“Quantum leaps”: the “new” idea of energy transfers in the realm of subatomic particles

 

Isaac Newton (1643 – 1727) ’s pivotal ideas are emblematic in terms of the canonic protocols enthroned as mandatory tools for dealing satisfactorily with time and space along our daily interactions in the material world. But they were not able to bring under the main spot the energy transfer mechanism at the level of atomic realm.

The core problem was a behavioral inconsistency detected: the event’s disobedience to the classical mood of natural phenomena. Mean, it looked like no time was elapsed between, for example, irradiation and due energy transfer (action) and the respective particle animation (reaction). It looked like an instant process: elapsed time between action and reaction equals zero, what would be an impossibility according to the well-established classical world. Alternative visions were brought in among the various attempts to reconcile classics parameters with that weird behavior. Downing our eyes to look at one sole electron orbiting around its related atomic nucleus, we will pick up a “model” proposed by a Danish physicist named Neils Bohr (1885 – 1962) in 1913. A key argument in Bohr´s model was his conception of a “set of allowed (possible) values of energy levels (states) ...”. so that atoms would absorb or emit radiation only when the electrons abruptly jump between those “allowed” (or stationary) states. Direct experimental evidence for the existence of such discrete states was obtained (1914) by the German-born physicists James Franck and Gustav Hertz.

Well, it represented a radical departure from the classical mood we mentioned above.

Niels Bohr proposed a theory for the hydrogen atom, which is the simplest among all the atoms in universe, once it is composed by one electron orbiting around a positively charged atomic nucleus. His argument was based on the assumption that “some physical quantities only take discrete values”.

Well, I guess it is useful to point out here that immediately before 1913, an atom was thought of as consisting of a tiny positively charged heavy core, called a nucleus, surrounded by light, planetary negative electrons revolving in circular orbits of arbitrary radii.

In other words, electrons move around a nucleus, but only in prescribed orbits, and If electrons jump (a quantum leap) to a lower-energy orbit, the energy difference is sent out as radiation. In fact, those quantum leaps between two states are typically tiny, that it is precisely why they weren’t noticed sooner. Our focal point here is to stress that it happens so sudden, that many of the pioneers of quantum mechanics assumed they were instantaneous.

My dear human brothers and sisters, let us overact our words here and emphasize that due to these primary ideas set to reconcile theoretic flaws with standing or even outstanding scientific moods, the world evolved from, let’s say, a Morse Code based telegraph message transfer from point #1 to point # 2 two to nowadays satellite based world communication, since them.

Bohr’s model consists of a small nucleus (positively charged) surrounded by negative electrons moving around the nucleus in orbits. Bohr found that an electron located away from the nucleus has more energy, and the electron which is closer to nucleus has less energy.

Bohr organized his ideas under a set of postulates so to comprise a (complete?) model of an Atom: the postulates are:

• In an atom, electrons (negatively charged) revolve around the positively charged nucleus in a definite circular path called orbits or shells.
• Each orbit or shell has a fixed energy and these circular orbits are known as orbital shells.
• The energy levels are represented by an integer (n=1, 2, 3…) known as the quantum number. This range of quantum number starts from nucleus side with n=1 having the lowest energy level. The orbits n=1, 2, 3, 4… are assigned as K, L, M, N…. shells and when an electron attains the lowest energy level, it is said to be in the ground state.
• The electrons in an atom move from a lower energy level to a higher energy level by gaining the required energy and an electron moves from a higher energy level to lower energy level by losing energy.

 

Dears, let us meet again soon over here!

 

I am Mawo Adelson Adewale de Brito, a Voodoo priest, a physicist, a Professor with a MSc degree on “Impacts of Environmental Radon on Health”

 

References:

1.     Quantum Leaps, Long Assumed to Be Instantaneous, Take Time; https://www.quantamagazine.org/quantum-leaps-long-assumed-to-be-instantaneous-take-time-20190605/ (February 12, 2023)

2.     Enery fundamentas; https://home.uni-leipzig.de/energy/energy-fundamentals/01.htm (February 12, 2023)

3.     BYJU´S Bohr Model of an Atom; https://byjus.com/chemistry/bohrs-model/ ; (February 12, 2023);

4. Cover image: Neils Bohr; https://en.wikipedia.org/wiki/Niels_Bohr 

 

The frisson about quantum physics

 Let us use the regular classic physics jargon to describe a situation: Every time an “A person” is introduced to a “B person” and, by chance, they mention their individual professional status to one another, and it happens that “A person” says “I am a physicist”, so what follows next, invariantly, in case “B person” does not share any professional link or whatsoever association with that natural science? That “B person” goes freak in a matter of a millionth of second and asks:” Are you in quantum physics???”

At the end of the day, let us sigh out a breath of tranquility, sit down while sipping a glass of wine and go trying to set somethings about “quantum physics” under some rational history light.

Beforehand, let us put it out clear for once and for all that a quantum (a Latin word which plural is quanta) is the smallest discrete unit of a phenomenon. For example, a quantum of light is a photon, and a quantum of electricity is an electron. The word quantum comes from Latin, meaning "an amount". If something is quantifiable, then it can be measured.

Well, there are some interesting events we could bring here to help us shed simple non-mathematical light on some of the reasons the idea of energy quanta was brought in. We will pick the photoelectric effect, a study that ultimately claimed the 1921 Nobel Prize for Albert Einstein (1879 – 1955), who was not an enthusiast of “quantum physics”, despite of taking the quantum concept of energy to help explaining his theory on the above mentioned effect.

The problem: It was noticed that when electromagnetic radiation (like light for instance) is incident on a metal surface, transference of energy to the irradiated electrons occurs. According to classical physics a lag between irradiation and subsequent emission of some of the electrons would take place. But it simply does not materialize, because the transference happens “instantly”, in frontal contrast with the prediction by classical physics. Mean, there is not a “time lag” for the electrons to acquire the incident energy. In other words, emission takes place as soon as the light shines on the surface; there is no detectable delay.

Einstein defended that the energy transference is a function of the incident radiation frequency and its relation with the so-called frequency threshold of the metal surface. So, if incident radiation frequency is of a value below that threshold, it will not be able to promote electrons ejection from the metal surface. Looking at the practical aspects of the problem, Einstein moved to the conclusion that the energy transference occurs under the form of “unitary blocks” or “quanta”. And he extended the ad hoc relation fist devised by Max Planck to express quantitatively the amount of energy transfer: E = h 𝛎, where E is the energy, 𝛎 f its frequency, and h is the Planck’ s constant, given in the MKS as 6.62607015 × 10^-34 m² kg/s.

 

References:

1.     BYJUS; https://byjus.com/question-answer/why-photoelectric-effect-cannot-be-explained-by-the-classical-physics/ ; (accessed on February 10, 2023);

2.     Wikipedia; Albert Einstein; https://en.wikipedia.org/wiki/Albert_Einstein ; (accessed on February 10, 2023);

3.     https://socratic.org/questions/what-was-einstein-s-explanation-for-the-photoelectric-effect ; (accessed on February 10, 2023)

The Simple Harmonic Oscillator (SHO) in Einstein concept of specific heat

Temperature reflects the average randomized kinetic energy of particles in matter. Heat is the transfer of thermal energy across a system boundary into the body or from the body to the environment. Translation, rotation, and a combination of the two types of energy (kinetic and potential) in vibration of atoms represent the degrees of freedom of motion which classically contribute to the heat capacity of matter, but loosely bound electrons may also participate

At the first decade of the twentieth century thermodynamics and solid states physics obeyed the classical expression for the molar specific heat capacity of a crystal known as the “Dulong–Petit law”. It was a “chemical law” proposed in 1819 by French physicists Pierre Louis Dulong and Alexis Thérèse Petit. Experimentally the two scientists had found that the heat capacity per weight (the mass-specific heat capacity) for a number of substances became close to a constant value, after it had been multiplied by number representing the presumed relative atomic weight of the substance. These atomic weights had shortly before been suggested by Dalton. Dulong and Petit found that the heat capacity of a mole of many solid substances is about 3R (where R is the modern constant called the universal gas constant). The value of 3R is about 25 joules per Kelvin, and Dulong and Petit essentially found that this was the heat capacity of crystals, per mole of atoms they contained.

The “Debye model” is a method developed by Peter Debye in 1912 for estimating the phonon contribution to the specific heat (heat capacity) in a solid. It treats the vibrations of the atomic lattice (heat) as phonons in a box. The Debye model is a solid-state equivalent of Planck's law of black body radiation, where electromagnetic radiation is treated as a “gas of photons” in a box. Thus, as the solid is heated up, it should be a reasonable first approximation to take all the atoms to be jiggling about independently, and the “Equipartition of Energy” as seen by classical physics, would assure us that at temperature T each atom would have on average energy 3kT, k being Boltzmann’s constant. 

The “Dulong–Petit” law offers fairly good prediction for the specific heat capacity of many solids with relatively simple crystal structure at high temperatures. This is because in the classical theory the heat capacity of solids approaches a maximum of 3R per mole of atoms, due to the fact that full vibrational-mode degrees of freedom amount to 3 degrees of freedom per atom each corresponding to a quadratic kinetic energy term and a quadratic potential energy term. By the Equipartition theorem, the average of each quadratic term is ¹⁄₂kT, or ¹⁄₂RT per mole. Multiplied by 3 degrees of freedom and the two terms per degree of freedom, this amounts to 3R per mole heat capacity.

However, the Dulong–Petit law fails at room temperatures for light atoms bonded strongly to each other, such as in metallic beryllium, and in carbon as diamond, for example. The problem starts when it predicts higher heat capacities than are actually found, with the difference due to higher-energy vibrational modes not being populated at room temperatures in these substances.

In the very low (cryogenic) temperature region, where the quantum mechanical nature of energy storage in all solids manifests itself with larger and larger effect, the law fails for all substances.

The modern day theory states that the heat capacity of solids is due to lattice vibrations in the solid. It was first derived from this assumption by Albert Einstein, in 1907. The “Einstein solid” model thus gave for the first time a reason why the Dulong–Petit law should be stated in terms of the classical heat capacities for gases. For quantum mechanical reasons, at any given temperature, some of these degrees of freedom may be unavailable, or only partially available in terms of capacity for storing thermal energy. In such cases, the specific heat capacity is a fraction of the maximum. As the temperature approaches absolute zero, the specific heat capacity of a system also approaches zero, due to loss of available degrees of freedom. Einstein realized that exactly the same considerations must apply to mechanical oscillators, such as atoms in a solid.  He assumed each atom to be an independent simple harmonic oscillator, and, just as in the case of black body radiation, the oscillators can only absorb energies in “quanta”. Consequently, at low enough temperatures there is rarely sufficient energy in the ambient thermal excitations to excite the oscillators, and they freeze out.

Later on some improvements were introduced and the basic set of oscillators was taken to be standing sound wave oscillations in the solid rather than individual atoms (even more like black body radiation in a cavity) but the main conclusion was not affected.  In the more modern picture of sound waves in a solid, the “elementary” sound wave, analogous to the photon, is called the phonon, and has energy hf, where h is again Planck’s constant, and f is the sound frequency. Oscillations of molecules can usually be analyzed fairly accurately as simple harmonic oscillations, in particular the diatomic molecule.

References:

1.      Albert Einstein; Wikipedia; https://en.wikipedia.org/wiki/Albert_Einstein (accessed on: 6/21/13);

2.      Fowler, M.; The Simple Harmonic Oscillator; University of Virginia; Access: http://galileo.phys.virginia.edu/classes/751.mf1i.fall02/SimpleHarmonicOscillator.htm  (accessed on: 6/21/13);

3.      Einstein solid; Wikipedia; Access: http://en.wikipedia.org/wiki/Einstein_solid  (accessed on: 6/21/13);

4.      The heat capacity of a solid; Access: http://ruelle.phys.unsw.edu.au/~gary/PHYS3020_files/SM3_6.pdf (accessed on: 6/21/13);

5.      Ilustration  www.wikipedia.org/wiki/Debye_modlel (accessed on: 6/21/13);

The Origins of Quantum Physics

The so called classical physics in which the main Isaac Newton  (1642-1727)´s ideas are in the center of  an organized set of analytical tools used to explains matter and energy at the macroscopic level, including the behavior of astronomical bodies. It remains the key to measurement for much of modern science and technology; but at the end of the 19th Century observers discovered phenomena in both the large (macro) and the small (micro) worlds that classical physics could not explain Coming to terms with these limitations led to the development of quantum mechanics, a major revolution in physics. Some aspects of quantum mechanics can seem counter-intuitive, because they describe behavior quite different than that seen at larger length scales, where classical physics is an excellent approximation. New concepts are arise so dare in propositions such as the concept of a “ pack unit of light” named “ photon” that  behave in some respects like particles and in other respects like waves. Quantum mechanics predicts the energies, the colours, and the spectral intensities of all forms of electromagnetic radiation and that explains the behavior of matter and its interactions with energy on the scale of atoms and atomic particles as well.
Quantum mechanics ordains that the more closely one pins down one measure (such as the position of a particle), the less precise another measurement pertaining to the same particle (such as its momentum) must become. Put another way, measuring position first and then measuring momentum does not have the same outcome as measuring momentum first and then measuring position; the act of measuring the first property necessarily introduces additional energy into the micro-system being studied, thereby perturbing that system. Even more disconcerting, pairs of particles can be created as "entangled twins." As is described in more detail in the article on Quantum entanglement, entangled particles seem to exhibit what Einstein called "spooky action at a distance," matches between states that classical physics would insist must be random even when distance and the speed of light ensure that no physical causation could account for these correlations.
Quantum physics in a general sense became the branch of science that deals with the evolution of discrete, indivisible units of energy called quanta as described by the Quantum Theory in which five main ideas are in the basis of its methodology:

1. Energy is not continuous, but comes in small but discrete units.
2. The elementary particles behave both like particles and like waves.
3. The movement of these particles is inherently random.
4. It is physically impossible to know both the position and the momentum of a particle at the same time. The more precisely one is known, the less precise the measurement of the other is.
5. The atomic world is nothing like the world we live in.  

Particle/Wave Duality
Particle/wave duality is perhaps the easiest way to get aquatinted with quantum theory because it shows, in a few simple experiments, how different the atomic world is from our world.

The behavior of light in its interaction with matter was indeed a key problem of 19^th century physics. Max Planck (1848 – 1047) was interested in the two theories that overlapped in this domain. The first was the electrodynamics, the theory of electricity, magnetism, and light waves, brought to final form by James Clerk Maxwell (1831 – 1879) in the 1870s.

The second, dating from roughly the same period, was thermodynamics and statistical mechanics, governing transformations of energy and its behavior in time. A pressing question was whether these two grand theories could be fused into one, since they started from different fundamental notions.

Beginning in the mid-1890s, Planck took up a seemingly narrow problem, the interaction of an oscillating charge with its electromagnetic field. These studies, however, brought him into contact with a long tradition of work on the emission of light. As a practical result of the related developments, Planck made a very remarkable discovery: the law of radiation of bodies as a function of temperature could not be derived solely from the Laws of Maxwellian electrodynamics. To arrive at results consistent with the relevant experiments, radiation of a given frequency f had to be treated as though it consisted of energy atoms (photons) of the individual energy hf, where h is Planck's universal constant. This concept turned to be the beginning of a quantum revolution that continues to unfurl its veil today.

REFERENCES:

1.      Wikipedia (2012) ; Introduction to quantum mechanics ; http://en.wikipedia.org/wiki/Introduction_to_quantum_mechanics

2.      Think Quest (2012) ; http://library.thinkquest.org/3487/qp.html

3.      Carson, Cathyrin (2000) ; The origins of quantum theory ; http://www.slac.stanford.edu/pubs/beamline/30/2/30-2-carson.pdf

4.      The Quantum Theory of Albert Einstein (2012) ; http://www.spaceandmotion.com/quantum-theory-albert-einstein-quotes.htm

5.       The Solvay Congress of 1927´s photo source : American Institute of Physics  http://www.aip.org/history/einstein/quantum1.htm