Planck's Law

Definition

Planck's Law describes the electromagnetic radiation emitted by a black body in thermal equilibrium at a definite temperature. It states that the intensity of radiation emitted at a given frequency is proportional to the frequency and inversely proportional to the wavelength, resulting in a spectrum that peaks at a particular wavelength based on the temperature of the black body. This law is foundational for understanding how matter interacts with light, especially in optical absorption and emission processes.

5 Must Know Facts For Your Next Test

1. Planck's Law shows that as the temperature of a black body increases, the peak wavelength of emitted radiation shifts to shorter wavelengths, known as Wien's Displacement Law.
2. The law introduces the concept of quantization, stating that energy is emitted or absorbed in discrete packets called quanta or photons.
3. At lower temperatures, a black body emits primarily in the infrared spectrum, while at higher temperatures it emits more in the visible spectrum.
4. Planck's Law was pivotal in leading to the development of quantum mechanics, addressing the ultraviolet catastrophe predicted by classical physics.
5. The mathematical expression for Planck's Law includes constants like Planck's constant (h), speed of light (c), and Boltzmann's constant (k), illustrating their roles in thermal radiation.

Review Questions

• How does Planck's Law relate to the behavior of black bodies at different temperatures?
  • Planck's Law explains how black bodies emit radiation depending on their temperature. As the temperature increases, the intensity of emitted radiation rises and shifts towards shorter wavelengths. This relationship is quantified through Wien's Displacement Law, which states that the peak wavelength decreases as temperature increases. Therefore, a hotter black body will emit more visible light compared to a cooler one that primarily radiates in the infrared region.
• Evaluate how Planck's Law addresses discrepancies found in classical physics regarding black body radiation.
  • Planck's Law resolved issues known as the ultraviolet catastrophe, where classical physics predicted an infinite amount of energy would be emitted at short wavelengths. Instead, Planck introduced quantization, proposing that energy is emitted in discrete amounts (quanta) rather than continuously. This breakthrough laid the groundwork for quantum mechanics and provided a more accurate description of thermal radiation, aligning theoretical predictions with experimental observations.
• Synthesize how Planck's Law influences modern technology related to optical absorption and emission.
  • Planck's Law has profound implications for modern technology, particularly in fields like photovoltaics and LED technology. By understanding how materials absorb and emit radiation at different wavelengths based on temperature, engineers can design more efficient solar cells that optimize light absorption and improve emission properties in light sources. Additionally, this understanding aids in developing sensors and imaging devices that rely on precise control over light-matter interactions, showcasing how foundational concepts in physics translate into practical applications.

Related terms

Black Body: An idealized physical object that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence, and re-emits that energy as thermal radiation.

Quantum Theory: A fundamental theory in physics that describes the physical properties of nature at the scale of atoms and subatomic particles, which underpins Planck's Law and the concept of quantized energy levels.

Photons: Elementary particles that are the quantum of electromagnetic radiation, including light, which can be absorbed or emitted by materials as described by Planck's Law.