Planck’s Law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature
Key Points:
- Black Body: A black body is an idealized object that perfectly absorbs all electromagnetic radiation that falls on it. It also emits radiation at all wavelengths.
- Thermal Equilibrium: The body and its environment are at the same temperature. There is no net flow of energy between them.
- Spectral Density: This refers to the amount of energy emitted by the black body at different wavelengths or frequencies.
Significance:
- Quantum Theory: Planck’s Law was a groundbreaking discovery that laid the foundation for quantum mechanics. It introduced the concept of quantization of energy, meaning energy is not continuous but comes in discrete packets called quanta.
- Understanding Radiation: It helps us understand how objects emit electromagnetic radiation based on their temperature. This has applications in various fields, including astrophysics, thermal engineering, and remote sensing.
Mathematical Representation:
Planck’s Law is typically expressed as:
B(ν, T) = (2hν³/c²) * 1 / (exp(hν/k_B T) – 1)
where:
- B(ν, T) is the spectral radiance (energy emitted per unit area, per unit time, per unit solid angle, per unit frequency)
- ν is the frequency of the radiation
- T is the absolute temperature of the black body
- h is Planck’s constant
- c is the speed of light
- k_B is Boltzmann’s constant
Visual Representation:
Planck’s Law is often visualized as a series of curves, each representing the spectral radiance at a different temperature. As the temperature increases, the peak of the curve shifts to shorter wavelengths (higher frequencies), and the overall intensity of the radiation increases