Black Body Radiation: 17 flashcards

A black body is an idealized object that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence, and emits radiation in a characteristic, continuous spectrum that depends only on its temperature.

Black body radiation is the electromagnetic radiation emitted by a black body in thermal equilibrium with its surroundings. Its spectral distribution depends only on the body's temperature.

It refers to the fact that the body absorbs all incident radiation, making it appear black at low temperatures. At higher temperatures, it emits visible radiation, but the name remains.

It is continuous and depends only on temperature, not on the material or shape of the body.

The total energy emitted per unit surface area per unit time is proportional to the fourth power of the absolute temperature (Stefan-Boltzmann law: $E \propto T^4$).

It states that the total power radiated per unit area of a black body is given by $P = \sigma A T^4$, where $\sigma$ is the Stefan-Boltzmann constant ($5.67 \times 10^{-8} \, \text{W m}^{-2} \text{K}^{-4}$), $A$ is the surface area, and $T$ is the absolute temperature.

It states that the wavelength at which the emission intensity is maximum is inversely proportional to the temperature: $\lambda_{\max} = \frac{b}{T}$, where $b$ is Wien's displacement constant ($2.898 \times 10^{-3} \, \text{m K}$).

It shifts to shorter wavelengths (higher frequencies).

It describes the spectral energy density of black body radiation: $u(\lambda, T) = \frac{8\pi h c}{\lambda^5} \frac{1}{e^{hc/(\lambda k_B T)} - 1}$, where $h$ is Planck's constant, $c$ is the speed of light, $k_B$ is Boltzmann's constant, $\lambda$ is wavelength, and $T$ is temperature.

It was the failure of classical physics (Rayleigh-Jeans law) to predict the observed black body spectrum, as it predicted infinite energy at short wavelengths. Planck's quantum hypothesis resolved this by quantizing energy.

Planck's constant ($h = 6.626 \times 10^{-34} \, \text{J s}$) is the fundamental quantum of action. It appears in the Planck formula and represents the quantization of energy, which was a key step in the development of quantum mechanics.

Emissivity is the ratio of the radiation emitted by a surface to the radiation emitted by a black body at the same temperature. For a perfect black body, emissivity is exactly 1.

A small hole in a cavity (like a box with a tiny opening) acts as a black body because any radiation entering the hole is trapped and absorbed after multiple reflections, and the radiation emitted from the hole is characteristic of the cavity's temperature.

A black body is a perfect absorber and a perfect emitter. At thermal equilibrium, the rate of absorption equals the rate of emission, and the emitted spectrum depends only on temperature.

At low temperatures (e.g., room temperature), it emits infrared radiation (invisible). As temperature increases, it glows red, then orange, yellow, white, and eventually blue-white at very high temperatures.

It led to the development of quantum mechanics, as Planck's explanation of the spectrum introduced the concept of energy quantization. It also helps explain phenomena like the cosmic microwave background radiation and the spectra of stars.

It is the black body radiation left over from the Big Bang, with a temperature of about 2.725 K. Its spectrum matches a perfect black body, providing strong evidence for the Big Bang theory.