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Physical Science:

Subsection 7.1.1 Blackbody Radiation

A blackbody in physics describes an ideal object which can absorb all electromagnetic radiation that falls on it, at any wavelengths. Because it absorbs all frequencies of light, a perfect blackbody would appear completely black to the human eye. While perfect blackbodies don’t exist in nature, the concept is very useful in understanding how real objects emit and absorb radiation. It is our experience that when a metal rod is heated, it turns red at low temperature, then as the temperature increases its color changed into orange, yellow, white, and blue. Stars are often approximated as blackbodies, which helps us understand how they radiate light at different temperatures.
Blackbody radiation is the theoretical description of the electromagnetic radiation emitted by a perfect blackbody, which is an object that absorbs all radiation falling on it and reflects none. In 1900, Max Planck proposed a theoretical model to explain the spectral distribution of blackbody radiation, which was in agreement with experimental observations. Planck’s model proposed that energy is emitted and absorbed in discrete packets, called quanta, rather than continuous. Quanta is the plural form of quantum (in Latin, quantum means how much). The higher the frequency of the light, the more the energy per quantum. This was a major departure from classical physics and marked the beginning of quantum mechanics. Planck’s work laid the foundation for the understanding of the nature of light and electromagnetic radiation and has had a profound impact on modern physics. The study of blackbody radiation helps understand the nature of heat and light.
Figure 7.1.2. Blackbody Radiation
The blackbody radiation plot shows the spectral distribution of the electromagnetic radiation emitted by a blackbody as a function of wavelength or frequency. The plot is typically represented as a curve that shows the intensity of the radiation emitted at each wavelength or frequency. The shape of the blackbody radiation curve depends on the temperature of the blackbody. At low temperatures, the curve peaks at longer wavelengths in the infrared region. As the temperature increases, the peak of the curve moves towards shorter wavelengths, and at high temperatures, the peak is in the ultraviolet region. The blackbody radiation plot is an important tool for understanding the nature of heat and light. Figure 7.1.2 shows how the brightness of the light varies with wavelength emitted by the objects at four different temperatures. It has been observed that all objects radiate electromagnetic radiation and the strongest wavelength depends on its temperature. The higher the temperature of the body, the shorter the brightest wavelength (or, the higher the frequency). For example, a hot iron bar that glows yellow is hotter than one that glows red. For an object at room temperature, most of the radiation emits in infrared region and hence is invisible.
According to Plank the energy emited in radiation is given by
\begin{equation} E = h f = \frac{hc}{\lambda}\tag{7.1.1} \end{equation}
Here \(E\) is quantum of energy, \(h =6.63\times 10^{-34} J \cdot s\) is Planck’s constant,, \(c = 3\times 10^{8}\) m/s is a velocity of light, \(\lambda\) is a wavelength of light, and \(f\) is frequency of light.
Planck described that at higher frequency the quanta were less likely excited so the average energy would decrease with the frequency. The exact expression for the average energy of each quanta is given as
\begin{equation*} E = \frac{hf}{exp(hf/KT)-1}. \end{equation*}

Example 7.1.3.

Find the energy of a photon emitted from a red light of frequency \(5.00\times 10^{14} Hz\text{.}\)
Solution.
From equation (7.1.1), we have
\begin{align*} E \amp = hf \\ or, \quad E \amp = 6.63\times 10^{-34} (\,Js) \times 5.00\times 10^{14} (1/s) \\ \therefore E \amp = 3.32\times10^{-19} \,J \end{align*}