Tru Physics

Blackbody Radiation

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Understanding Blackbody Radiation

A black body in physics is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. The radiation emitted by such a body, known as blackbody radiation, is a fundamental concept in quantum mechanics and thermodynamics.

Blackbody Radiation Spectrum

The radiation from a black body is not monochromatic—it comes in a range of frequencies. This distribution of frequencies, known as the blackbody spectrum, is characterized by a unique curve that depends only on the body’s temperature.

The blackbody radiation spectrum is given by Planck’s radiation law:

I(\nu, T) = \dfrac{8\pi h \nu^3}{c^3} \dfrac{1}{e^{\left(\frac{h\nu}{k_BT}\right)}-1}

where:

  • I(\nu, T) is the intensity of the radiation at frequency \nu and absolute temperature T,
  • h is Planck’s constant,
  • c is the speed of light,
  • k_B is Boltzmann’s constant.

Wien’s Displacement Law

As the temperature of a black body increases, the peak of the blackbody spectrum shifts to higher frequencies. This phenomenon is described by Wien’s Displacement Law:

\lambda_\text{max} = \dfrac{b}{T}

where \lambda_\text{max} is the wavelength at which the blackbody spectrum peaks, T is the absolute temperature, and b is Wien’s displacement constant.

Stefan-Boltzmann Law

The total power radiated per unit area of a black body is proportional to the fourth power of its absolute temperature. This relationship is described by the Stefan-Boltzmann law:

P = \sigma T^4

where P is the power per unit area, T is the absolute temperature, and \sigma is the Stefan-Boltzmann constant.

Significance of Blackbody Radiation

The study of blackbody radiation and the development of these laws played a key role in the development of quantum mechanics. Understanding blackbody radiation is fundamental to a variety of fields, including astronomy, climatology, and materials science.

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