Understanding Wien’s Displacement Law

Usefulness in Physics and Astronomy

Wien’s displacement law is a fundamental principle in the study of blackbody radiation. A blackbody is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle, and emits thermal radiation. Wien’s law describes the relationship between the absolute temperature (\(\mathbf{T}\)) of a blackbody and the wavelength (\(\mathbf{\lambda_{\text{max}}}\)) at which it emits the most radiation.

In Astronomy, this law is indispensable. By measuring the peak wavelength of light emitted by a star, astronomers can accurately determine its surface temperature. For instance, a blue star peaks at a shorter, hotter wavelength, while a red star peaks at a longer, cooler wavelength. It directly links an observable property (color/wavelength) to a fundamental property (temperature).

The Main Formula

$$\lambda_{\text{max}} = \frac{b}{T}$$

Where:

• \(\mathbf{\lambda_{\text{max}}}\) = peak wavelength (measured in meters, \(\text{m}\))
• \(\mathbf{T}\) = absolute temperature (measured in Kelvin, \(\text{K}\))
• \(\mathbf{b}\) = Wien’s displacement constant, which is approximately \(2.8976 \times 10^{-3} \ \text{m·K}\) (Giá trị cập nhật)

How to Use the Calculator

1. Decide what you are calculating: You can either find the Peak Wavelength (\(\lambda_{\text{max}}\)) or the Absolute Temperature (\(T\)).
2. Enter a single value: Input the known value into the corresponding field (\(\lambda_{\text{max}}\) in meters or \(T\) in Kelvin).
3. Crucially, leave the other field empty. The calculator must have only one input to perform the operation.
4. Click “Calculate Result”: The calculated value will appear in the result box.
5. Click “Clear Inputs”: Use this button to reset both fields for a new calculation.