What is Wien's displacement law?

Wien's displacement law states that the peak wavelength of radiation emitted by a black body is inversely proportional to its temperature.

Wien's displacement law helps us understand how the colour of light emitted by an object changes with its temperature. A black body is an idealised object that absorbs all radiation falling on it and re-emits it perfectly. According to this law, as the temperature of a black body increases, the wavelength at which it emits the most radiation decreases. This means that hotter objects emit light at shorter wavelengths, which corresponds to higher energy.

The mathematical expression for Wien's displacement law is given by the formula: \(\lambda_{\text{max}} = \frac{b}{T}\), where \(\lambda_{\text{max}}\) is the peak wavelength, \(T\) is the absolute temperature in Kelvin, and \(b\) is Wien's constant, approximately equal to \(2.898 \times 10^{-3} \text{ m K}\). This formula shows that if you double the temperature of a black body, the peak wavelength of the emitted radiation will be halved.

For example, the Sun, with a surface temperature of about 5,800 K, emits most of its radiation in the visible spectrum, which is why it appears white or yellow to us. On the other hand, a cooler object like a red-hot piece of metal, which might be around 1,000 K, emits most of its radiation in the infrared spectrum, making it appear red.

Understanding Wien's displacement law is crucial in various fields, including astrophysics and climate science, as it helps scientists determine the temperatures of stars and other celestial bodies by analysing the light they emit.