# Planck's Law

on . Posted in Relativity

Planck's law, also known as the Planck radiation law, describes the spectral distribution of electromagnetic radiation emitted by a black body at a given temperature.  It provides a mathematical formula that relates the intensity of radiation at different wavelengths or frequencies to the temperature of the black body.   Planck's law explains how the energy of electromagnetic radiation emitted by a black body is distributed over different wavelengths or frequencies at a specific temperature.  It accounts for the observed phenomenon of black body radiation and played a pivotal role in the development of quantum mechanics.

Planck's law has broad applications in various fields, including astrophysics, thermal radiation, and the study of the cosmic microwave background radiation.  It provides a foundation for understanding the behavior of light and radiation emitted by objects at different temperatures, as well as the concept of quantization of energy associated with electromagnetic radiation.

## Planck's Law Formula

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