Black-body Radiation

What is a Black Body?

A black body is an idealized physical object that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. It is a perfect absorber and emitter of radiation.

In reality, no perfect black bodies exist, but some materials approximate this behavior.

Characteristics of Black-body Radiation

• Absorption: A black body absorbs all radiation that falls on it without reflecting any.
• Emission: It emits radiation at all wavelengths, with the intensity and distribution depending on its temperature.
• Temperature Dependence: The total energy emitted increases with temperature.
• Spectrum: The radiation emitted by a black body is called black-body radiation and follows a characteristic spectrum.

Variation of Intensity with Wavelength

The intensity of black-body radiation varies with wavelength and temperature. This relationship is described by Planck's Law:

$$I(\lambda, T) = \frac{2hc^2}{\lambda^5} \cdot \frac{1}{e^{\frac{hc}{\lambda kT}} - 1}$$

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
• k is Boltzmann's constant

Wien's Displacement Law

Wien's Displacement Law states that the wavelength $\lambda_{max}$ at which the emission of a black body is maximum is inversely proportional to its temperature:

$$\lambda_{max} = \frac{b}{T}$$

Where $b$ is Wien's displacement constant.

Applications of Black-body Radiation

• Solar Collectors: Designed to absorb maximum solar energy, similar to black bodies.
• Astronomy: Stars are often modeled as black bodies to determine their temperature and other properties.
• Thermal Imaging: Uses principles of black-body radiation to detect heat emitted by objects.