# Black-Body Curves

### Planck's Law of Black-body Radiation:

According to Planck's law of black-body radiation, spectral energy density of radiation emitted from a black-body in \(W \over m^3\) as a function of wavelength \( \lambda \) at a temperature \(T\) in Kelvin is given by the equation: $$ R = {{2 \pi h c^2} \over \lambda^5}{1\over {e^{{hc}\diagup{k_B T}}}-1} $$ Where \(h\) is Planck's constant \(6.63 \times 10^-23\) \({Joule*second}\), \(c\) is the speed of light \({3 \times 10^8} {meter \over second}\), and \(k_B\) is Boltzmann's constant \(1.39 \times 10^{-23} {Joule \over Kelvin}\)

### Peak Wavelength from Wein's Displacement Law:

Wein's displacement law allows for calculating the peak of the radiation curve which shifts with the temperature as described in Planck's law of black-body radiation. The peak wavelength \( \lambda_{peak}\) of the black-body emission curve can be calculated by the following equation. $$\lambda{peak} = {{hc} \over x}{1 \over {k_B T}} $$ In this equation \(x\) is a constant parameter equal to \(4.965114231744276\).

*Note: Black body radiation relies on an idealized concept. In application, radiation curves may experience wavelength dependence based on material characteristics.*

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Celsius \( ^\circ C\)

Fahrenheit \( ^\circ F\)

\(\lambda_{peak} \) \(um\)

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