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Blackbody Radiation.

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Introduction

Blackbody Radiation:

It is well-known that when a body is heated it emits electromagnetic radiation. For example, if a piece of iron is heated to a few hundred degrees, it gives off e.m. radiation which is predominantly in the infra-red region. When the temperature is raised to 1000C it will begin to glow with reddish color which means that the radiation emitted by it is in the visible red region having wavelengths shorter than in the previous case. If heated further it will become white-hot and the radiation emitted is shifted towards the still shorter wave-length blue color in the visible spectrum. Thus the nature of the radiation depends on the temperature of the emitter.

A heated body not only emits radiation but it also absorbs a part of radiation falling on it. If a body absorbs all the radiant energy falling on it, then its absorptive power is unity. Such a body is called a black body.

An ideal blackbody is realized in practice by heating to any desired temperature a hollow enclosure (cavity) and with a very small orifice. The inner surface is coated with lamp-black. Thus radiation entering the cavity through the orifice is incident on its blackened inner surface and is partly absorbed and partly reflected. The reflected component is again incident at another point on the inner surface and gets partly absorbed and partly reflected.

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Middle

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Rayleigh-Jean's expression and Wien's displacement law are special cases of Planck's law of radiation. Planck's formula for the energy distribution of blackbody radiation agrees well with the experimental results, both for the long wavelengths and the short wavelengths of the energy spectrum.

Please click on the simulation below to see nice interactive demonstration of the physics of Blackbody radiation.

Simulation on Blackbody Radiation

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Photoelectric Effect:

Planck's postulate regarding the discrete nature of the possible energy states of an oscillator marked a radical departure from the ideas of classical physics. According to the laws of classical mechanics, the energy of an oscillator can vary continuously, depending only on the amplitude of the vibrations - this is in total contrast to Planck's hypothesis of discrete energy states of an oscillator. Photoelectric effect is another classic example which can not be explained with classical physics. Einstein was awarded Nobel prize for his explanation of the physics of photoelectric effect.

The basic experiment of photoelectric effect is simple. It was observed that a metal plate when exposed to ultraviolet radiation became positively charged which showed that it has lost negative charges from its surface. These negatively charged particles were later identified to be electrons (later named photoelectrons). This phenomenon is known as photoelectric effect.

Please check out the physics applet below which shows the effect of light on various metals.

Simulation on Photoelectric effect

The main results of the experiment can be summarized as follows:

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Conclusion

l' on the scattering angle and l was predicted by Compton to be:

l' - l = (h/mec)[ 1- cosq ]= l0 [ 1- cosq ].

The factor l0=h/mec, also known as Compton wavelength can be calculated to be equal to 0.00243 nm.

The physics of Compton effect:

To explain his observations Compton assumed that light consists of photons each of which carries an energy hf and a momentum hf/c (as p = E/c = hf/c). When such a photon strikes a free electron the electron gets some momentum (pe) and kinetic energy (Te) due to the collision, as a result of which the momentum and energy of the photon are reduced.

Considering energy and momentum conservation (For the detail derivation please click here) one can derive the change in wavelength due to Compton scattering:

l' - l = (h/mec)[ 1- cosq ].

Note that the result is independent of the scattering material and depends only on the angle of scattering.

The appearance of the peak at the longer wavelength in the intensity vs. wavelength curve is due to Compton scattering from the electron which may be considered free, since its energy of binding in the atom is small compared to the energy hf of the photon. The appearance of the other peak at the wavelength of the incident radiation is due to scattering from a bound electron. In this case the recoil momentum is taken up by the entire atom, which being much heavier compared to the electron, produces negligible wavelength shift.

Conclusion:

Compton effect gives conclusive evidence in support of the corpuscular character of electromagnetic radiation.

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