Yes, the equation that describes the number of photons emitted by a black body as a function of wavelength and temperature is known as Planck's law. It was formulated by the physicist Max Planck in 1900 and revolutionized our understanding of the quantization of energy.
Planck's law is typically expressed in terms of the spectral radiance or spectral energy density, which represents the amount of energy radiated per unit area, per unit solid angle, and per unit wavelength. The equation for Planck's law is as follows:
B(λ, T) = (2hc²/λ^5) * (1 / (e^(hc/λkT) - 1))
Where:
- B(λ, T) represents the spectral radiance at a given wavelength (λ) and temperature (T).
- h is the Planck constant (approximately 6.62607015 × 10^-34 J·s).
- c is the speed of light in a vacuum (approximately 299,792,458 m/s).
- λ is the wavelength of the emitted radiation.
- k is the Boltzmann constant (approximately 1.380649 × 10^-23 J/K).
- T is the temperature of the black body in Kelvin.
The equation describes the distribution of photon energies across different wavelengths for a given temperature. It shows that as the temperature increases, the peak of the distribution shifts towards shorter wavelengths, meaning more high-energy photons are emitted. The quantity (hc/λkT) in the denominator of the equation plays a crucial role in determining the shape of the curve.
It's important to note that Planck's law is a theoretical equation that describes the ideal behavior of a black body, which is an object that absorbs all incident radiation and emits radiation at all wavelengths. In reality, no perfect black body exists, but Planck's law serves as a useful approximation for many real-world scenarios.