Planck's Law

Definition

Planck's Law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature. This law is significant because it provides a formula to calculate the intensity of radiation emitted at different wavelengths, fundamentally linking the concepts of temperature, energy quantization, and radiation.

5 Must Know Facts For Your Next Test

1. Planck's Law introduces the concept of quantized energy levels, suggesting that electromagnetic radiation is emitted in discrete packets called quanta or photons.
2. The formula for Planck's Law is given by $$I(\lambda, T) = \frac{2\pi hc^2}{\lambda^5} \cdot \frac{1}{e^{\frac{hc}{\lambda kT}} - 1}$$, where I is the intensity, $$\lambda$$ is the wavelength, T is the absolute temperature, h is Planck's constant, c is the speed of light, and k is Boltzmann's constant.
3. As the temperature increases, the peak wavelength of emitted radiation shifts towards shorter wavelengths, which is described by Wien's displacement law.
4. Planck's Law resolved the ultraviolet catastrophe by demonstrating that high-frequency radiation does not emit infinite energy, as previously thought in classical physics.
5. This law forms the foundation for understanding black body radiation and has wide applications in fields like astrophysics and thermal imaging.

Review Questions

• How does Planck's Law explain the relationship between temperature and radiation emitted by a black body?
  • Planck's Law illustrates that as the temperature of a black body increases, the intensity of radiation it emits also increases across all wavelengths. The law also states that the peak wavelength of emitted radiation decreases with increasing temperature, indicating that hotter bodies emit more radiation at shorter wavelengths. This means a hotter black body will emit more ultraviolet light compared to one at a lower temperature, thus showing a direct connection between temperature and spectral emission.
• Discuss how Planck's Law addresses the limitations of classical physics in explaining black body radiation.
  • Classical physics predicted that a black body would emit infinite energy at high frequencies, leading to what was termed the 'ultraviolet catastrophe.' Planck's Law corrected this by introducing the idea of quantization of energy, indicating that energy is emitted in discrete packets or quanta. This shift from classical to quantum concepts not only explained observed phenomena but also laid the groundwork for modern physics.
• Evaluate the impact of Planck's Law on modern physics and its implications for our understanding of quantum theory.
  • Planck's Law marked a pivotal shift in our understanding of energy and matter, leading to the birth of quantum theory. By establishing that energy levels are quantized, it challenged classical ideas and paved the way for subsequent developments such as quantum mechanics and statistical mechanics. The implications are vast; they not only enhance our understanding of black body radiation but also have profound effects on fields like thermodynamics and quantum field theory, influencing how we interpret interactions at atomic scales.

Related terms

Black Body: An idealized physical object that absorbs all incoming radiation and re-emits energy as thermal radiation based on its temperature.

Quantum Mechanics: A branch of physics that deals with the behavior of matter and energy at atomic and subatomic scales, emphasizing quantization.

Stefan-Boltzmann Law: A law stating that the total energy radiated per unit surface area of a black body is proportional to the fourth power of its absolute temperature.