Planck Radiation Calculator — Formula
## Planck's Law of Blackbody Radiation
Planck's law gives the spectral radiance of a blackbody as a function of wavelength and temperature.
### Formula
**B(lambda, T) = (2hc^2 / lambda^5) / (exp(hc / (lambda k_B T)) - 1)**
- *h* = 6.626 x 10^-34 J s
- *c* = 2.998 x 10^8 m/s
- *k_B* = 1.381 x 10^-23 J/K
This resolved the ultraviolet catastrophe and launched quantum mechanics.
Planck's law gives the spectral radiance of a blackbody as a function of wavelength and temperature.
### Formula
**B(lambda, T) = (2hc^2 / lambda^5) / (exp(hc / (lambda k_B T)) - 1)**
- *h* = 6.626 x 10^-34 J s
- *c* = 2.998 x 10^8 m/s
- *k_B* = 1.381 x 10^-23 J/K
This resolved the ultraviolet catastrophe and launched quantum mechanics.
Exemplo Resolvido
Sun (5778 K) at 500 nm (green light).
- Numerator: 2hc^2 / lambda^5
- 2 * 6.626e-34 * (2.998e8)^2 = 1.191e-16
- (5e-7)^5 = 3.125e-32
- Numerator = 1.191e-16 / 3.125e-32 = 3.811e15
- Exponent: hc/(lambda k T) = 6.626e-34 * 2.998e8 / (5e-7 * 1.381e-23 * 5778) = 4.97
- exp(4.97) - 1 = 143.6
- B = 3.811e15 / 143.6 = 2.654e13 W/m2/sr/m