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In addition to the revision notes for Thermal Radiation. Photon as the Quantum of Light on this page, you can also access the following Modern Physics learning resources for Thermal Radiation. Photon as the Quantum of Light
| Tutorial ID | Title | Tutorial | Video Tutorial | Revision Notes | Revision Questions | |
|---|---|---|---|---|---|---|
| 19.1 | Thermal Radiation. Photon as the Quantum of Light |
In these revision notes for Thermal Radiation. Photon as the Quantum of Light, we cover the following key points:
In classical physics, light was considered as a (transverse) wave. This is because light possesses all physical properties of waves such as reflection, refraction, interference, diffraction and polarization. However, this approach did not give satisfactory answers to a number of light-related phenomena observed in experiments. Such a shortcoming gave rise to a new era in modern physics.
In a given temperature above the absolute zero, a thermal motion produces various types of motion in atoms and molecules of matter such as electronic, vibrational and rotational (when spinning around themselves). When particles move to lower energetic levels, they produce EM radiation, otherwise known as thermal radiation. The Sun is the main contributor of thermal (EM) radiation coming to the Earth.
EM spectrum is a continuous spectrum, which theoretically includes wavelengths from 0 to infinity. Different wavelengths give different contributes in the transportation of energy produced by thermal radiation. However, there is a characteristic wavelength λm which gives the main contribution in this process for a given temperature. This characteristic wavelength decreases with the increase in temperature of material.
The energy radiated by the unit area of an object in every second from all possible wavelengths is known as the total emissivity E of an object. It is measured in [J/(s·m2)] or [W/m2]. All wavelengths of thermal radiation contribute in the total emissivity.
Spectral emissivity e(λ) is a function of wavelength. It depends from the type of object and its temperature and represents the contribution of a particular wavelength in thermal emissivity. The maximum value of thermal emissivity reached for λ = λm. Other wavelengths close to λm also give a considerable contribution in thermal emissivity and transportation of energy of radiation. Wavelength that are 10 times greater or smaller than λm give little or no contribution in this regard.
A black body is the best absorber (and therefore the best emitter at high temperature) of EM radiation. An irregularly shaped cavity with a very thin hole, just enough to allow a light ray enter in the cavity represents a perfect pattern of a black body.
Different objects have different reflecting abilities. This ability is mathematically represented through the reflection coefficient r, which in general depends on the incident wavelength and temperature of the object. On the other hand, the absorption coefficient of an object is denoted by a. They are dimensionless coefficients between 0 and 1. From the law of conservation of energy, we have
An ideal mirror has r = 1 and a = 0, while an ideal black body has r = 0 and a = 1.
We denote the spectral emissivity of a black body by e0(λ) and that of a whatever body (not black) as e(λ). The relationship between these two quantities (known as the Kirchhoff's Law of Thermal Emissivity) is
Stefan-Boltzmann Law expresses the relationship between the total emissivity of a black body and its temperature. It says:
"Total emissivity of a black body is proportional to the fourth power of absolute temperature."
Mathematically, this law is written as:
where σ = 5.67 × 10-8 J/K4m2s is a constant; it is known as the Stefan-Boltzmann constant.
Wien's Law gives the relationship between the characteristic wavelength λm of thermal radiation emitted by a black body and the body temperature. This relationship is an inverse variation given by the equation
where b = 2.9 × 10-3 m · K is known as the Wien's constant.
Wien's Law is otherwise known as the "law of displacement".
used to calculate the emission ability of a black body, was suitable only for long EM wavelength. For short wavelengths, the curve obtained by applying this formula deflects too much from the curve found experimentally. When using the Rayleigh-Jeans equation, the emission ability of objects points towards infinity when wavelength points towards zero. This nonsense represents a notable failure of the classical theory of thermal radiation, which is known in the history of physics as the "ultraviolet catastrophe".
In 1900, Max Planck overcame this handicap by proposing a new hypothesis. According to him, the radiation emitted from atoms and molecules do not occur in a continuous way but with interruptions and in very small portions called quanta (quantum in singular). Moreover, the energy E of a quantum of light (known as photon - the particle of light) is proportional to the frequency of radiation, i.e.
where h (which is a pseudo-letter; it is not the traditional h of our alphabet) represents the Planck constant. It has the value of 6.626 × 10-34 J/s.
The above equation represents the fundamental equation of quantum theory in Modern Physics.
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