# 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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Kelvin
$$K$$
Celsius
$$^\circ C$$
Fahrenheit
$$^\circ F$$
$$\lambda_{peak}$$
$$um$$

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