In 1893, 29-year-old German physicist Wilhelm Wien (1864–1928) published a paper in Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften zu Berlin titled “Eine neue Beziehung der Strahlung schwarzer Körper zum zweiten Hauptsatz der Wärmetheorie”.
Wien derived Wien’s Displacement Law, proving that the peak emission wavelength ($\lambda_{\text{max}}$) of blackbody radiation is inversely proportional to absolute thermodynamic temperature ($T$).
Derivation of Wien’s Displacement Law¶
Wien applied adiabatic compression to a photon gas inside a spherical cavity with perfectly reflecting walls undergoing Doppler shift:
$$\lambda_{\text{max}} \cdot T = b$$
Where:
- $\lambda_{\text{max}}$ is peak emission wavelength ($\text{meters}$).
- $T$ is absolute temperature ($\text{Kelvin}$).
- $b = 2.897771955 \dots \times 10^{-3}\,\text{m}\cdot\text{K}$ is Wien’s Displacement Constant.
Physical Significance¶
As a body is heated, its blackbody radiation spectrum shifts toward shorter wavelengths (higher frequencies):
- Room Temperature ($300\,\text{K}$): Peak in far-infrared ($\lambda_{\text{max}} \approx 9.6\,\mu\text{m}$).
- Glowing Red Metal ($1000\,\text{K}$): Peak in near-infrared ($\lambda_{\text{max}} \approx 2.9\,\mu\text{m}$).
- Solar Photosphere ($5778\,\text{K}$): Peak in visible green light ($\lambda_{\text{max}} \approx 500\,\text{nm}$).
Nobel Prize in Physics (1911)¶
Wien was awarded the 1911 Nobel Prize in Physics for his laws governing thermal radiation.
In quantum mechanics, Wien’s displacement constant $b$ is derived directly from Max Planck’s quantum law by setting $d u(\lambda) / d\lambda = 0$:
$$b = \frac{h c}{x k_{\text{B}}} \quad \text{where } x \approx 4.965114$$
Key Takeaways¶
- Year: 1893
- Key Figure: Wilhelm Wien (German Physicist)
- Core Discovery: Formulated Wien’s Displacement Law ($\lambda_{\text{max}} T = b$).
- Nobel Laureate: Awarded the 1911 Nobel Prize in Physics.
- Quantum Relevance: Derived by Max Planck directly from quantum constants ($h, c, k_{\text{B}}$).