# Black-body radiation and Planck’s law

###### Priyanka Devan
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In 1901, Max Planck published an analysis in which he succeeded in reproducing the observed spectrum of light emitted by a glowing object. In order to accomplish this, Planck had to make a mathematical assumption of quantized energy of the oscillators .Einstein later proposed that it is not the energy of radiating atoms, but the electromagnetic radiation itself is quantized.

The emission of electromagnetic energy due to an object’s heat, could not be explained from classical arguments alone. According to equipartition theorem of classical mechanics an object’s energy is partitioned equally among the object’s vibrational modes. But in case of electromagnetic emission of  a thermal object applying the same reasoning was not so successful. Physicists hoped to describe this emission via classical laws since light was known to be waves of electromagnetism. This is known as the black body problem. It was natural to assume that equipartition theorem would perform equally well in describing the radiative emission of such objects, since equipartition theorem worked so well in describing the vibrational modes of thermal object itself. But a problem would arise if each mode received an equal partition of energy, the short wavelength modes would consume all the energy. This became clear when plotting the Rayleigh Jeans law, which, while correctly predicting the intensity of long wavelength emissions, predicted infinite total energy as the intensity diverges to infinity for short wavelengths. This is known as the ultraviolet catastrophe.

The characteristics of blackbody radiation can be explained in terms of several laws:

## 1. Planck’s Law

Planck’s Law of blackbody radiation helps to determine the spectral energy density of the emission at a particular temperature.

## 2. Wien’s displacement Law

Wien’s displacement Law, states that the frequency of the peak of the emission  increases with absolute temperature. Conversely, as the temperature of the body increases, the wavelength at the emission peak decreases

## 3. Stefan–Boltzmann Law

Stefan–Boltzmann Law, relates the total energy emitted and the absolute temperature .

The blackbody radiation curves have quite a complex shape. The spectral profile at a specific temperature corresponds to a specific peak wavelength, and vice versa. As the temperature of the blackbody increases then the peak wavelength decreases. Similarly the intensity at all wavelengths increases, as the temperature of the blackbody increases. Moreover the total energy being radiated increases rapidly as the temperature increases. Even though the intensity may be very low at very short or long wavelengths, at any temperature above absolute zero energy is theoretically emitted at all wavelengths.

In 1965 Penzias and Wilson discovered the cosmic radiation, who later won the Nobel Prize for their work. The radiation spectrum was measured by the COBE satellite. It is found to be a remarkable fit to a blackbody curve with a temperature of 2.725 K and is interpreted as evidence that the universe has been expanding and cooling for about 13.7 billion years. A more recent mission, WMAP, has measured the spectral details to much higher resolution, finding tiny temperature fluctuations in the early Universe which ultimately led to the large-scale structures.

## Planks Equation

Max Planck discovered that energy is transferred in the form of chunks called quanta. The constant value of h is equal to 6.63 x 10-34 JS. Energy of photons is calculated when their frequencies are known. If the wavelength is known then we can use the wave equation to calculate the energy and then apply the equation of Planck’s equation. The relevancy of the energy per quantum is described by Plank’s constant.

## Conclusion

According to the topic, the energy of photons is calculated when their frequencies are known. If the wavelength is known, we can use the differential equation to calculate the energy and then apply Planck’s equation. Moreover different atoms and molecules can emit and absorb energy in different quantities and the smallest amount of energy that can be absorbed is known as quantum. Small packets of energy are called as quanta where the energy of each quantum is determined by the amount of radiation and it is proportional to frequency.

When black body gets cooled down then change in wavelength is (delta lambda = 9 micron) corresponding to maximum energy density.

Whenever a blackbody emits radiation, it corresponds to an electron jumping from higher energy state to a lower energy state and because of this an electron in excited state has a very large number of ‘energy levels below’, it can jump into any of the empty states giving a continuous spectrum.

The radiation from the Sun is continuously distributed over all the wavelengths, therefore the Sun can be considered as a perfect black body. <br> In another way, temperature on the surface of the Sun is about 5800 K. The radiation from a black body at this temperature is almost similar to that from the Sun.

black body is an idealized object that absorbs all electromagnetic radiation it comes in contact with. It then emits thermal radiation in a continuous spectrum according to its temperature. Stars behave approximately like blackbodies, and this concept explains why there are different colors of stars.

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