Lecture 7: The Nature of Matter

The ignorant man marvels at the exceptional; the wise man marvels at the common; the greatest wonder of all is the regularity of nature.

-- George Dana Boardman

7.1 The Constituents of Matter

(Discovering the Universe, 5th ed., §4-5)

• Newton's laws are completely general, and apply not only to the motion of planets but also to the motion of the tiniest objects in the Universe such as protons, neutrons, and electrons.
  
   
  
• These three subatomic particles are the basic constituents of matter, the stuff which makes up stars, planets, the Earth, and you and me.
  
  It is therefore important to have an understanding of their basic behavior.
  
   
  
• Another fundamental particle, the neutrino, does not show up in ordinary material objects, but its interaction with the other three particles has great importance in astronomy.
  
   
  
• The electron was the first to be discovered, by J. J. Thomson in 1897.
  
  Wilhelm Wien discovered the proton shortly thereafter in 1898.
  
  The neutron was discovered much later, in 1932, by James Chadwick.
  
  The neutrino followed in 1949, discovered by Chalmers Sherwin.
  
   
  
• The most fundamental characteristic of these particles is their mass.
  
  Protons and neutrons have roughly the same mass.
  
  They are both much more massive than the electron, which in turn is much more massive than the neutrino (whose exact mass is unknown):
  
  m_proton = 1.7 x 10^-27 kg
  m_neutron = 1.0016 x m_proton
  m_electron = 0.00054 x m_proton
  10^-7 x m_electron < m_neutrino < 10^-4 x m_electron
  
   
  
• Another basic characteristic is their size; protons and neutrons have roughly the same diameter, while electrons and neutrinos have no measureable extent:
  
  D_proton ~ 2 x 10^-15 m
  D_neutron ~ 2 x 10^-15 m
  D_electron ~ 0
  D_neutrino ~ 0

7.2 Electricity

(Discovering the Universe, 5th ed., not!)

• In addition to their mass and size, these particles also have electric charge:
  
  

  qproton = +e
  qneutron = 0
  qelectron = -e
  qneutrino = 0

  
   
  
• Charged particles interact with each other via the electric force, which has the same form as the gravitational force:
  
  
  
  Here, k is a constant, Q and q are two electric charges, and r is the separation between them.
  
   
  
• Because charges can be both positive and negative, the electric force can be both attractive (between unlike charges) and repulsive (between like charges).
  
   
  
• Although the form of the force laws are the same, the electric constant k ~ 10⁺¹⁰ (in metric units) is much larger than the gravitation constant G ~ 10^-10, so electricity is a much stronger force.
  
   
  
• In nature, there is an equal amount of positive and negative charge.
  
  As a result, an isolated charged particle will usually attract the opposite charge from its surrounding environment to quickly form a neutral system.

7.3 Magnetism

(Discovering the Universe, 5th ed., not!)

• In addition to electric charge, protons, neutrons, electrons, and neutrinos also have an intrinsic magnetic dipole moment, which means that they act like tiny bar magnets.
  
  They have a magnetic axis with a north magnetic pole at one end and a south magnetic pole at the other.
  
   
  
• Magnetic dipole moment is measured in units of A-m².
  
  While a typical bar magnet might have a few A-m², atomic dipoles are much smaller:
  
  µ_proton = 1.4 x 10^-26 A-m²
  µ_neutron = 0.69 x µ_proton
  µ_electron = 660 x µ_proton
  µ_neutrino = ?
  
   
  
• To understand how magnetism works, it is helpful to think in terms of a magnetic field.
  
  Every magnet creates a magnetic field in the space around it.
  
  The field has a direction associated with it; it emanates from the north pole of the magnet and wraps around back into the south pole (the field lines are continuous, though, without beginning or end).
  
   
  
• When another magnet is placed in the field, it experiences a magnetic force which rotates it so that its magnetic dipole moment aligns with the field, i.e. its poles are opposite to the original magnet's.
  
  This is why a compass needle turns towards the Earth's north pole, to align itself with the planet's magnetic field.
  
   
  
• Note that this alignment tends to cancel out the magnetic field far away, since the second magnet's field is opposite to the first's.
  
  A bar magnet is formed from materials such as iron, which can hold the intrinsic magnetic dipoles of electrons so that they all align in the same direction.
  
  They then add up to form a large total magnetic dipole moment.
  
   
  
• Magnetic fields also have a direct affect on moving electric charges (i.e. electric current), independent of their magnetic dipole moment.
  
  If a charged particle is moving through a magnetic field, it is forced to spiral around the field.
  
   
  
• Moving electric charges also produce their own magnetic field!
  
  As a result, the electric current in a wire can deflect a compass needle.
  
  This might be expected from a magnetic field's effect on a moving charge and Newton's third law, which requires that there always be an equal and opposite effect.
  
   
  
• There are therefore two basic sources of magnetic fields, intrinsic magnetic dipole moments and motion of electric charges.
  
  The former can be thought of as arising from the latter, if a subatomic particle is a rotating sphere of charge.
  
  This "rotation" is called intrinsic or spin angular momentum, or spin, for short.
  
  This is simply an analogy, though -- while spin is a very real characteristic of subatomic particles, its actual source is a mystery; there are great problems with describing these particles as rotating spheres (for example, remember that electrons have no measureable extent!).

7.5 Radioactivity

(Discovering the Universe, 5th ed., §4-5, §17-4)

• Nuclei with an excess of protons over neutrons, or that have many protons, tend to be unstable, since large number of protons can produce a long-ranged electric repulsion which exceeds the attraction of the short-ranged strong nuclear force.
  
  Such nuclei may therefore split into two smaller nuclei with kinetic energy, a process called spontaneous nuclear fission.
  
  Question: where does the kinetic energy come from?
  
  Spontaneous nuclear fission is a form of radioactive decay, and such unstable nuclei are said to be radioactive.
  
  Uranium (²³⁸U), for example, naturally decays into thorium (²³⁴Th) and helium (⁴He).
  
  Question: what other radioactive materials have you heard of?
  
  Extra: the Saturn-bound Cassini spacecraft is so distant from the Sun that it must rely on radioactive decay to generate power.
  
   
  
• Neutron decay is another form of radioactivity in which a neutron spontaneously decays into a proton, an electron, and a neutrino:
  
  
  
  Neutron decay is a result of the fourth fundamental force in nature, the weak nuclear force.
  
  Neutron decay can occur both in isolated neutrons and also inside nuclei (generally those that have many more neutrons than protons).
  
  Question: after neutron decay in a nucleus, what happens to a nucleus' atomic number? its atomic mass?
  
   
  
• The rate at which a radioactive material decays is described by its half-life, the time it takes for half of the material to decay into its end products.
  
  The half-life of a radioactive material is independent of the beginning amount.
  
  Half-life can be used to judge the age of, for example, a meteorite, by comparing the relative amounts of a radioactive material and its decay products.
  
  For example, the half-life of uranium (²³⁸U) is 4.5 Gy; rocks containing uranium commonly have an equal amount of its decay products, making them about 4.5 Gy old (assuming other sources of the decay products can be ruled out).
  
  Question: what does that suggest about the age of our solar system?
  
   
  
• Many radioactive nuclei are isotopes of stable elements, with either an excess of protons or neutrons, and they commonly have half-lives of hours, days, or years.
  
  The neutron has a half-life of only 17 minutes.
  
  Because the Earth is very old, most of these materials have decayed away, and aren't generally found in nature.
  
   
  
• For any element with an atomic number greater than 83 (bismuth), all isotopes are radioactive.
  
  Uranium, with an atomic number of 92, is the heaviest nucleus that exists in our solar system in large quantities, due to its long half-life.
  
  Most of the other high-mass elements, however, have extremely short half-lives.

7.6 Atoms

(Discovering the Universe, 5th ed., §4-5)

• Because positively charged nuclei and negatively charged electrons have an electric attraction, they routinely join together to form a stable structure called an atom.
  
  The experiments of Ernest Rutherford in 1910 demonstrated that atomic structure was much like the solar system, with light electrons orbiting the massive nucleus.
  
  Extra: You can explore Rutherford's experiments yourself with this Java applet from the University of Virginia.
  
   
  
• The electrons form a "cloud" around the nucleus which gives the atom a diameter of roughly 10^-10 m, 10,000 times larger than the nucleus.
  
   
  
• Atoms usually have the same number of electrons as there are protons in their nucleus; the atom then has a neutral charge.
  
  Occasionally a neutral atom may lose or gain some electrons; it is then positively or negatively charged, respectively.
  
  Such an atom is called an ion, and it is said to be ionized.
  
  In astronomy, neutral atoms and positive ions are most common, and a roman numeral is used to indicate the degree of ionization.
  
  For example, Fe I is neutral, Fe II has one electron removed, Fe XIV has thirteen electrons removed, etc.
  
   
  
• Because atoms interact with their surroundings via their electron cloud, the number of electrons they have distinguishes them from each other.
  
  Since the number of electrons is usually the same as the number of protons, this is why atomic number characterizes the different elements that we see in nature.

7.7 Molecules

(Discovering the Universe, 5th ed., §4-5)

• Some atoms, such as helium and neon, do not easily join with others, usually remaining in their atomic form.

The Gateway to Educational Materials (GEM) is the key to one-stop, any-stop access to thousands of high quality lesson plans, curriculum units and other education resources on the Internet! GEM is a project of the U.S. Department of Education. The Introduction to Astronomy Webbook is catalogued in the Gateway, and Scott R. Anderson is a member of the GEM Consortium.