temperature is a constant value, captures this inverse relationship accurately. Understanding this principle is fundamental in astronomy, as it helps explain phenomena such as the color of stars, where hotter stars emit radiation at shorter wavelengths, appearing blue, and cooler stars emit at longer wavelengths, appearing red.