Planck's Law

Definition

Planck's Law describes the electromagnetic radiation emitted by a black body in thermal equilibrium at a definite temperature. It explains how the intensity of radiation emitted at different wavelengths varies with temperature, leading to the concept that energy is quantized and emitted in discrete packets called photons. This law is foundational in understanding black body radiation and plays a crucial role in quantum mechanics and thermodynamics.

5 Must Know Facts For Your Next Test

1. Planck's Law introduces the concept of quantization of energy, stating that energy is emitted or absorbed in discrete amounts, which are integer multiples of a fundamental unit.
2. The law can be expressed mathematically as $$I(\lambda, T) = \frac{2hc^2}{\lambda^5} \cdot \frac{1}{e^{\frac{hc}{\lambda kT}} - 1}$$, where $$I$$ is the intensity of radiation, $$\lambda$$ is the wavelength, $$T$$ is the absolute temperature, and $$h$$ is Planck's constant.
3. As temperature increases, the peak wavelength at which radiation is emitted shifts to shorter wavelengths, a phenomenon described by Wien's Displacement Law.
4. Planck's Law successfully resolved the ultraviolet catastrophe predicted by classical physics, providing an accurate description of black body radiation across all wavelengths.
5. This law laid the groundwork for the development of quantum theory and has profound implications for modern physics, influencing fields such as thermodynamics and astrophysics.

Review Questions

• How does Planck's Law explain the relationship between temperature and the spectral distribution of emitted radiation?
  • Planck's Law establishes that as the temperature of a black body increases, it emits more radiation across all wavelengths but shifts the peak emission to shorter wavelengths. This means that hotter objects not only emit more total energy but also change the characteristics of that energy distribution. The law quantitatively describes this shift and is essential for understanding thermal radiation phenomena.
• In what ways did Planck's Law resolve issues present in classical physics regarding black body radiation?
  • Classical physics predicted that a black body would emit an infinite amount of energy at short wavelengths, known as the ultraviolet catastrophe. Planck's Law addressed this by introducing quantized energy levels, demonstrating that energy is emitted in discrete packets (photons), thus preventing infinite emission. This breakthrough was pivotal in shifting scientific understanding towards quantum mechanics.
• Evaluate the impact of Planck's Law on modern physics and its significance in areas beyond thermodynamics.
  • Planck's Law significantly impacted modern physics by providing critical insights into quantum mechanics and thermodynamics. Its introduction of quantization has influenced various fields such as astrophysics, where it aids in understanding stellar emissions, and materials science, affecting how we interpret light-matter interactions. The implications extend to technologies like lasers and semiconductors, showcasing how foundational principles can lead to groundbreaking 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 radiation based on its temperature.

Photon: A quantum of electromagnetic radiation, which can be thought of as a particle representing a discrete unit of light or other electromagnetic energy.

Quantum Mechanics: The branch of physics that deals with the behavior of matter and energy at very small scales, typically atomic and subatomic levels, where classical physics does not apply.