Question

Define and describe the following, if you can, site some example/simple analogy.

1. Wave-particle duality of light
2. Energy quantization
3. Black body
4. Ultraviolet catastrophe

Answer 1

1) Wave-particle duality of light

In physics and chemistry, wave-particle duality holds that light and matter exhibit properties of both waves and of particles.

Wave-particle duality is the concept in quantum mechanics that every particle or quantum entity may be described as either a particle or a wave. In physics and chemistry, wave-particle duality holds that light and matter exhibit properties of both waves and of particles. The explanation marked one of the major steps toward quantum theory. Through the work of Albert Einstein, Louis de Broglie and many others, it is now authenticated that all objects have both wave and particle nature and that a suitable understanding of quantum mechanics provides the over-arching theory resolving this notable paradox.

2 )Energy quantization

The quantization of energy refers to the fact that at subatomic levels, energy is best thought of as occuring in discreet "packets" called photons. ... The red and blue photons are therefore "quantized" just as dollar bill denominations are "quantized". Each photon contains a unique amount of discreet energy

BLACK BODY

A black body or blackbody is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. The name "black body" is given because it absorbs radiation in all frequencies, not because it only absorbs. Indeed, a black body can also emit radiation.

Blackbody, in physics, a surface that absorbs all radiant energy falling on it. The term arises because incident visible light will be absorbed rather than reflected, and therefore the surface will appear black. The concept of such a perfect absorber of energy is extremely useful in the study of radiation phenomena

Black Body Radiation

Solids, when heated, emit radiation varying over a wide range of wavelengths. For example: when we heat solid color, changes continue with a further increase in temperature. This change in color happens from a lower frequency region to a higher frequency region as the temperature increases. For example, in many cases, it changes from red to blue. An ideal body which can emit and absorb radiation of all frequencies is called a black body. The radiation emitted by such bodies is called black body radiation.

Thus, we can say that variation of frequency for a black body radiation depends on the temperature. At a given temperature, the intensity of radiation is found to increase with an increase in the wavelength of radiation which increases to a maximum value and then decreases with an increase in the wavelength. This phenomenon couldn’t be explained with the help of Maxwell’s suggestions. Hence, Planck proposed the Planck’s quantum theory to explain this phenomenon.

blackbody radiation: the electromagnetic radiation from a blackbody

The Ultraviolet Catastrophe

A blackbody is an idealized object which absorbs and emits all frequencies. Classical physics can be used to derive an equation which describes the intensity of blackbody radiation as a function of frequency for a fixed temperature--the result is known as the Rayleigh-Jeans law. Although the Rayleigh-Jeans law works for low frequencies, it diverges as ; this divergence for high frequencies is called the ultraviolet catastrophe.

Max Planck explained the blackbody radiation in 1900 by assuming that the energies of the oscillations of electrons which gave rise to the radiation must be proportional to integral multiples of the frequency, i.e.,

(1)

Using statistical mechanics, Planck derived an equation similar to the Rayleigh-Jeans equation, but with the adjustable parameter . Planck found that for J s, the experimental data could be reproduced. Nevertheless, Planck could not offer a good justification for his assumption of energy quantization. Physicicsts did not take this energy quantization idea seriously until Einstein invoked a similar assumption to explain the photoelectric effect.

Rayleigh- Jeans considered intensity as a function of energy/wave length and temperature and derived an expression as follows –

ρ(λ,T) =frac2cKbTlambda4

The relation works fine at frequencies lower than 105GHz. But at high frequencies or lower wavelength,

×Rayleigh’s relation predicts infinite intensity as λ → 0. As intensity, is a finite quantity, the impossible predicted event of infinite intensity by the wave model of electromagnetic radiation was known as ‘ultraviolet catastrophe’.