Planck's quantum theory summary-Jayam chemistry learners

By V. Sai Kalyani

 Overview of Planck's quantum theory

Introduction

Planck quantum theory is a game changer in classical physics assumptions of electromagnetic energies. It clarified that energy transfers as intermittent discrete granules. To enumerate blackbody radiant emittance, Max Planck introduced quantum as a tiny energy particle.

It is an energy quantization pictorial description of Planck's quantum theory.
Planck quantum law

A quantum is an energy clump that a body transmits. Energy less than quantum is unavailable. Hence, a quantum is the minimum energy quantity.

Table of contents

It is a list of covered topics in the blog post. Click on your desired option to move the selected section directly.

Introduction

How does the little energy bundle measure light energies?

Planck's quantum theory-postulates

Mind map of Planck quantum theory

Questions and answers on Planck quantum theory concept

Reasoning questions and answers

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How does the little energy bundle measure light energies?

Let us think about rice godowns. We never store rice as heaps in godowns. Instead, we pack them well in bags and store those rice bags in godowns. Each rice packet has a fixed weight, say 50 kg, 100 kg, etc. It helps to weigh rice easily. In the same way, if we count rice grains, it may be a bit confusing and funny.

Classical physics exposed the same problem by considering energy as waves. The continuous energy emissions seemed gigantic at shorter wavelengths. But blackbody curves did not support this theoretical conception. Moreover, spectral radiance calculations gave irrelevant results at infinite energies.

After thorough research on experimental observations of blackbody curves, Planck proved that energy flow is discontinuous. The periodic energy installments quantified infinite energy shifts at shorter wavelengths. Besides, quantum energy is solely dependent upon radiation frequencies and directly proportional to each other.

It is a timeline of pre-history to the Planck quantum theory.
Planck quantum theory pre-history 

Gustav Kirchhoff envisioned an ideal absorber of the whole electromagnetic spectrum. It is a hollow, enclosed rigid solid with a black surface. It intakes light of all frequencies and re-emits every radiation on heating. Kirchhoff's imaginary object absorbs electromagnetic light and emits heat assimilated electromagnetic energy as thermal radiation, commonly named blackbody radiation. As a consequence, blackbody radiation releases from hot bodies.

Additional reference:

Here is a video description of  blackbody radiations.

In 1678, Dutch physicist Christian Huygens introduced the wave theory of light. When an ordinary body absorbs light energy and re-emits it, this shows a difference in absorbing and emitting energy amounts due to loss by different means, such as reflection and transmission. The energy calculations for light waves were accurate for ordinary bodies by that time. So, folks believed the light propagates as a wave. James Clerk Maxwell, in 1864, elucidated electromagnetic wave theory. It insisted that light propagates as an oscillating wave of electric and magnetic fields. All these classical physics hypotheses strongly supported the light energies as a wave.

But Gustav Kirchhoff's imaginary object did not lose absorbed energy by reflection, transmission, or other means. It emits 100% absorbed electromagnetic radiation on heating. So, when the hypothetical body is at a constant temperature in thermal equilibrium, we feel it did not exchange energy.

Conversely, the ideal body absorbs and emits energy constantly to maintain thermal equilibrium. It did not mean that the blackbody absorbs and emits the same energy radiations in every instance. For example- when heating a red glass in a furnace to a high temperature, it emits green light after being removed from the heater. Actually, red and green are complementary colors on the color wheel. The glass piece absorbs green light and reflects red light more at ordinary temperatures. Hence, it seems red. After heating in a furnace, it emits green light following Kirchhoff's law of thermal radiation.

So, classical physics interpretations of light energy waves led to continuous energy additions that escalated the heat capacities to infinite levels. It led to immense energy discharges at higher frequencies, i.e., in the ultraviolet region of the blackbody spectrum. It is an ultraviolet catastrophe.

Let us try to understand it with a general observation topic. Jugglers start their juggling of balls with 2-3 balls initially. Slowly, they add a single ball after one complete cycle. With time, they rotate so many balls. Classical physics energy escalations are like juggling. It increases with the temperature of the blackbody over time.

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Contrarily, Planck's quantum theory is like automatic Tennis Ball Machines. It holds all balls but ejects a single ball at a specific interval. It won't keep balls with it at the end. But every ball has to wait for its time of ejection.

I don't say Planck's quantum theory elucidates a single quantum release. Instead, I stress that it releases individually distinct energy particles per unit time per unit range of wavelengths. As a result, the blackbody emits all electromagnetic spectrum wavelengths without bounds.

Kirchhoff emphasized that the energy particles cannot have any arbitrary value at a particular frequency. And it is always an integral multiple of hν. It expresses the quantization of energy of electromagnetic radiation.

Additional reference:

Postulates of Planck's quantum theory

What are the applications of Planck's constant?

Planck's quantum theory-postulates

Here are Planck's quantum theory postulates;

Postulate-1: Discrete energy chunks exchange intermittently between bodies. 

Distinct blackbody curves for different temperatures mention energy transmission is discontinuous and periodic. The particle assumption of energy laid the foundation for quantum mechanics. Quantum mechanics interprets matter and light interaction at atomic and sub-atomic levels. Hence, it started a new era of energy as a particle for microscopic objects. It leads to the invention of new theories like the photoelectric effect. 

Postulate-2: The amount of quantum energy varies with the radiation frequency.

Planck mentioned that the number of radiations emitted from a pinhole of a blackbody in one second determines the magnitude of radiant energies. Both these quantities E and v hike mutually, thus holding a directly proportional relationship.

E ∝ ν

The size of the quantum is minimum at lower frequencies. But, at higher frequencies, it enlarges. Planck needed a fixed physical quantity to match the radiant frequencies to determine the quantum size. He discovered a universal constant value 6.626 x 10-34 joule second. It is h, the Planck's constant.

Additional reference:

What is the difference between Planck's constant and reduced Planck's constant?

Postulate-3: Integral bundles of quantum participate in energy transmission.

Identically shaped blackbody curves obtained at different temperatures showed that quantum energies grow in whole number multiples with temperatures. Fragmenting a quantum depending on the body's energy requirement is impossible. Fractional quanta do not exist in reality.

E = nhν

 When the quantum energy is more than the body's requirement, the body takes it and uses excess energy for various purposes, such as electron ejection.

Mind map of Planck quantum theory

Planck's quantum theory depicts the quantum nature of electromagnetic radiant energies with the matter. The phenomenon of blackbody and photoelectric effect proved the energy particle existence. Besides, Planck quantum law for energy distribution succeeded in overcoming the limitations of Rayleigh-Jeans law. So, Planck's quantum theory became the basic theory of quantum mechanics to laid the new foundation for particle physics. It explained the interaction of light with matter at atomic and sub-atomic levels. And it successfully measured the size of the quantum from the radiation frequencies.

Atomic line spectra and de-Broglie dual nature principles further supported the quantum existence of photons. Hence, the Planck quantum theory has many applications, such as atomic clocks, semiconductor gadgets, and medical field MRI scans.

Here is a mind map of Planck's quantum theory that discusses all these points briefly.

Questions and answers on Planck quantum theory concept:

1. Which law explains the continuous frequency spectrum of the black body?

A. Planck law

B. Kirchhoff law

C. Rayleigh-Jeans law

D. Wein displacement law

Answer: Planck law

Explanation:

Black body radiations exhibit a continuous spectrum of frequency of radiations that depend only on the body’s temperature is known Planck spectrum.

2. What are the laws that govern blackbody emissions?

A. Planck law

B. Wien displacement law

C. Stefan-Boltzmann law

D. All the above

Answer: All the above

Explanation:

Planck law calculates the spectral energy density of blackbody radiation at a particular frequency and temperature conditions. Besides, it considered that each oscillation mode of charged bodies associated with a specific number of energy particles. In this way, it quantized the energies of blackbody radiations.

Wien displacement law depicts the inversely proportional relationship between the blackbody radiation wavelength with maximum intensity and the absolute temperature of the blackbody.

Stefan-Boltzmann law shows the relationship between the radiant emittance of a blackbody with its temperature. Moreover, it elucidated that the energy radiated by the blackbody per unit time per unit area varies directly as the fourth power of the absolute temperature of the blackbody.

3. Planck quantum law is successful to _____________________wavelengths of blackbody emissions

A. Shorter

B. Longer

C. Both longer and shorter

Answer: Both longer and shorter

Explanation:

Given blackbody radiation wavelengths, we come across three laws. They are Rayleigh-Jeans law, Wien displacement law, and Planck law.

Rayleigh-Jeans law is the classical interpretation of blackbody energy emissions that became successful at longer wavelengths of blackbody emissions.

Wien displacement law explained the correlation between the maximum intensity blackbody radiation wavelength and the absolute temperature. It gave accurate results for shorter wavelength blackbody emissions.

Planck law gave mathematical relation to calculate energies of discrete energy packets of radiation emissions at a particular frequency and temperature conditions. It applies to all wavelengths of blackbody radiations without any failures.

Additional reference:

A PowerPoint notes of Wien displacement law.

4. How can you distinguish Rayleigh-Jeans law and Planck law?

A. Based on blackbody radiation energies interpretation

B. Based on absolute temperature conditions

C. Based on experimental conditions and the nature of substances taken for study

Answer:

Based on blackbody radiation energies interpretation

Explanation:

It distinguishes between Rayleigh-Jeans law &Planck quantum law

Rayleigh-Jeans law considered that charged particle oscillations in the blackbody proceed with continuous energy changes, either absorptions or emissions. The addition of negligible fractions of energy to the blackbody without a break ended with enormous energy releases at higher frequencies. It did not match with the blackbody curves obtained in the laboratories. The derivative form of Rayleigh-Jeans law is here;

Planck quantum theory considered intermittent energy particle ejections by the blackbody at particular temperature conditions. The energy particles are discrete energy packets in whole number multiples that helped enumerate the size of blackbody energies. The mathematical expression for Planck energy distribution for the blackbody is here;

5. What is the necessity of the Planck constant in the quantum equation?

A. A constant quantity is a must for every empirical relationship.

B. Planck wanted to keep his discovery named to him by introducing a fixed quantity.

C. Planck constant determines the proportionality relationship between the quantum energy and radiation frequency.

Answer:

Planck constant determines the proportionality relationship between the quantum energy and radiation frequency.

Explanation:

While comparing the blackbody emission energies with their frequencies, Planck found discrepancies in different temperature conditions for various substances. He tried to make his empirical relationship accurate at all wavelengths and temperature conditions. So, the Planck constant introduction with a fixed value for all substances without limitations calculated quantum energies accurately. Hence, the Planck constant is a universal numerical quantity that determines the directly proportional variation of radiation frequency with its quantum size under all circumstances in spectral evaluations.

Reasoning questions:

1. Even though Planck quantum theory elucidated blackbody emissions are discrete and intermittent, the Planck blackbody spectrum for frequencies of blackbody radiations is continuous at particular temperature conditions. Why?

Answer:

Planck quantum theory simplifies blackbody emission energies with energy particles called quantum. These discrete energy particles release discontinuously in integral multiples. So, Planck clarified that blackbody energy emissions are quantized.

But, the Planck spectrum for blackbodies is the pattern of frequencies of thermal radiation at various temperature conditions. It is a continuous emission spectrum of blackbody radiations. On account of no specific boundaries for separating the spectral emissions, it became a continual spectrum of electromagnetic radiation. Besides, one spectral band consolidates into the other without defined margins.   

2. Why are the names of energy packets for light and other forms of energy different?

Answer:

In Planck quantum theory, we heard of two names- quantum and photon for denoting the energies of light and other forms separately. Quantum is an energy packet for energy forms except for light. And Max Planck introduced the term quantum to depict thermal electromagnetic energies of blackbodies in thermal equilibrium conditions.

Photon is a light energy particle. Isaac Newton, while depicting photoelectron energies, introduced it. And it was become a popular single word for quantized light energies since then. Besides, Newton perceived that a photon is a light quantum with no mass. As light travels at constant speed in a vacuum, it does not have rest mass by the theory of relativity.

In my opinion, it may be one reason for special consideration of light energies than the other.

Conclusion:

The interaction of light with matter helps in electric devices, quantum computing, and medical treatments. The quantum nature of energy laid new grounds in particle physics. It brought Max Planck the Nobel Prize in 1918.