Planck's Law

on . Posted in Quantum Mechanics

Planck's law, abbreviated as B, is a fundamental physical constant that relates the energy of one photon of electromagnetic waves to the frequency of that wave used in classic mechanics and quantum mechanics.  Planck units are based on physical constants rather than human scales.  The law states that the spectral radiance (the amount of radiation emitted per unit area, per unit solid angle, per unit frequency) of a black body at a specific wavelength and temperature is proportional to the product of the frequency of the radiation and the temperature, raised to the power of -1, and multiplied by a constant known as the Planck constant


Planck's Law Formula

\(\large{ B_{f, T_a} = \frac{ 2 \; h \; c^2 }{ f^5 } \; \frac{ 1 }{ e^{ \left(\frac{ h \; c  }{ f \;k_b \; T_a }\right)  } \;-\; 1  } }\) 
Symbol English Metric
\( B_{f, T_a} \) = special radiance of a body \( lbf-ft \)  \( J \)
\( T_a \) = absolute temperature \(F\) \(K\)
\( k_b \) = Boltzmann constant \( lbf-ft \)  \( J \)
\( e \) = Euler number \( 2.718 281 828 459 045 ... \)   
\( f \) = frequency \(Hz\) \(s-1\)
\( h \) = Planck constant \(lbf-ft\;/\;sec\) \(J-s\)
\( c \) = speed of light in the medium \(ft\;/\;sec\)  \(m\;/\;s\) 


Planck's Law has several practical applications across various fields

  • Blackbody Radiation  -  Planck's law accurately describes the spectral distribution of electromagnetic radiation emitted by a blackbody at a given temperature.  This is crucial in fields like astrophysics for understanding the radiation emitted by stars and galaxies, as well as in engineering for designing and analyzing thermal systems.
  • Thermography  -  Infrared thermography relies on the principles of Planck's law to measure temperature distributions by detecting the infrared radiation emitted by objects.  This is useful in applications such as building inspections, industrial monitoring, and medical diagnostics.
  • Lighting and Display Technology  -  Understanding Planck's law helps in designing efficient lighting systems and displays.  For example, it's used in the development of LEDs (light emitting diodes) and OLEDs (organic light emitting diodes) to control the color temperature and spectral characteristics of emitted light.
  • Remote Sensing  -  Planck's law is utilized in remote sensing applications, such as satellite imaging and environmental monitoring.  By analyzing the radiation emitted or reflected by earth's surface and atmosphere, scientists can gather information about temperature, vegetation health, atmospheric composition, and more.
  • Materials Science  -  In materials science, Planck's law is employed to study the thermal properties of materials and to characterize their emissivity and absorptivity.  This knowledge is essential for applications like designing coatings for solar panels, understanding thermal insulation properties, and developing sensors for temperature measurement.
  • Climate Science  -  Understanding the radiation emitted and absorbed by gases in earth's atmosphere is crucial for climate modeling.  Planck's law helps in quantifying the energy balance between incoming solar radiation and outgoing thermal radiation, which is essential for predicting and understanding climate change.

Planck's law provides a fundamental framework for understanding and predicting the behavior of electromagnetic radiation emitted by objects at different temperatures, enabling a wide range of applications across science, engineering, and technology.  It explains a phenomena such as the black body radiation spectrum and the dependence of the color of light emitted by heated objects on their temperature.  It is a cornerstone in understanding the behavior of light and radiation at the atomic and subatomic levels.

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