By Dr. John Millam1
Quantum mechanics is the powerful yet mystifying set of rules that govern the atomic and subatomic realms. In this series of short articles we have already presented an overview of quantum mechanics (part 1), wave-particle duality (part 2), quantum tunneling (part 3), and quantum entanglement (part 4). (For a quick review, see Appendix: Overview of Quantum Mechanics.) For this final part, we will shift to the most practical manifestation of quantum mechanics: chemistry. Our world is constructed of atoms, and quantum mechanics governs the behavior of atoms.
A Brief History of the Atom
Everything we see around us—our food, clothes, and even our bodies—is constructed of atoms. This fact is well known today, but that has not always been the case. The story of how we came to our modern understanding of atoms is long, but vital for understanding the world around us (see Figure 1).2
The idea that matter is made up of tiny indivisible particles is ancient, appearing in many cultures, such as Greece and India. One important early advocate for the existence of atoms was Democritus (5th century BC), who proposed that all matter is composed of tiny indivisible particles called atoms. The term “atom” comes from the Greek atomos, meaning “uncuttable.” Democritus postulated that atoms are too small for the human senses to detect, they are infinitely many, they come in infinitely many varieties, and that they have always existed.
Some early thinkers went a step further by speculating about the shapes of atoms to explain particular observed properties of bulk materials. For example, some thought iron atoms possessed small hooks that linked with neighboring atoms as an attempt to explain why iron is a solid. Similarly, water atoms were assumed to be smooth and slippery to account for water being a liquid.
The first direct scientific evidence for atoms came from John Dalton in the early 1800s. Through a long series of experiments, he demonstrated the “law of multiple proportions,” where components of a reaction are related by small whole-number ratios. For example, the reaction of 2 liters of hydrogen gas with 1 liter of oxygen gas yields 2 liters of water.3 The simple, fixed proportions in this and many other reactions provided clear evidence that reactions involved rearranging chemically indivisible components, that is, atoms. Distinct chemical compounds could therefore be understood as collections of different elements (kinds of atoms). Reactions involve exchanging atoms to create new compounds. At the time, no one knew anything about the structure of atoms, so they were assumed to be featureless solid spheres, like billiard balls.
1 Ph.D. in Theoretical Chemistry from Rice University. Full permission is given to reproduce or distribute this document, or to rearrange/reformat it for other media, as long as credit is given, and no words are added or deleted from the text.
2 Discussion summarized from “The History of the Atom – Theories and Models,” Compound Interest, https://www.compoundchem.com/2016/10/13/atomicmodels/.
3 This result reflects the underlying stoichiometric relationship: 2H2 + O2 → 2H2O.
2
The next significant development in atomic structure did not come until nearly a century later. In 1897, J. J. Thomson investigated the nature of particles emitted in cathode ray tubes. Through experiments, he determined that cathode rays were comprised of a previously unknown type of negatively charged particle that we now call an electron. His critical insight was to recognize that electrons were a component of atoms. This discovery meant that atoms were not truly indivisible as had long been assumed. Because atoms are electrically neutral, he reasoned the negatively charged electrons must be counterbalanced by a corresponding positively charged component. Nothing was known of the internal structure of atom, so Thomson proposed that the positive charge was spread evenly throughout the atom. This conception became known as the plum pudding model (1904), where the negatively charged “plums” are embedded in a sphere of diffuse positively charged “pudding.” For his work, Thomson received the Nobel Prize in 1906.
Further insight came from a series of experiments performed from 1908 to 1913 by Hans Geiger and Ernest Marsden under the direction of Ernest Rutherford. To probe the internal structure of atoms, they bombarded thin metal foils with positively charged alpha particles (helium nuclei). Based on Thomson’s plum pudding model, the alpha particles should have passed through the metal atoms with minimal resistance. However, some particles were strongly deflected. To Rutherford’s astonishment, about one of every 8,000 alpha particles rebounded nearly back along the direction they came. This observation was so shocking that he declared, “It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you.” The only way to
Figure 1: A history of the atom: theories and models.
Credit: Compound Interest.
Figure 2: “It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you.” Ernest Rutherford.
Credit: Internet.
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explain the experimental results was if almost all the atom’s mass was concentrated in an extremely small, dense core called the nucleus. The rest of the atom would be mostly empty space.
Rutherford had expected the Geiger-Marsden experiments would confirm Thomson’s plum pudding model of the atom; instead, they demolished it. This experimental result led Rutherford to propose a new model for the atom in 1911. According to his nuclear model, atoms consisted of a tiny, positively-charged nucleus orbited by the negative electrons. This model treated the electrons in the atom like planets orbiting a star.
Rutherford’s nuclear model was a significant advance over previous models, but it had one glaring flaw. According to Maxwell’s equations of electromagnetism, electrons moving in a circular path should emit electromagnetic radiation. If that happened, the electrons would steadily lose energy, causing them to spiral inward until reaching the nucleus. Atoms should immediately collapse in a flash of radiation. Without atoms, life would be impossible anywhere in the universe! We exist, so how do we explain the existence of stable atoms?
The resolution to this conundrum came from an unexpected direction. In 1885, Johann Balmer identified six distinct emission lines for hydrogen atoms in the visible light range. These lines are known as the Balmer series. Balmer was subsequently able to show that these wavelengths could be computed using a simple mathematical formula that became known as the Balmer formula. Using the formula, each wavelength is specified by a simple integer. In 1888, Johannes Rydberg generalized Balmer’s formula and concluded that there must be additional emission lines in the ultraviolet and infrared range.
It was later shown that Rydberg’s formula could be re-expressed in terms of energy. In this form, Niels Bohr (1913) quickly realized that hydrogen’s spectrum could be explained if the electrons could only occupy a few allowed orbits with specific energies. The observed wavelengths would then correspond to transitions between these energy levels (see Figure 3). The remaining mystery was why electrons in atoms were constrained to just these specific orbits.
Figure 3: Electronic transitions for the hydrogen atom.
Credit: Course Hero with Balmer lines insert from Wikipedia commons.
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Applying ideas from the emerging field of quantum mechanics, Bohr was able to successfully model the spectrum of hydrogen atoms using just three postulates:
- Electrons are only allowed in fixed orbits and jump directly from one allowed orbit to another.4
- The orbital angular momentum of an electron is quantized, i.e., angular momentum = nh/2, where h is Planck’s constant and n is a positive integer.
- The frequency of light emitted or absorbed is given by the difference in energy levels, i.e., E = h, where is the frequency of the emitted light.
Bohr’s quantum model (1913) largely followed Rutherford’s model but with two crucial differences: the orbits were replaced with perfectly circular ones, and the radii of these orbits were restricted to very specific values. This is sometimes referred to as a planetary model because it resembles a miniature version of our solar system. Bohr’s model was a significant advancement over previous models but had several flaws. One major limitation was that it could not predict the energy levels of elements heavier than hydrogen.
The most important contribution of Bohr’s model was that it explained why atoms are stable. The electrons are restricted to fixed orbits and can only jump from one orbit to another and nowhere else. This restriction effectively prevented electrons from spiraling inward because that would not correspond to one of the fixed orbits. Electrons cannot go below the minimum energy orbit thus are prevented from falling into the nucleus. Saving the atom was a major triumph for quantum mechanics.
The final stage in our understanding of atoms was ushered in by Erwin Schrödinger who published an equation governing quantum mechanical behavior in 1926. This model replaced the ad hoc rules of old quantum theory with a unified mathematical framework. When Schrödinger’s equation was applied to the hydrogen atom, it accurately described the energy levels but in a more general way than Bohr’s model. This new approach successfully described all elements and chemical systems. Two years later, Paul Dirac modified Schrödinger’s equation to satisfy Einstein’s theory of special relativity, but it mostly just refined Schrödinger’s model.
Where is the electron?
Schrödinger’s equation completely revolutionized our understanding of atoms. One of the most profound changes involved how the electrons in atoms were described. In a radical departure from classical mechanics, quantum mechanics does not designate where an electron is, only where it might be. Precise formulas for the electron’s position or velocity were replaced with statistical probabilities.
In both Rutherford and Bohr’s atomic models, electrons were treated as simple point particles following well-defined orbits. Schrödinger’s model completely upended this notion by treating electrons as waves. Bohr’s circular orbits were replaced by orbitals—complex mathematical solutions to Schrödinger’s equation. The square of an orbital is the probability density used to calculate the probability of finding the electron at a given location. These orbitals and associated densities extend over all of space. Still, the bulk of the probability is concentrated in specific areas defining where the electron is most likely to be found. According to this model, electrons are treated as being smeared out over an area of space like a diffuse cloud.
4 One detail that bothered scientists about Bohr’s model was the notion that the electrons undergo quantum jumps between energy levels. That is, the electrons were thought to abruptly disappear from one orbit and instantly reappear in another orbit without moving in between. This situation posed considerable conceptual difficulties, but at the time theoreticians had little choice but to accept this description. Scientists today have replaced these discontinuous jumps with transitions that involve a smooth evolution from one energy level to another.
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Energy Levels of Hydrogen
Solving Schrödinger’s equation for any system (not just
atoms) yields a set of wavefunctions. Consider the time-independent
Schrödinger equation:
ˆH
(r) = E (r)
n n n
, Equation 1
where Ĥ is the Hamiltonian operator, n(r) is the set of
wavefunctions, En are the associated energies, and n is an
integer.
The Hamiltonian operator, Ĥ, describes all the forces and properties
of a given system. One can use the Hamiltonian to solve for the set
of possible wavefunctions, n(r), and their associated energies, En.
Each solution is identified by an integer quantum number, n (or
several quantum numbers). The presence of integer quantum
numbers is a hallmark of quantum mechanics.
To better understand these energy levels, it is often helpful to
visualize the orbital energies arranged vertically by increasing energy
starting with the lowest energy at the bottom. This arrangement is
comparable to shelves in a bookcase (see Figure 4). Just as books
can only rest on a shelf and never in between shelves, electrons
occupy only one energy level at a given time. Electrons can jump
from one “shelf” to another by emitting or absorbing a photon of light.
However, the spacing between the “shelves” is governed by the nature
of the system and is generally not equally spaced.
A guitar string serves as another analogy for these energy levels. A plucked guitar string
will produce a specific tone known as its fundamental frequency. This pitch represents the lowest
frequency vibration for that string. But the same string can create a series of higher frequency
vibrations known as overtones. This discrete set of harmonic frequencies is a useful analog to the
discrete energy levels in quantum systems.
Quantum numbers
Bohr only required a single quantum number, n, to explain the spectrum of hydrogen.5 In
1915, Arnold Sommerfeld generalized Bohr’s model to allow for elliptical rather than circular
orbits. In doing so, he introduced a second quantum number that he termed the azimuthal quantum
number, l, describing the orbital angular momentum. In 1920, Sommerfeld added a third quantum
number, the magnetic quantum number, m. This addition was needed to explain the Zeeman effect
where the usual emission lines split into multiple lines in the presence of a magnetic field. The
Bohr-Sommerfeld model resolved numerous issues with atomic spectra but still had several
shortcomings. A fourth quantum number, spin, will be discussed later.
These three quantum numbers were invoked to explain specific experimental results. This
situation changed when theoreticians solved Schrödinger’s equation for the hydrogen atom and
found these quantum numbers to be the natural byproducts of mathematics. The atomic orbitals
of hydrogen are defined by a set of three quantum numbers:
- Principal quantum number (n) has values 1, 2, 3…
5 Discussion summarized from Dr. Helen Klus, How We Came to Know the Cosmos, Chapter 11, “Sommerfield’s
Atom.”
Figure 4: Bookcase analogy
for quantum energy levels.
Credit: John Millam.
6 - Angular momentum quantum number (l) has values 0 to n-1.
- Magnetic quantum number (ml) has values –l to l.
Quantum number n determines the radial form of an orbital, while l and ml define its shape. The principal quantum number, n, corresponds to an element’s row in the periodic table.
Atomic orbitals for hydrogen
Just what do these atomic orbitals look like? Figure 5 shows a cross-section of various orbitals of the hydrogen atom. (The orbitals for other elements are similar to these.) Each of the displayed orbitals is identified by a set of three quantum numbers (n, l, and ml).
A detailed understanding of the shapes of these orbitals is not essential for our discussion. The primary purpose of viewing them is to highlight just how radically different orbitals are compared to classical orbits. The shapes of orbitals are defined by mathematics and so are very difficult to visualize and defy intuition.
Atomic spectroscopy
Spectroscopy is the study of the absorption and emission of light by matter. It has proved to be an invaluable tool for studying the inner workings of atoms.
Before considering the spectra of atoms, let us briefly discuss black-body radiation—the light given off by an object due to its temperature. Black-body radiation is the result of the vibrational motion of the atoms due to their thermal energy. Although all bodies emit black-body radiation, only those that are hot enough (temperature > 500 °C) will have a visible glow. The color of the emitted light depends on the temperature varying from red (1000 °C), to orange-white (3000 °C), to white (6000 °C), and to blue (12000 °C). White light sources are of particular interest because they include all the visible colors in approximately equal amounts. Our sun (surface temperature 5500 °C) is the most recognizable white-light source. Incandescent light bulbs (temperatures 2000-3000 °C) are another common example.
When analyzing the composition of a light source, it is necessary to spread out the light so that we can examine the intensity of individual frequencies. One simple way to do this is by passing the light through a prism. For example, passing sunlight through a prism will cause it to split into a rainbow of colors. In scientific applications, a diffraction grating is employed to accomplish the same effect.
When light from the sun (or other black-body radiators) passes through a prism, we get a continuous spectrum. That is, all the light frequencies are possible, although the amount of light at a particular frequency depends on the object’s temperature. In contrast, atoms absorb or emit light only at specific frequencies, as previously discussed for hydrogen atoms. This is known as a discrete spectrum. Each element produces a distinct set of frequencies that is unique to that element.
Figure 5: Atomic orbitals for hydrogen.
Credit: Wikipedia commons.
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The simplest way to obtain the spectrum of an element is to place a small sample in a vacuum-sealed bulb and pass electricity through it. This causes electrons in the atoms to jump to a higher energy state and then emit light as they drop back down to a lower energy state. The resulting spectra is referred to as an emission spectrum (see Figure 6).
A complementary way to find these frequencies is to pass white light through a cool gas. What passes through will be the original continuous spectrum but with small gaps corresponding to the frequencies absorbed by the gas. This is known as an absorption spectrum (see Figure 6).
Spectra of multi-electron atoms
Hydrogen atoms possess a single electron making their spectra relatively simple. The situation is more complicated for other elements due to the interactions between the electrons. As a result, the simple formula used for hydrogen’s energy levels does not apply to these cases. It was not until Schrödinger’s equation (1926) and the Dirac equation (1928) that finally allowed theoreticians to correctly predict the energy levels of all elements.
A second challenge in describing non-hydrogen atoms was determining how the electrons distribute themselves among the available energy levels. It was eventually worked out that each orbital may contain no more than two electrons due to the Pauli exclusion principle (explained later). Electrons first fill the lowest energy orbitals, then progressively fill higher energy orbitals once the lower energy orbitals are filled.
Because of the complicated nature of the interactions, the energy levels and corresponding spectra of each element are unique, like a fingerprint. This feature has many practical applications. Some specific examples: - Stellar spectra. All stars, including our sun, emit light across the visible spectrum. Just beyond the surface of a star, cooler atoms will absorb some of the light, resulting in an
Figure 7: Spectra of the sun, hydrogen, helium, mercury, and unranium.
Credit: Elliot Science.
Figure 6: Three types of spectra: white light, absorption, and emission.
Credit: Alex Montwill and Ann Breslin, The Quantum Adventure, p 36.
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absorption spectrum (see Figure 7). From this data, astronomers can determine which elements are present in the star as well as their abundance. - Discovery of helium. When scientists were studying the sun’s spectrum (see Figure 7) in 1868, they noticed yellow absorption lines that did not correspond to any elements known at the time. Based on this observation, they proposed a new element, helium, from the Greek helios for “sun.” It was not until 1895 that helium was observed here on earth.
- Elemental analysis. In atomic emission spectroscopy, a sample is atomized and heated in a flame (or similar mechanism), causing the atoms to emit at their characteristic frequencies. The quantity of an element present in the sample can be determined by carefully examining its spectral lines. Atomic absorption spectroscopy operates similarly except it studies the absorbed rather than emitted light.
- Fireworks. Fireworks make for an exciting Fourth of July. Exploding fireworks can display many colors depending on which elements are included (see Figure 8).
What is Spin?
Spin is a form of angular momentum intrinsic to elementary particles. It is a fundamental property like mass and charge. All elementary particles (e.g., electrons and quarks), composite particles (e.g., protons and neutrons), and atomic nuclei possess spin. Spin was first discovered in electrons and has no classical counterpart.
Our understanding of spin emerged piecemeal during the 1920s, with the first piece of the puzzle coming from the Stern-Gerlach experiment. In 1921, Otto Stern conceived of an
Figure 8: The Chemistry of Firework Colours.
Credit: Compound Interest.
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experiment to measure angular momentum in atomic systems, with the work being carried out by Walther Gerlach in 1922. The Stern-Gerlach apparatus (see Figure 9) sends a stream of silver atoms through a strong inhomogeneous magnetic field. Silver atoms have a single unpaired electron that will receive a slight upward or downward push from the magnetic field depending on its angular momentum. (The effect on the remaining electron pairs cancels and therefore can be ignored.) The silver atoms will then accumulate on a glass plate where the experimentalists can determine the degree to which the magnetic field deflected them.
In the classical understanding of angular momentum, all possible orientations of the angular momentum would be allowed, so we should expect to see a continuous streak running above and below the centerline. Quantum mechanics, however, predicted their angular momentum would be quantized with only select orientations possible. In this case, we should only observe discrete spots corresponding to each allowed possibility. In the experiment, two spots were detected, proving that angular momentum was quantized. (For a quick visual introduction to the Stern-Gerlach experiment, watch this 1 ½ minute animated video.)
Despite the success of the Stern-Gerlach experiment, a major problem remained. Theory had predicted that there should have been an odd number of spots rather than two. In the Bohr-Sommerfeld model, there should be one spot for each possible magnetic quantum number, ml. For an electron in an orbital with angular momentum, l, there should be 2*l+1 possible values of ml and therefore an odd number of spots. So, the observed result would only make sense if l = ½ rather than an integer. Later, physicists resolved the problem when they realized that the deflection resulted from electron’s spin rather than its orbital angular momentum.
Theoreticians were soon grappling with a different mystery. By 1924, scientists recognized that each energy level in an atom could be occupied by up to two electrons. Wolfgang Pauli realized this could only be explained if the electrons had a fourth quantum number with two possible values. The following year, George Uhlenbeck and Samuel Goudsmit developed Pauli’s idea and named this new quantum number “spin.” They proposed a simple physical interpretation of spin as the rotation of a particle around its own axis. Physicists quickly objected that this could not be entirely correct because elementary particles are point-like and therefore do not rotate. Nevertheless, spin does obey the same mathematics as quantized angular momentum. The main difference is that spin allows both integer and half-integer values. For electrons, the spin quantum number, s, has two possible values, s = ±½.
In 1927, Pauli combined spin with Schrödinger’s equation to develop what became known as the Pauli exclusion principle. Pauli’s work established that electrons in atoms are forbidden from having the same set of quantum numbers. This meant that electrons must either be located in
Figure 9: Stern-Gerlach apparatus. (1) furnace, (2) beam of silver atoms, (3) inhomogeneous magnetic field, (4) classically expected result, (5) observed result.
Credit: Wikipedia commons.
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different orbitals (quantum numbers n, l, and ml) or in the same orbital but with opposite spins (quantum number s).
Schrödinger’s equation does not include spin, so spin had to be incorporated ad hoc to fit experimental results. Later when Paul Dirac extended Schrödinger’s work to satisfy special relativity in 1928, spin was revealed to be a natural consequence. Dirac’s equation provided a rigorous theoretical description of spin, including the possibility of half-integer spin quantum numbers.
Orbital angular momentum versus spin
Orbital angular momentum and spin are two physically and mathematically similar concepts yet are distinct and separate. Orbital angular momentum (quantum number l and ml) describes the motion of the electron with respect to the nucleus. Spin angular momentum (quantum number s) designates the electron’s intrinsic angular momentum. As an analogy, orbital angular momentum can be compared to the Earth orbiting the sun, while spin is analogous to the Earth rotating about its own axis.
Fermions and Bosons
All elemental particles possess spin. While the spin of an electron is 1/2, other particles possess other values. In all cases, spin must be either an integer or a half-integer. For example, quarks have spin 1/2, photons (particles of light) have a spin of 1, and the recently discovered Higgs boson has a spin of 0 (see Figure 10). Elementary particles are divided into two classes: fermions with half-integer spins and bosons with integer spins. Of the elementary particles, matter particles (e.g., quarks and electrons) are fermions, and force-carrying particles (e.g., photons, gluons, and Higgs particles) are bosons.
Figure 10: Standard Model of Elementary Particles.
Credit: Wikipedia commons.
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Composite particles consist of two or more elementary particles bound together in a single unit. The two most important examples are protons and neutrons, each comprised of three quarks. Composite particles have a spin derived from their component particles’ spin, but the details are complicated. Protons and neutrons each have a spin of 1/2, making them fermions.
Atomic nuclei are comprised of sets of protons and neutrons whose number is determined by the isotope of the element. Nuclei can have a variety of spin values but are always fermions if they have an odd number of protons and neutrons, and bosons if they have an even number. Some examples of nuclear spin: 2H (deuterium) has spin 1, 17O has spin 5/2, 55Fe has spin 3/2, and 57Co has spin 7/2.6
Table 1: Comparison of fermions and bosons.
Fermions Bosons Values Half integer (e.g., 1/2, 3/2, 5/2, …) Integer (e.g., 0, 1, 2, …) Described by Enrico Fermi and Paul Dirac Satyendra Nath Bose and Albert Einstein Examples Protons, neutrons, and electrons Photons and Higgs bosons Role Matter particles Force carriers Obeys the Pauli Exclusion Principle Yes No
The most fundamental distinction between fermions and bosons is that only fermions obey the Pauli exclusion principle. Simply put, bosons are like horses that prefer to travel together in herds. In contrast, fermions are like cats being extremely individualistic and avoiding what other cats are doing.
Why half-integer spins?
What does it mean that fermions have half-integer spins? Why not just multiply by 2 to make all spins plain integers? Theoreticians recognize that the factor of ½ has fundamental mathematical significance and must be retained. Orbital angular momentum only allows integer values because a complete orbit (360°) always leaves the particle’s wavefunction unchanged. For spin of a fermion, a full rotation simply reverses the sign of the wavefunction. It takes another full rotation (for a total of 720°) to leave the wavefunction unchanged. The factor of one-half in the spin quantum numbers reflects the need for two complete rotations rather than one.
A pictorial way of understanding spin quantum numbers is given in Appendix: Understanding Spin.
Importance of Spin
So far, we have only considered individual particles. The distinction between bosons and fermions is best demonstrated when contemplating a collection of identical particles. With some simple math, we can show how this leads to some interesting consequences. If you are uncomfortable with math, feel free to skip to the next section.
Groups of indistinguishable particles (such as electrons) must be treated as part of the same wavefunction—rather than being treated separately. We can write the wavefunction () of two such particles, with the first at position 1 and the second at 2 as (1,2). When we say two particles
6 Values taken from http://hyperphysics.phy-astr.gsu.edu/hbase/Nuclear/nspin.html#c2.
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are indistinguishable in quantum mechanics, we mean that nothing observable would change if the
particles suddenly switched places. More precisely, the probability density (the square of the
wavefunction) would remain unchanged after the switch:
2(1,2) = 2(2,1).
Taking the square root of both sides, we find the sign of the wavefunction may change in the
process:
(1,2) = (2,1)
Swapping the locations of two identical particles is equivalent to rotating the particle’s
wavefunction by 360°. Under these conditions, the wavefunction of a fermion will change sign,
but a boson will not: - ( , ) for bosons
( , ) =
( , ) for fermions
−
2 1
1 2
2 1
This difference in sign under particle exchange is the principal reason that fermions and bosons
behave so differently. Now, let us consider what would happen in each case if both particles
attempted to occupy the same location.
Fermion case: (1,2) = –(2,1) - Consider both particles at position 1: (1,1) = –(1,1)
- Therefore, (1,1) = 0 and 2(1,1) = 0
The conclusion indicates that there is zero probability of two identical fermions residing at the
same location. This result is the origin of the Pauli exclusion principle!
Boson case: (1,2) = +(2,1) - Consider both particles at position 1: (1,1) = +(1,1)
- Therefore, (1,1) = (1,1) ✓
For bosons, there is no restriction on the wavefunction! Therefore, two bosons may occupy the
same location.
Fermions and Chemistry
As previously discussed, the arrangement of electrons in atoms is primarily determined by
the fact that electrons are fermions and must obey the Pauli exclusion principle. Now let us
imagine what would happen if electrons were bosons instead of fermions. In this scenario, all the
electrons in an atom would accumulate in the lowest energy orbital. For progressively higher
atomic numbers, this orbital becomes progressively lower in energy because of the increasing
attraction to the growing positive charge of the nucleus. The lower the energy of the orbital, the
more tightly bound the electron is to the atom. Electrons in most elements would be too tightly
bound to participate in chemical bonding. This result would prevent complex chemistry, and
therefore, life chemistry would not be possible in such a universe!
Our existence is permitted because the Pauli exclusion principle forces electrons in atoms
into progressively higher energy levels where they are less tightly bound. This requirement
ensures that the outermost (valence) electrons can participate in chemical reactions. This situation
is comparable to standing on a ladder and slowly sinking into mud. As the ladder rungs move
down, you periodically step up to the next rung, keeping yourself out of the mud. Life is possible
because electrons are subject to the Pauli exclusion principle!
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Bosons
Bosons were named in honor of Satyendra Nath Bose, who along with Albert Einstein, worked out the details of their behavior in the early 1920s. Because the Pauli exclusion principle does not restrict bosons, bosonic systems tend to aggregate in the lowest energy state. Some important examples: - Lasers. Lasers consist of many photons of the same frequency traveling together. This action is only possible because photons are bosons.
- Superfluid helium. When 4He atoms (bosons) are cooled to a liquid (at -269 °C), they behave as a superfluid where they flow with zero viscosity. As a superfluid, 4He can even flow up the walls of a container.
- Superconductivity. Superconductivity is a state of a material where its electrical resistance is zero, thus allowing electrical currents to flow without loss. That state is only possible at extremely low temperatures although some materials can superconduct at liquid nitrogen temperatures (-195.8 °C). Superconductivity can occur even though electrons are fermions, because they can pair up to form boson-like Cooper pairs.
However, the most exotic example of bosonic behavior is Bose-Einstein condensates (BEC). A BEC is considered the fifth state of matter (after solid, liquid, gas, and plasma) and has many exotic properties. The BEC atoms overlap their wavefunctions and behave collectively like a super-atom. (For more details, see this 1 ½ minute animated video.) The existence of this bizarre state was predicted in 1924-25 by Bose and Einstein, but it was not until 1995 that Eric Cornell and Carl Wieman demonstrated it in the lab. They did it by cooling a gas of rubidium atoms down to 170 nanokelvins or less than a millionth of a degree above absolute zero. Cornell and Wieman shared the 2001 Nobel prize for their work.
Appendix: Resources on Quantum Mechanics
Robert Gilmore, Alice in Quantumland: An Allegory of Quantum Physics.
Erica W. Carlson, The Great Courses: Understanding the Quantum World.
James Kakalios, The Amazing Story of Quantum Mechanics.
Alex Montwill and Ann Breslin, The Quantum Adventure: Does God Play Dice?
Brian Clegg, The Quantum Physics Bible: The Definitive Guide to 200 Years of Subatomic Science.
Banesh Hoffmann, The Strange Story of the Quantum.
Amir D. Aczel, Entanglement: The Greatest Mystery in Physics.
George Musser, Spooky Action at a Distance.