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Planck Quantum Theory

According to Planck’s quantum theory;

1. Different atoms and molecules produce or absorb energy in discrete quantities only. The smallest amount of energy that can be emitted or absorbed by an electron in the form of electromagnetic radiation is termed as quantum.

2. The energy of the radiation which is absorbed or emitted is directly proportional to the frequency of the electromagnetic radiation as given below.

The energy of radiation is represented in terms of frequency as follows;

E = h ν

Where,

E signifies the Energy of the radiation

h signifies Planck’s constant (6.626×10–34 J.s)

ν signifies the Frequency of radiation

Later in the year 1905, famous German physicist, Albert Einstein re-explained Planck’s theory to further describe the photoelectric effect. He believed that when some source of light is focused on certain materials, then they eject electrons from the surface of that material. Planck’s work led Einstein in determining that light occurs in discrete quanta of energy, or these quanta of energy is termed as photons. Planck was successful in explaining the phenomenon of black body radiation by assuming that absorption and emission of radiation arise from an oscillator that is the atoms in the wall of a black body.

This theory states that;

(a) The radiation energy emitted or absorbed are present in the form of small packets of energy (that is in discrete quantities and not in a continuous manner). Such packets are termed as quantum or photons.

E ∝ ν

E = hν (h = 6.6 x 10-34 Js)

(b) Energy of each photon is directly proportional to the frequency of radiation. Where ‘h’ represents the Planck’s constant. E represents the energy of a photon.

Planck Quantum Theory

As progress in the science field was happening, Maxwell’s idea about the wave nature of electromagnetic radiation helped to describe phenomena such as interference, diffraction, etc. Though he was unable to explain several other phenomena such as the photoelectric effect, that is ejection of electrons from the surface of a metal compound when electromagnetic radiation strikes it, line spectra of atoms (specifically hydrogen), black -body radiation.

Black Body Radiation

Solids, when heated, produce radiation of a wide range of wavelengths. For instance: when we heat a solid colour, then a change of colour is observed and this continues with a further increase in temperature. This colour change generally happens from a lower frequency region to a higher frequency region as the temperature rises. For instance, in several cases, the colour changes from red to blue. An ideal body that can emit or absorb radiation of all frequencies is termed as a black body.

The radiation emitted by such bodies is termed black body radiation. Thus, it can be said that the variation of frequency for black body radiation generally depends on the temperature. At a certain temperature, it was found that the intensity of radiation increases with an increase in the wavelength of radiation. This phenomenon was not explained by Maxwell’. Hence, Planck projected Planck’s quantum theory to explain this phenomenon.

Electromagnetic Radiation

Electromagnetic radiation is referred to as a form of energy that can propagate in a vacuum or any material medium and hence shows both wave-like and particle-like properties.

Radio waves, microwaves, infrared, visible light, UV-rays, X-rays, gamma rays are some examples of electromagnetic radiation.

Materials having low temperature generally emit radiowaves or microwaves (low-frequency waves) while objects having high temperature usually emit visible light or ultraviolet light.

A black body is referred to as an idealized object that absorbs all electromagnetic radiation that comes in contact with it. After absorption, it starts producing thermal radiation in the form of a continuous spectrum according to its temperature. The radiation emitted by a black body is termed as black body radiation.

What is Planck Quantum Theory?

Planck’s quantum theory describes the emission and absorption of radiation by electrons. Postulates of Planck’s quantum theory are given below;

1. Matter emits or absorbs radiation in the form of small packets or bundles.

2. These small bundles or packets of energy are termed as quantum.

3. The energy of the quantum absorbed or produced is directly proportional to the frequency of the radiation. So, the energy of the radiation is generally stated in terms of its frequency as follows-

A body can emit or absorb energy in whole-number multiples of a quantum given by nhv.

Where n represents a positive integer

The Energy can be absorbed or radiated as hv, 2hv, 3hv, 4hv……etc but it cannot emit or absorb radiation in the form of 1.5hv, 2.5hv…etc.

After Max Planck, a German physicist named Albert Einstein enhanced the theory and also explained the photoelectric effect.

Evidence in Support of Planck Quantum Theory

Many experiments were executed to examine Planck’s quantum theory. But, all experimental explanations supported and worked as solid evidence for quantum theory. It thus shows that the energy of an electron in the matter is always quantized. The emission spectrum of nitrogen gas thus supports Planck’s quantum theory of radiation.

Applications of Planck Quantum Theory

Planck’s quantum theory is considered to be an important theory of quantum mechanics. Some applications of Plank’s quantum theory includes;

Electrical Appliances

Medical Field

Quantum Computing

Lasers

Quantum Cryptography and many more.

Planck Quantum Theory Examples

Q1. A violet light has a wavelength of 380nm. Determine the energy for the violet light in joules.

Solution: To find the Frequency , the formula used is ,

c = λ×v

Where,

c represents the speed of light

λ represents the wavelength of violet light

v represents the frequency of light

Now,

v = 3×108 / 380 × 10-9 [ 1 nm = 10-9 m]

Hence,

v = 7.89×1014/s

To find the Energy , we know that E = h×ν

Where, h represents the planck’s constant

= (6.626×10−34)×(7.89×1014)

= 8.39 ×10−19 joule /photon

Planck Quantum Theory Citations

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