A blackbody spectrum refers to the electromagnetic radiation emitted by a perfect blackbody, which is an idealized object that absorbs all incoming radiation and reflects none. When a blackbody is heated, it emits radiation across a range of wavelengths. The characteristics of this emitted radiation depend on the temperature of the blackbody.
Key Points of a Blackbody Spectrum:
- Continuous Spectrum: A blackbody emits radiation across a continuous range of wavelengths (or frequencies), without any gaps or lines. This radiation includes visible light, infrared, ultraviolet, and other forms of electromagnetic radiation.
- Wien’s Displacement Law: The wavelength at which the emission of radiation is most intense shifts to shorter wavelengths as the temperature increases. Mathematically, this is given by the formula: λmax=bT\lambda_{\text{max}} = \frac{b}{T} where:
- λmax\lambda_{\text{max}} is the wavelength at which the radiation is most intense.
- bb is Wien’s displacement constant (approximately 2.898 × 10⁻³ m·K).
- TT is the absolute temperature of the blackbody in Kelvin.
- Stefan-Boltzmann Law: The total energy radiated by a blackbody per unit surface area is proportional to the fourth power of its temperature: E=σT4E = \sigma T^4 where:
- EE is the total energy emitted per unit area.
- σ\sigma is the Stefan-Boltzmann constant (approximately 5.67 × 10⁻⁸ W·m⁻²·K⁻⁴).
- TT is the absolute temperature.
- Planck’s Law: The spectral distribution of radiation emitted by a blackbody as a function of wavelength (or frequency) is described by Planck’s law. It shows how the intensity of radiation varies with wavelength at a given temperature. The law is: I(λ,T)=2hc2λ5⋅1ehcλkT−1I(\lambda, T) = \frac{2hc^2}{\lambda^5} \cdot \frac{1}{e^{\frac{hc}{\lambda k T}} – 1} where:
- I(λ,T)I(\lambda, T) is the intensity at wavelength λ\lambda and temperature TT.
- hh is Planck’s constant.
- cc is the speed of light.
- kk is Boltzmann’s constant.
- λ\lambda is the wavelength of the radiation.
- TT is the temperature of the blackbody.
The resulting spectrum is a smooth curve, with the intensity increasing as the temperature increases and the peak of the spectrum shifting to shorter wavelengths.
A real-world example of blackbody radiation is the radiation emitted by stars, including our Sun. The Sun emits a spectrum of light that is close to that of a blackbody at around 5,778 K, and the spectrum is visible light mixed with infrared and ultraviolet radiation.