Why are p orbitals lobed?

Quantum physics

Quantum physics

Chapter 2 - Solid State Device Theory

"I think it's safe to say that no one understands quantum mechanics."

-Physicist Richard P. Feynman

To say that the invention of semiconductor devices is a revolution is no exaggeration. Not only was this an impressive technological achievement, but it paved the way for developments that would inevitably change modern society. Semiconductor devices have enabled miniaturized electronics, including computers, certain types of medical diagnostic and treatment equipment, and common telecommunications equipment, to name a few uses of this technology.

But behind this revolution in technology lies an even greater revolution in general science: the field of quantum physics. Without this leap into understanding the natural world, the development of semiconductor devices (and more advanced electronic devices that are still in development) would never have been possible. Quantum physics is an incredibly complex area of ​​science. This chapter is just a brief overview. When scientists of Feynman's caliber say that "nobody understands", one can be sure that it is a complex subject. However, without a basic understanding of quantum physics, or at least an understanding of the scientific discoveries that led to its formulation, it is impossible to understand how and why semiconductor electronic devices work. Most of the introductory electronic textbooks I've read try to explain semiconductors in terms of "classical" physics, which leads to more confusion than understanding.

Many of us have seen diagrams of atoms that look similar to Figureebelow.

Rutherford atom: negative electrons orbit a small positive nucleus.

Small particles of matter, called protons and neutrons, form the center of the atom; Electrons orbit like planets around a star. The nucleus carries a positive electrical charge due to the presence of protons (the neutrons have no electrical charge at all), while the negative charge of the atom lies in the orbiting electrons. The negative electrons are attracted to the positive protons, just as planets are attracted to the sun, while the orbits are stable due to the movement of the electrons. We owe this popular model of the atom to the work of Ernest Rutherford, who experimentally established around 1911 that the positive charges of atoms are concentrated in a tiny, dense nucleus instead of being evenly distributed across the diameter, as by an earlier researcher suggested to JJ Thompson.

Rutherford's scattering experiment consisted of bombarding a thin gold foil with positively charged alpha particles as shown in the figure below. Young PhD students H. Geiger and E. Marsden experienced unexpected results. Some alpha particles were deflected at wide angles. A few alpha particles were backscattered and jumped nearly 180 Degrees back . Most of the particles did not pass through the gold foil, which suggests that the foil was mostly blank. The fact that some alpha particles have experienced large deflections indicates the presence of a tiny positively charged nucleus.

Rutherford scattering: a beam of alpha particles is scattered by a thin gold foil.

Although Rutherford's atomic model was better than Thompson's for experimental data, it was still not perfect. Further attempts to define the atomic structure were made, and these efforts helped pave the way for the bizarre discoveries in quantum physics. Today our understanding of the atom is much more complex. Despite the revolution in quantum physics and its contribution to our understanding of atomic structure, Rutherford's solar system image of the atom has become so embedded in popular consciousness that it persists even in inappropriate areas in some areas of study.

Consider this brief description of electrons in an atom, taken from a popular electronics textbook:

Circumferential negative electrons are therefore drawn to the positive nucleus, which leads us to the question of why the electrons do not fly into the atomic nucleus. The answer is that the orbiting electrons remain in their stable orbit due to two equal but opposite forces. The centrifugal outward force exerted on the electrons due to the orbit counteracts the attractive internal force (centripetal) which tries to pull the electrons towards the nucleus because of the dissimilar charges.

In accordance with the Rutherford model, this author throws the electrons as solid chunks of matter on circular orbits, whose internal attraction to the oppositely charged nucleus is balanced by their movement. The reference to "centrifugal force" is technically wrong (even for planets in orbit), but is easily given due to its acceptance in the population: In reality there is no force that pushes an orbital body away from its orbit point. It seems to be because the inertia of a body tends to keep it in a straight line, and since a trajectory is a constant deviation (acceleration) from rectilinear motion, there is constant inertia to any force exerting the body towards the track attracts center (centripetal), be it gravity, electrostatic attraction or even the tension of a mechanical connection.

The real problem with this explanation, however, is the notion of electrons moving in circular orbits first. It is a demonstrable fact that accelerated electrical charges emit electromagnetic radiation, and this fact was known even in Rutherford's time. Since orbital motion is a form of acceleration (the orbiting object at constant acceleration away from normal rectilinear motion), electrons in a gyrating state should eject radiation like mud from a spinning tire. Electrons are known for this, which are accelerated around circular orbits in synchrotrons, so-called particle accelerators. The result is called synchrotron radiation. If electrons were to lose energy in this way, their orbits would eventually decay, which would lead to collisions with the positively charged nucleus. However, this does not usually happen within atoms. Indeed, electron "orbits" are remarkably stable over a wide range of conditions.

In addition, experiments with "excited" atoms showed that electromagnetic energy emitted by an atom occurs only at certain, certain frequencies. Atoms that are "excited" by external influences such as light absorb this energy and reproduce it as electromagnetic waves of certain frequencies, like a tuning fork that rings at a fixed distance, regardless of how it is hit. When the light emitted by an excited atom is divided into its constituent frequencies (colors) by a prism, distinct color lines appear in the spectrum, the pattern of the spectral lines being unique for this element. This phenomenon is commonly used to identify atomic elements and even measure the proportions of each element in a compound or chemical mixture. According to Rutherford's solar system atomic model (regarding electrons as chunks of matter that can freely circle around any radius) and the laws of classical physics, excited atoms should return energy over a practically unlimited range of frequencies instead of a few. In other words, if Rutherford's model were correct, there would be no "tuning fork" effect, and the spectrum of light emitted by any atom would appear as a continuous band of colors rather than a few separate lines.

Bohr hydrogen atom (with orbits drawn to scale) only inhabit electrons in discrete orbitals. Electrons falling from n = 3, 4, 5 or 6 to n = 2 are responsible for Balmer spectral lines.

A pioneering researcher named Niels Bohr attempted to improve on Rutherford's model after studying in Rutherford's laboratory for several months in 1912. In order to harmonize the results of other physicists (especially Max Planck and Albert Einstein), Bohr suggested each electron. They had a certain, specific amount of energy, and their orbits were quantized so that each could occupy certain places around the nucleus, since marbles, which were fixed in circular orbits around the core, earlier than the free-moving satellites were. Out of consideration for the laws of electromagnetics and accelerating charges, Bohr alluded to these "orbits" as stationary states in order to avoid the implication that they were in motion.

Bohr's ambitious attempt to reformulate the structure of the atom in such a way that it came closer to the experimental results, while a milestone in physics, was not complete. His mathematical analysis made better predictions of experimental events than analyzes of previous models, but there were still some unanswered questions about why electrons should behave in such strange ways. The claim that electrons existed in stationary, quantized states around the atomic nucleus was better suited for experimental data than Rutherford's model, but he had no idea what would force electrons to manifest those particular states. The answer to this question had to come from another physicist, Louis de Broglie, about a decade later.

De Broglie postulated that electrons as photons (light particles) manifest both particle-like and wave-like properties. Building on this proposal, he suggested that an analysis of orbiting electrons from a wave perspective rather than a particle perspective might make more sense of their quantized nature. Indeed, another breakthrough in understanding has been achieved.

String that oscillates between two fixed points at resonance frequency standing wave .

According to de Broglie, the atom was made up of electrons that existed as standing waves, a phenomenon known to physicists in various forms. How the plucked string of a musical instrument (pictured above) vibrates at a resonant frequency, with "knots" and "opposing knots" in stable positions along its length. De Broglie envisioned electrons around atoms curved like waves around a circle, as in FigureBelow.

"Orbiting" the electron as a standing wave around the nucleus, (a) two cycles per revolution, (b) three cycles per revolution.

Electrons could only exist in certain, certain "orbits" around the nucleus, because these were the only distances at which the shaft ends would fit together. In any other radius, the wave should self-destruct and thus cease to exist.

De Broglie's hypothesis gave both mathematical support and a practical physical analogy to explain the quantized states of electrons in an atom, but his atomic model was still incomplete. Within a few years, the independently working physicists Werner Heisenberg and Erwin Schrödinger built on de Broglie's concept of a matter-wave duality in order to generate more mathematically rigorous models of subatomic particles.

This theoretical advance from de Broglie's primitive standing wave model to Heisenberg's matrix and Schrödinger's differential equation models was dubbed quantum mechanics and brought a rather shocking property to the world of subatomic particles: the characteristic of probability or uncertainty. According to the new quantum theory, it was impossible to determine the exact position and the exact momentum of a particle at the same time. The common explanation for this "uncertainty principle" was that it was a measurement error (e.g. by measuring the position of an electron accurately, perturbing its momentum and thus not being able to know what it was before taking the position measurement, and vice versa) versa). The astonishing effect of quantum mechanics is that particles do not have precise positions and impulses, but rather balance the two quantities in such a way that their combined uncertainties never fall below a certain minimum value.

This form of "uncertainty" relationship exists in areas other than quantum mechanics. As discussed in the Mixed-Frequency AC Signals chapter in Volume II of this book series, there is a mutually exclusive relationship between the security of a waveform's time domain data and its frequency domain data. In simple terms, the more precisely we know its constituent frequency (s), the less precisely we know their amplitude in time and vice versa. To quote myself:

A waveform of infinite duration (infinite number of cycles) can be analyzed with absolute accuracy, but the fewer cycles the computer has available to analyze, the less precise the analysis. . . The fewer waves a wave passes through, the less certain its frequency is. Taking this concept to a logical extreme, a short pulse - a waveform that doesn't even complete a cycle - actually has no frequency, but rather acts as an infinite range of frequencies. This principle is common to all wave-based phenomena, not just alternating voltages and currents.

In order to accurately determine the amplitude of a varying signal, we need to sample it over a very narrow period of time. However, this limits our view of the frequency of the wave. Conversely, in order to determine the frequency of a wave with great accuracy, we have to scan it over many cycles, which means that at any point in time we lose sight of its amplitude. Therefore, we cannot know the instantaneous amplitude and total frequency of a wave at the same time with unlimited accuracy. Stranger still, this uncertainty is much more than the inaccuracy of the observer; it is in the nature of the wave. It's not as if with the right technology it would be possible to get accurate measurements of both instantaneous amplitude and frequency at once. Literally, a wave cannot have a precise, instantaneous amplitude and a precise frequency at the same time.

The minimal uncertainty of the position and the momentum of a particle, which is expressed by Heisenberg and Schrödinger, has nothing to do with a limitation of the measurement; rather, it is an intrinsic property of the particle's matter-wave double characteristic. Electrons do not really exist in their "orbits" as precisely defined parts of matter or even as precisely defined wave forms, but rather as "clouds" - the technical term is wave function - the probability distribution as if every electron "were". spread or smeared over a number of positions and moments.

This radical view of electrons as imprecise clouds initially seems to contradict the original principle of quantized electron states: that electrons exist in discrete, defined "orbits" around atomic nuclei. It was ultimately this discovery that led to the formation of quantum theory to explain it. How strange it seems that a theory developed to explain the discrete behavior of electrons eventually explains that electrons exist as "clouds" rather than individual pieces of matter. However, the quantized behavior of electrons does not depend on electrons that have certain position and momentum values, but rather on other properties called quantum numbers. In essence, quantum mechanics dispenses with general terms of absolute position and absolute momentum and replaces them with absolute terms that have no analogous experience.

Although electrons are known to exist in ethereal, "cloud-like" forms of distributed probability rather than discrete chunks of matter, these "clouds" have other properties that are discrete. Each electron in an atom can be described by four numerical measurements (the quantum numbers mentioned earlier) that represent the Principal, Angular Momentum, Magnetic and Spin Numbers are called. The following is a summary of the meanings of each of these numbers:

Principal Quantum Number: Symbolized by the letter n this number describes the shell in which an electron is located. An electron shell is a region of space around the atomic nucleus in which electrons are allowed to exist, according to the stable "standing wave" pattern of de Broglie and Bohr. Electrons can "jump" from shell to shell, but cannot exist between the shell areas .

The principal quantum number must be a positive integer (an integer greater than or equal to 1). In other words, the principal quantum number for an electron cannot be 1/2 or -3. These integer values ​​were not determined arbitrarily, but through the experimental detection of light spectra: The different frequencies (colors) of the light emitted by excited hydrogen atoms follow a sequence that is mathematically dependent on specific, integer values, as shown in Figure 6.

Each shell has the capacity to hold several electrons.An analogy for electron shells are the concentric rows of seats in an amphitheater. Just as a person sitting in an amphitheater has to choose a row of seats (you cannot sit between the rows), the electrons have to "choose" a particular shell. As in rows of amphitheaters, the outermost shells hold more electrons than the inner shells. In addition, electrons tend to seek the lowest available shell, as people in an amphitheater seek the closest seat to the main stage. The higher the number of shells, the greater the energy of the electrons in it.

The maximum number of electrons each shell can hold is given by equation 2n 2 described, where "n" is the principal quantum number. Thus the first shell (n = 1) can hold 2 electrons; the second shell (n = 2) 8 electrons and the third shell (n = 3) 18 electrons. (Picture below)

Principal quantum number n and maximum number of electrons per shell, both divided by 2 (n 2 ) were predicted and observed. Orbitals not to scale.

Electron shells in an atom used to be called letters rather than numbers. The first bowl (n = 1) was filled with K, the second bowl (n = 2) L, the third bowl (n = 3) M, the fourth bowl (n = 4) N, the fifth bowl (n = 5) designated. O, the sixth shell (n = 6) P and the seventh shell (n = 7).

Angular Momentum Quantum Number: A shell consists of lower shells. One might be inclined to think of sub-shells as simple subdivisions of shells, as streets dividing a street. The subshells are a lot stranger. Subshells are regions of space in which electrons "clouds" are allowed to exist and different subshells actually have different shapes. The first subshell has the shape of a sphere (FigureBelow (s)), which is useful if it is visualized as a cloud of electrons that surrounds the atomic nucleus in three dimensions. The second lower shell, however, resembles a dumbbell, made up of two "lobes" joined together at a single point near the center of the atom. (Figure below (p)) The third subshell resembles a group of four "praises" that are grouped around the atomic nucleus. These subshell shapes are reminiscent of graphical representations of the radio antenna signal strength, with bulbous, lobed areas extending from the antenna in different directions. (Figure below (d))

Orbitals: (s) triple symmetry. (p) Shown: p x, one of three possible orientations (p x, p y, p z ) around their respective axes. (d) Shown: d x2 - y2 similar to d xy, d Y Z, d xz . Shown: d z2 . Possible d orbital orientations: five.

Valid angular momentum quantum numbers are positive whole numbers like main quantum numbers, but also contain zero. These quantum numbers for electrons are given by the letter l symbolizes. The number of subshells in a shell corresponds to the main quantum number of the shell. Therefore the first shell (n = 1) has a subshell with the number 0; the second shell (n = 2) has two sub-shells, numbered 0 and 1; The third shell (n = 3) has three sub-shells, numbered 0, 1 and 2.

An older convention for subshell descriptions used letters instead of numbers. In this notation, the first partial shell (l = 0) was designated with s, the second partial shell (l = 1) with p, the third partial shell (l = 2) with d and the fourth partial shell (l = 3) with f. The letters come from the words sharp, principal (not to be confused with the main quantum number, n), diffuse and fundamental. You will still see this notation convention in many periodic tables to denote the electronic configuration of the outermost or valence shells of atoms. (Picture below)

(a) Bohr representation of the silver atom, (b) subshell representation of Ag with subdivision of the shells into subshells (angular quantum number l). This diagram does not imply anything about the actual position of electrons, but rather represents energy levels.

Magnetic Quantum number : The magnetic quantum number for an electron classifies which direction its subshell shape is directed. The "praises" for subshells point in several directions. These different orientations are called orbitals. For the first subshell (s; l = 0), which resembles a sphere that does not point in any "direction", there is only one orbital. For the second (p; l = 1) lower shell in each shell, which resembles dumbbells, point them in three possible directions. Imagine three dumbbells crossing at the origin, each aligned along a different axis in a three-axis coordinate space.

Valid numerical values ​​for this quantum number consist of integer numbers from -l to l and are called in atomic physics m l and in nuclear physics as l symbolizes. To calculate the number of orbitals in a given subshell, double the subshell number and add 1, (2 · l + 1). For example, the first subshell (l = 0) in each shell contains a single orbital, numbered 0; the second subshell (l = 1) in any shell contains three orbitals, numbered -1, 0 and 1; the third subshell (l = 2) contains five orbitals with the numbers -2, -1, 0, 1 and 2; and so on.

As with the main quantum numbers, the magnetic quantum number arose directly from experimental evidence: the Zeeman effect, the division of spectral lines by exposing an ionized gas to a magnetic field, hence the name "magnetic" quantum number.

Spin quantum number : Like the magnetic quantum number, this property of atomic electrons was discovered experimentally. Close observation of the spectral lines showed that each line was actually a pair of lines very close together, and this so-called fine structure was hypothesized that each electron "rotates" on an axis as if it were a planet. Electrons with different "spins" would give off slightly different light frequencies when excited. The name "Spin" was assigned to this quantum number. The concept of a rotating electron is obsolete today and is better suited for the (incorrect) consideration of electrons as discrete pieces of matter than as "clouds"; but the name remains.

Spin quantum numbers are called in atomic physics m s and in nuclear physics as s called . For each orbital in each subshell in each shell there can be two electrons, one with a spin of +1/2 and the other with a spin of -1/2.

The physicist Wolfgang Pauli developed a principle that explains the order of electrons in an atom according to these quantum numbers. His principle, called the Pauli Exclusion Principle, states that no two electrons in the same atom can occupy exactly the same quantum states. That is, every electron in an atom has a unique set of quantum numbers. This limits the number of electrons a given orbital, subshell, and shell can occupy.

Here is the electron arrangement for a hydrogen atom:

With a proton in the nucleus, an electron electrostatically equilibrates the atom (the positive electrical charge of the proton is exactly balanced by the negative electrical charge of the electron). This one electron is located in the lowest shell (n = 1), the first subshell (l = 0), in the only orbital (spatial orientation) of this subshell (ml = 0), with a spin value of 1/2. A common way to describe this organization is to list the electrons by their shells and subshells in a convention called spectroscopic notation. In this notation, the shell number is represented as an integer, the subshell as a letter (s, p, d, f) and the total number of electrons in the subshell (all orbitals, all spins) as superscript. Thus, hydrogen with its lone electron, which is in the basic concentration, is called 1s 1 described .

Moving on to the next atom (in order of atomic number), we have the element helium:

A helium atom has two protons in its nucleus, and this requires two electrons to balance the double positive electrical charge. Since two electrons - one with spin = 1/2 and the other with spin = -1 / 2- fit into an orbital - the electron configuration of helium does not require any additional subshells or shells to hold the second electron.

However, an atom that needs three or more electrons needs additional subshells to hold all the electrons, since only two electrons fit into the bottom shell (n = 1). Consider the next atom in order of increasing atomic numbers, lithium:

A lithium atom uses a fraction of the capacity of the L-shell (n = 2). This shell actually has a total capacity of eight electrons (maximum shell capacity = 2n 2 Electrons). If we examine the organization of the atom with a completely filled L-shell, we will see how all combinations of sub-shells, orbitals, and spins are occupied by electrons:

Often times, when specifying spectroscopic notation for an atom, all shells that are completely filled are omitted and the unfilled or filled shell with the highest level is displayed. For example, the element neon (shown in the previous figure), which has two completely filled shells, can be spectroscopically simply referred to as 2p 6 and not as 1s 2 2s 2 2p 6 will be described . Lithium, whose K-shell is completely filled and a single electron in the L-shell, can simply be called 2s 1 and not as 1s 2 2s 1 to be described .

Omitting fully-filled bowls at a lower level isn't just an emergency convenience. It also illustrates a fundamental principle of chemistry: that the chemical behavior of an element is mainly determined by its unfilled shells. Both hydrogen and lithium have a single electron in their outermost shells (1s 1 or 2s 1 ), which gives the two elements similar properties. Both are very reactive and react in a similar way (binding to similar elements in similar modes). It doesn't matter that lithium has a completely filled K-shell under its almost empty L-shell: the unfilled L-shell is the shell that determines its chemical behavior.

Elements with completely filled outer shells are classified as noble and are characterized by an almost complete non-reactivity with other elements. These elements were previously classified as inert when they were thought to be completely unreactive but are now known to form compounds with other elements under certain conditions.

Since elements with identical electron configurations in their outermost shell (s) have similar chemical properties, Dmitri Mendeleev has organized the various elements in a table accordingly. Such a table is called the Periodic Table of the Elements, and modern tables follow this general form

Picture below.

Periodic table of the chemical elements.

Dmitri Mendeleev, a Russian chemist, was the first to develop a periodic table of the elements. Although Mendeleev organized his table by atomic mass rather than atomic number, and produced a table that was not as useful as the modern periodic table, his development is an excellent example of scientific evidence. Seeing the patterns of periodicity (similar chemical properties according to atomic mass), Mendeleev hypothesized that all elements should fit into this ordered scheme. When he discovered "empty" places in the table, he followed the logic of the existing order and questioned the existence of previously undiscovered elements. The later discovery of these elements granted Mendeleev's hypothesis scientific legitimacy, encouraged future discoveries, and resulted in the form of the periodic table we use today.

This is how science should work: Hypotheses followed their logical conclusions and were accepted, modified, or rejected as determined by the consistency of the experimental data with those conclusions. Any fool can formulate an after-fact hypothesis to explain existing experimental data, and many do. What distinguishes a scientific hypothesis from post hoc speculation is the prediction of future experimental data that has not yet been collected and the possibility of rebuttal as a result of that data. To courageously pursue a hypothesis to its logical conclusion and to dare to predict the results of future experiments is not a dogmatic leap of faith, but a public test of this hypothesis, accessible to anyone who can produce contradicting data. In other words, scientific hypotheses are always "risky" because of the pretense of predicting the results of experiments that have not yet been conducted, and are therefore prone to rebuttal if the experiments do not turn out as predicted. So if a hypothesis successfully predicts the results of repeated experiments, then its falsity is refuted.

Quantum mechanics, first as a hypothesis and later as a theory, has proven extremely successful in predicting experimental outcomes, hence the high level of scientific confidence that has been placed in it. However, many scientists have reason to believe that this is an incomplete theory, as their predictions are on microphysical scales rather than macroscopic dimensions, but it is still an extremely useful theory for explaining and predicting the interactions of particles and atoms.

As you have already seen in this chapter, quantum physics is essential for describing and predicting many different phenomena. In the next section we will see its importance for the electrical conductivity of solids, including semiconductors. Put simply, nothing in chemistry or solid state physics makes sense within the popular theoretical framework of electrons that exist as discrete layers of matter and swirl around atomic nuclei like miniature satellites. If electrons are viewed as "wave functions" in certain, discrete states, the regular and periodic behavior of matter can be explained.

  • REVIEW:
  • Electrons in atoms exist in "clouds" of distributed probability, not as discrete chunks of matter that orbit the nucleus like tiny satellites, as common images of atoms show.
  • Individual electrons around an atomic nucleus look for unique "states" described by four quantum numbers: the main quantum number, known as the shell; the Angular Momentum Quantum Number, known as the sub-shell; the magnetic quantum number that describes the orbital (subshell orientation); and the spin quantum number or just spin. These states are quantized, which means that there are no "in-between" conditions for an electron, except for those states that fit into the quantum numbering scheme.
  • The Principal Quantum Number (n) describes the ground plane or shell in which an electron is located. The greater this number, the greater the radius of the electron cloud from the atomic nucleus and the greater the energy of this electron. Principal quantum numbers are whole numbers (positive whole numbers).
  • The Angular Momentum Quantum Number (l) describes the shape of the electron cloud within a certain shell or level and is often referred to as "subshell". There are as many subshells (electron cloud shapes) in any given shell as the main part of that shell is quantum number. Angular momentum quantum numbers are positive integers that start at zero and end at one below the principal quantum number (n-1).
  • The magnetic quantum number (ml) describes the orientation of a lower shell (electron cloud shape). Subhells can have as many different orientations as the double subshell number (1) plus 1, (2l + 1) (e.g. for l = 1, ml = -1, 0, 1) and each unique orientation is called an orbital. These numbers are integers ranging from the negative value of the partial shell number (1) to the positive value of the partial shell number.
  • The Spin Quantum Number (m s ) describes another property of an electron, and may be a value of +1/2 or -1/2.
  • Pauli's Exclusion Principle says that no two electrons in an atom may share the exact same set of quantum numbers. Therefore, no more than two electrons may occupy each orbital (spin = 1/2 and spin = -1 / 2), 2l + 1 orbitals in every subshell, and n subshells in every shell, and no more.
  • Spectroscopic notation is a convention for denoting the electron configuration of an atom. Shells are shown as whole numbers, followed by subshell letters (s, p, d, f), with superscripted numbers totaling the number of electrons residing in each respective subshell.
  • An atom's chemical behavior is solely determined by the electrons in the unfilled shells. Low-level shells that are completely filled have little or no effect on the chemical bonding characteristics of elements.
  • Elements with completely filled electron shells are almost entirely unreactive, and are called noble (formerly known as inert).