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Planck’s Quantum Theory

Introduction

By the end of the 19th century, scientists were able to explain most of the natural phenomenon by Newton’s Laws of classical mechanics or classical theory. By this time, matter and energy used to be considered distinct and unrelated. Scientists were able to define the properties of radiant energy by Maxwell’s equations given by James Clerk Maxwell, a Scottish physicist, in 1873. However, by the 20th-century scientists were able to discover that phenomena such as black body radiation, the photoelectric effect can’t be explained by classical theory or classical mechanics. During this time, the German physicist Max Planck put forward his theory of the quantized nature of the energy of electromagnetic waves. In this article, we will discuss Max Planck’s quantum theory of radiation or quantum theory of radiation, black body radiation, electromagnetic radiation, evidence for a particle theory of energy, etc. Let us start by understanding electromagnetic radiation in the coming section.

 

Electromagnetic Radiation 

It is a form of energy that can propagate in a vacuum or material medium and shows both wave-like and particle-like properties. Radio waves, microwaves, infrared, visible light, UV-rays, X-rays, gamma rays are electromagnetic radiation. 

 

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Black Body Radiation 

According to the temperature, all objects emit electromagnetic radiation. Objects having low temperature emit radio or microwaves (low-frequency waves) while objects having high temperature emit visible or ultraviolet light or even higher frequency radiations. 

 

A black body is an idealized object that can absorb all electromagnetic radiation that comes in contact with it. After this, it starts emitting thermal radiation in a continuous spectrum according to its temperature. The radiation which a black body emits is called black body radiation. Stars almost behave like black bodies. 

 

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The intensity of the radiation varies according to the wavelength and temperature of the object. At a given temperature, the intensity of light varies according to wavelength. This phenomenon was not explained by classical theory or Maxwell’s equation. Hence, Max Planck put forward his theory of quantization of energy or Planck’s quantum theory of radiation to explain this phenomenon. 

 

What is Planck’s Quantum Theory? 

Planck’s quantum theory explains the emission and absorption of radiation. Postulates of Planck’s quantum theory are as follows – 

  1. Matter radiates energy or absorbs energy in discrete quantities, discontinuously in the form of small packets or bundles. 

  2. The smallest bundle or packet of energy is known as quantum. In the case of light, a quantum of light is known as a photon. 

  3. The energy of the quantum absorbed or emitted is directly proportional to the frequency of the radiation. So, the energy of the radiation is expressed in terms of frequency as follows- 

 

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A body or matter can radiate energy or absorb energy in whole-number            multiples of a quantum as nhv. Where n is a positive integer. So, energy can be absorbed or radiated as hv, 2hv, 3hv, 4hv……etc. not in the form of 1.5hv, 2.5hv…etc. 

 

After Max Planck, German physicist Albert Einstein revisited the theory and explained the photoelectric effect. 

 

The Discovery of Quantum

The photoelectric effect is difficult to account for using the wave model. When light is focused on certain metals, it emits electrons, creating this effect. There is a minimum frequency of EM radiation at which the effect will occur for each metal. In contrast to what would be expected if light functioned strictly like a wave, replacing light with twice the intensity and half the frequency will not produce the same result. In that situation, light's effect would be cumulative-the light would start increasing until it caused electrons to be emitted. Instead, electron ejection is triggered by a specific minimum frequency of light. The implication was that frequency and energy are directly proportional, with higher light frequencies having greater energy. This study led to the discovery of the minimum amount of energy that an atom could gain or lose. This minimum amount was given the name "quantum" by Max Planck, plural "quanta," which means "how much." One quantum of energy is carried by one photon of light.

 

Planck is regarded as the father of quantum theory. According to Planck, E=hν, Where h is Planck's constant (6.62606957(29) x 10-34 J s), v is frequency, and E is the energy of the electromagnetic wave. Planck (cautiously) stated that this was just a side effect of the absorption and emission of radiation and that it had nothing to do with the physical reality of the radiation. However, Albert Einstein reinterpreted Planck's quantum hypothesis in 1905 and used it to explain the photoelectric effect, which occurs when light shines on certain materials and causes electrons to be ejected.

 

Evidence in Support of Planck’s Quantum Theory 

Many experiments were performed to analyze Planck’s quantum theory. All experimental observations supported and worked as strong evidence for quantum theory. All shows that the energy of electron motion in the matter is quantized. A prism can separate the light according to its wavelengths. If light behaves only as a wave, then the prism should give a continuous rainbow. This also supports Planck’s Quantum Theory. The emission spectrum of nitrogen gas also supports Planck’s quantum theory of radiation.  

 

Applications of Planck’s Quantum Theory 

Planck’s quantum theory is the fundamental theory of quantum mechanics. So, it has applications in all those fields where quantum mechanics is being used. It has applications in electrical appliances, the medical field, quantum computing, lasers, quantum cryptography etc.

 

Key Points

  • Newtonian physics dominated the scientific worldview until the late 19th century. However, physicists discovered in the early 20th century that the laws of classical mechanics do not apply at the atomic scale.

  • The photoelectric effect could not be explained using existing light theories since an increase in light intensity did not result in the same outcome as an increase in light energy.

  • Planck proposed that the energy of light is proportional to frequency, and Planck's constant (h) is the constant that relates them. Albert Einstein determined that light is made up of discrete quanta of energy called photons as a result of his research.

FAQs on Planck’s Quantum Theory

1. What is a Planck curve?

The blackbody energy density between λ and λ + dλ is the energy of the mode E = hc / λ multiplied by the density of photon states, multiplied by the probability of the mode being filled. This is Planck's famous blackbody energy density formula.

2. How is blackbody radiation produced?

All objects generate electromagnetic radiation based on their temperature.  The idealized object that consumes electromagnetic energy that it comes into contact with is a black body.  In the continuum, then heat radiation is emitted according to its temperature. 

3. What is Planck’s number?

The Planck constant is currently calculated by scientists as 6.62607015 x 10^(-34) Joule seconds. In 1900, Planck determined his game-changing constant by describing how the smallest bit of matter releases energy in discrete beams called quanta, and essentially put "quanta" in quantum mechanics.

4. What is Planck’s constant in simple terms?

Planck's constant compares the total energy carried by a photon with its electromagnetic wave frequency. It is named after the physicist Max Planck. It is an essential quantity in quantum mechanics.

5. What is Stefan’s law of radiation?

The law of Stefan-Boltzmann states that a surface's overall radiant heat power is proportional to its fourth absolute temperature power. The rule only applies to black bodies, which are imaginary surfaces that accumulate heat from all events.

6. Explain Plank's Quantum theory

The main points of Plank's Quantum theory are as follows:

  1. Radiation energy does not emit or absorb continuously, but it can do so in discrete amounts. Quanta refers to these small bundles of energy, while photon refers to these bundles of light.

  2. The energy (E) of each quantum is proportional to its frequency, i.e.,

             E ∝ ν

            ⟹E=hν = hc/λ


where E= Energy, h= Plank's constant = 6.62×10 −34 Js,  c= Speed of light & λ=    Wavelength.​

  1. Any particle's total energy emitted or absorbed is an integral multiple of hv, i.e. E=n hv.


Thank you for reading this article. We hope you found this article on Planck’s Quantum theory helpful. If you have any doubts, let us know in the comments section below. We will be happy to help you.


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