Matter

Matter is that aspect of matter/energy we call material, and it comes packaged as particles. Although, as we shall see when we study quantum mechanics, matter sometimes exhibits wave-like behavior, like light, and can be described using Schrödinger’s wave equation: a particle’s exact position and speed are actually “clouds” of probability.

All matter has a shared property: its state of motion will remain constant—it will neither speed up or slow down—unless it is acted on by an external force (one of those four fundamental forces of the universe). This property of ‘resisting change in motion’ is called inertia; it varies between types of particles and measured in units of mass (e.g. grams). This is Newton’s First Law, the law of inertia: every object continues in a continuous state of motion unless acted on by a net external force. (It is possible that many external forces, acting against one another in different directions and strengths, can add up to zero and thus produce no change of motion.)

When an object’s speed changes (relative to our frame of reference), its kinetic energy changes. We perceive that its mass (i.e. inertia) changes—by a very small amount—according Einstein’s Special Theory of Relativity: E = mc2 (E is the change of kinetic energy, c is the speed of light in a vacuum and m is change in the object’s mass {inertia}).In essence, this extra mass is how the kinetic energy is packaged as long as the object is moving relative to us.

Each type of matter particle has a unique rest mass (that is, its intrinsic mass when the particle is at rest in our frame of reference). Particle have other properties: some have charge (i.e. positive or negative electric charge), they have spin (like a top, which imparts a magnetic field to charged particles), and they have other, more exotic quantum properties (e.g. parity, colour, flavour) that determine how they interact with one another and the four forces of nature. For every type of particle there is an anti-particle—if the two ever meet, they annihilate in a burst of energy.

Generally, matter particles are of two classes: quarks (which combine to form hadrons, composite particles such as protons and neutrons) and leptons (e.g. electrons). The sub-atomic particles that make up our everyday existence are protons, neutrons and electrons, which combine to form atoms. Other, more massive, particles show up in cyclotron (“atom smasher”) experiments and when high energy cosmic rays strike the atmosphere.

Interactions between matter and the four forces are conveyed via mediating particles: photons for the electromagnetic force, gravitons for gravity, gluons for the strong nuclear force, the W and Z bosons for the weak nuclear force. The four forces govern how matter interacts at different size scales. Gravity guides the motions of planets, stars and galaxies. Electromagnetism determines how atoms and molecules interact, making complicated things like life possible. The strong nuclear force binds protons and neutrons together in atomic nuclei. And the weak nuclear force affects the interaction of quarks. Photons and gravitons can act over vast distances. Gluons act over short distances (about 10 -15 m, which determines how large an atomic nucleus can grow before becoming unstable), and the W and Z bosons act over even shorter distances (10 -18 m, governing how quarks transform, causing neutrons to change into protons, transmuting one element into another).

©J Shepanski 2006

An important distinction between particles is their spin quantum number. Spin is the intrinsic angular momentum of the particle. One group of particles called fermions, which include electrons, protons and neutrons, have a spin of “½” (in quantum angular momentum units). In terms of Schrödinger’s wave equation fermions have an “antisymmetric wavefunction,” which has the consequence that no two fermions can occupy the same quantum mechanical state (Pauli exclusion principle). Mathematics aside, the important result is that atoms are made up of fermions and the Pauli exclusion principle prevents them from collapsing in on themselves. A second group of particles called bosons have an “integer” spin (e.g. 0, 1, 2…). All mediating force particles (e.g. photons, gluons, gravitons) are bosons. There is no exclusion principle for bosons. They have “symmetric wavefunctions,” so many bosons can occupy the same state—which makes things like laser beams possible.

While quantum mechanics successfully describes particle properties and how they behave, exactly what particles are is still a mystery. Are they solid balls zipping around in probability clouds? Are they zero-dimensional points? Are they seething clouds of matter/energy? Presently, one research conjecture is that particles are extremely small, 1-dimensional, vibrating strings of matter/energy. The precise manner and frequency of these vibrations determines the properties of the particle. And, these strings exist in at least ten dimensions: x, y, z and time we know, the other dimensions are tightly “wrapped up” at a sub-quantum mechanical level of existence (perhaps as small as the Planck length, 10-35 m).

Atoms are composed of electrons (lepton fermions), protons and neutrons (hadron fermions).Protons and neutrons group together, forming the atom’s nucleus. The electrons orbit around the nucleus, in an manner consistent with Schrödinger’s wave equation. In an electrically neutral atom, the number of protons and electrons are equal. The number of protons in the nucleus determines what type of element the atom is. The simplest element is hydrogen (one proton, no neutrons), whereas a very heavy element, 235uranium, has 92 protons, 143 neutrons and is radioactively unstable.

Each hadrons is composed of 3 quarks (fermions). There are six types of quarks, which have either ±1/3 or ±2/3 e (e: unit electric charge; an electron’s charge = -e). Protons and neutrons are made of up (+2/3e) and down (-1/3e) quarks, plus the binding gluons that hold them together: protons consist of 2 up + 1 down quarks, and neutrons = 2 down + 1 up. Free quarks have never been detected; they always seem bound together in composite particles.

The strong nuclear force—mediated by gluons—holds the quarks (and gluons themselves) together, and by extension, holds protons and neutrons together in a compact atomic nucleus about 10-15m in diameter. The strong force is VERY strong, because it has to overcome the tremendous electric repulsion exerted by the protons on one another. The presence of neutrons helps control this repulsive force and stabilize the nucleus. For example, 235uranium is unstable, and on the verge of splitting apart from the electrical repulsion of its protons. Adding three additional neutrons, 238uranium, greatly stabilizes the nucleus. On the other hand, the presence of too many neutrons stimulates the weak nuclear force to transmute an up quark into a down quark, ejecting an electron (beta radiation) and causing the element to change, perhaps by additional processes, such as alpha radiation (ejecting 2 protons and 2 neutrons in an alpha particle).

Matter (2 of 3)

©J Shepanski 2006

The number of protons in an atom (atomic number) determines what type of element it is; the element’s chemical properties are determined by the electrons pulled in orbit around the nucleus. Most elements have small variations in the numbers of neutrons in their nuclei (isotopes); the total mass of an element, including protons, neutrons and electrons, averaged over its various isotopes, is the element’s atomic mass. When speaking of a specific isotope, the total number of protons and neutrons in the nucleus is the isotope’s mass number, and is always an integer.

As described by Schrödinger’s equation, electrons in orbit have a wave-like nature: an exact integer number of electron wavelengths have to fit within an orbital circumference. The lowest orbit (1st shell) fits one full wavelength, the 2nd orbit (2nd shell) fits two full wavelengths, and so on. This constraint dictates that the average orbital radii can only take certain specific values. When an electron jumps orbits, either by absorbing or emitting a photon, only certain specific jumps (and certain specific photon energies) are allowed (atomic absorption/emission spectra).

The electrons orbits are spread over three dimensions and the “probability cloud” (orbitals) that describes them can take on some strange shapes. Because electrons are fermions, no two electrons can occupy the same orbital state. The lowest atomic shell is spherical and can accommodate two electrons (one spin-up, the other spin-down). The second shell can accommodate 8 total electrons: two orbitals are spherical, the other 6 are “dumbbell shaped”—two each oriented along the x, y and z axes. The orientation restrictions on electron orbitals determine the angular configuration of molecular bonds—multiple atoms can only attach to one another at certain bond angles. The third shell contains 18 orbitals—some look like two crossed dumbbells, and another like a dumbbell wearing a donut around the middle.

The electrons occupying the outmost shell, the valance shell, determine the chemical properties of the atom. Energetically, atoms favor either two or eight electrons in their valence shell, even if it means sharing these electrons with other atoms. Thus, atoms will form covalent bonds with other atoms to establish these energetically-favorable orbital configurations. A molecule consist of two or more bonded atoms. A molecule composed of identical atoms will share electrons evenly. More often, two different elements join. One atom will have a higher electronegativity (electron attraction) than the other, so it will keep a greater portion of the shared electron’s orbital in its immediate vicinity. This sets up a charge imbalance (a dipole) across the molecule—one side will be slightly more positively charged than the other. Water is the best known example of this: water is oxygen bonded with two hydrogen atoms. The oxygen’s electron orbitals bonding with hydrogen force a bond angle of 104.45° (neither 90° nor 180°). The oxygen has a higher electronegativity and it “hogs” the shared valence electrons, producing a dipole. Water is a polar molecule—the oxygen side has a negative pole, the hydrogen side has a positive pole—and this affects how it interacts with other molecules in its vicinity.

Sometimes two elements’ electron affinities are so different that it is energetically favorable for one element to “steal” the other’s valence electron—forming an ionic compound, (like salt for example, chlorine pulls the valence electron from sodium)—both atoms become ions.

Matter (3 of 3)

©J Shepanski 2006

1) What equation is used to describe the wave-like behavior of matter particles?

2) What is Newton’s 1st Law of Motion?

3) What is inertia?

4) Name four or five intrinsic properties that particles have.

5) What particles make up an atom of anti-hydrogen? What happens when it encounters a hydrogen atom.

6) What are the two common forms of hadrons? Of what are they composed?

7) Beside hadrons, what is the other general class of matter particles?

8) What sub-atomic particles make up an atom?

9) What are the four forces? What do they act on and in what manner? Over what range do they act?

10) What distinguishes fermions from bosons? Name three common fermions. Name one kind of boson.

11) What is the main concept of String Theory?

12) What determines what type of element an atom is?

13) Describe what quarks make up a proton and neutron? How do their charges add up to produce a +1e charge on a proton, but a 0e charge on a neutron?

14) How are nuclei held together? What prevents them from becoming too large?

15) What is an isotope?

16) What determines the orbital radii of electron shells?

17) What is mass number?

18) What governs an element’s absorption or emission spectrum?

19) What is the outmost electron shell of an atom called? What is its importance?

20) What is a polar molecule? What causes it? What is electronegativity?

21) What is a covalent bond?

22) What is an ionic compound?

Review Questions 2

©J Shepanski 2006