Note: This is an overview of nuclear energy, longer and more detailed than the one in section (S-8). It was prepared by David P. Stern as part of the Virginia Flexbook on Physics prepared under auspices of the CK-12 foundation, under the "creative commons, cite by attribution, share alike" protocol. It was meant to serve as supplemental text for high school physics. It also includes problems and questions.

    Nuclear energy has become an important energy resource for producing electricity in the United States and elsewhere. It may become even more important in the future, at least in the period when environmental problems limit the burning of carbon, but cheap solar energy is still being developed.

    Yet explaining it is not easy, requiring some familiarity with modern physics. A general understanding is all that can be offered here: a quantitative understanding and relevant calculations need too many prerequisites at a higher level.

1.     Matter is composed of tiny atoms. Atoms in nature exist in 92 varieties ("chemical elements"), ignoring here additional elements created artificially (and noting that technetium is too unstable to have survived on Earth). Atoms may combine chemically to create the great variety of molecules existing on Earth, corresponding to all materials found or created artificially.
   
2.     Chemical properties of atoms are determined by electrical forces--from lightweight negatively charged electrons, balanced by an equal number of much heavier protons with an equal but positive electric charge. Atoms also contain neutrons. similar to protons but without electric charge.

    In addition, ions form in rarefied gases when sufficient voltage is applied (and in other ways). They carry electric currents in fluorescent light fixtures (helped by free electrons), also in the ionosphere and in more distant space .

3.     Electrons may also be "boiled off" a hot object in a vacuum ( reference #3). Other methods allow the creation in a vacuum of "free" positive or free negative ions (atoms which have lost one or more electrons, or have attached extra electrons). Any of these may be accelerated in the laboratory by "accelerators" to velocities close to that of light, and given high energies. Much of our information about atoms comes from studies of collisions of such fast particles with atoms.
   
   
4.     The element with the lightest atom is hydrogen, and its positive part is knows as a "proton", 1836 times heavier than the electron. The "atomic weight" of other atoms gives the approximate number of times their atom is heavier than that of hydrogen, e.g. 4 for the main component of helium, 12 for that of carbon, 14 for nitrogen, 16 for oxygen and so on, up to 238 for the main variety of uranium, the heaviest atom found in nature.
   
   
   The nucleus of helium has the positive charge of 2 protons, although it is 4 times heavier. Similarly carbon has only 6 times the charge. That suggests these nuclei contain of an equal number of "uncharged protons", known as neutrons. The free neutron (discovered by Chadwick in 1931) is ejected from certain nuclear collisions (see further below), but is unstable --after an average of about 10 minutes it becomes a proton, electron and a very light uncharged neutrino

       1 gram of hydrogen, 4 grams of helium, 12 of carbon etc. all contain A = 6.022 10²³ atoms, a constant known as Avogadro's number . That too is the number of molecules in 2 grams of hydrogen (molecule H₂), 18 of water (molecule H₂O), 44 gram of carbon dioxide (molecule CO₂) and so forth--numbers formed by adding atomic weights of component to give the molecular weight .
   

5.    To denote an element in nature, an abbreviated symbol is used, e.g. H for hydrogen, O for Oxygen, C for carbon, U for Uranium, Na for sodium (Natrium), Pb for lead (Plumbum), Cl for chlorine, Fe for iron (Ferrum) etc. Actually, most atoms in nature have several varieties (isotopes), differing in weight by very close to the weight of a proton. To denote a specific isotope, a superscript giving its atomic weight is added to its symbol. For instance, chlorine in nature is a mixture dominated by approximately 75% ³⁵Cl and 25% ³⁷Cl.

       Hydrogen (H) has 3 known isotopes: Ordinary hydrogen ¹H , "heavy" hydrogen ²H (also known as "deuterium" D) forming 1/6000 of atoms in nature, and "tritium" ³H which is unstable, must be produced artificially, and decays with average time of 12.5 years ("half life", time after which only half its atoms are left). It turns into a helium isotope ³He as it emits an electron and one of its neutrons (see (7) below) becomes a proton.
   

6.     Apart from the electrons, the mass of the atom is concentrated in a very compact "atomic nucleus ."
   
   
7.     The nucleus of the most common isotope of helium has twice the positive charge of the proton, but close to 4 times the mass. It turns out (image above) that it contains two protons and two neutrons, particles similar to protons but slightly heavier and with no electric charge. Light atoms have about equal number of protons and neutrons, e.g. 6+6 in ¹²C, 8+8 in ¹⁶O. In heavier atoms neutrons have the majority, which increases as atomic weight rises, e.g. ²³⁸U has 92 protons and 146 neutrons. Isotopes of the same element have the same number of protons (which equals the number of electrons and determines the chemical properties) but different numbers of neutrons. This imbalance (further discussed below) plays a crucial role in the release of nuclear energy by the fission chain reaction.
   
   
8.    Atomic nuclei may be unstable---in particular, in very heavy elements and in isotopes whose number of neutrons differs significantly from their number in the most prevalent isotope. Unstable nuclei may undergo "radioactive decay" to a more stable state. Most radioactive nuclei do so by emitting one of three kinds of "nuclear radiation", denoted for historical reasons by the first 3 letters of the Greek alphabet--(α, β, γ) or (alpha, beta, gamma) radiation.

       Alpha (α) particles are nuclei of helium, and emitting them changes an atom to one with 2 fewer protons and 2 fewer neutrons (the alpha particle, after being slowed down by collisions, combines with two electrons of its surroundings to become regular helium, while the emitting atom sheds two electrons, which keep the surrounding material neutral). Alpha particles have a very short range in matter and can hardly penetrate skin. However, they cause great damage if ingested into the body--as in the case of Alexander Litvinenko, a Russian officer given asylum in London, who died in November 2006 after being poisoned with α-emitting polonium.

       Beta particles are fast electrons, emitted when a neutron is converted into a proton. This usually involves neutrons inside an unstable nucleus; However, free neutrons--produced in high-energy collisions in the lab (from accelerated particles, also by natural alpha particles hitting beryllium nuclei) also undergo such conversion, with a half-life of about 10 minutes, producing a proton, an electron and an uncharged, almost massless "neutrino" or rather its twin "anti-neutrino, which can pass through matter almost unhindered.

       Gamma rays are similar to X-rays, a kind of electromagnetic radiation [see next item below] related to light and radio waves. Just as visible light can be emitted at well-defined energies by atomic electrons in "excited" atoms jumping from one "energy level" to a lower one, gamma rays arise from nuclei passing from an excited energy level to another one--possibly to the lowest level, the stable "ground state."
   

9.     The word radiation should be used with caution. Physicists usually apply it to "electromagnetic (EM) radiation", a family of disturbances propagating through space and including radio waves, microwaves, light (visible, infra-red and ultra-violet), X-rays, gamma rays and ranges between the named ones. These differ in wavelength and are described qualitatively in reference #4.

       Nuclear radiation emitted from unstable nuclei may be electromagnetic (gamma rays) or consist of particles with mass (alpha and beta rays), perhaps accompanied by gamma rays. Artificial isotopes may in addition emit neutrons and positrons (positive electrons).

       Too many people do not realize the difference between "nuclear radiation" and "electromagnetic radiation"! Colloquially, we "nuke" food in a microwave oven, when in fact atomic nuclei are not involved, only very short wave radio waves, whose energy is absorbed by the bulk of the food (not by individual atoms) and heats it. This discussion of nuclear power involves mostly nuclear radiation, so here (only here! ) the unqualified word "radiation" implies nuclear radiation.
   

10.     In an atom negative electrons surround the positive nucleus and are held by electric attraction, similar to the way planets are held by the gravity of the Sun.

        A big difference exists however, because Newton's laws are modified on the atomic and subatomic scale of distances, to follow quantum mechanics. In a way, matter behaves like sand: on a large scale, it flows like a fluid, but its small-scale behavior depends on the existence of individual grains. The "graininess" which rules quantum phenomena is determined by "h", a constant of nature named "Planck's Constant" after its discoverer. For more about quantum phenomena, see reference #5 and the 7 web files linked from it (Q2 ... Q8.htm).

        A fundamental equation containing h involves light (or any other EM radiation). A frequently heard statement is that light can be both a wave and a particle. Basically, when EM radiation spreads, it does so like a wave with wavelength L (also denoted by lambda λ, the Greek letter L), spreading with velocity c (the speed of light, 300,000 km/sec). As the wave passes a point in (empty) space, a total "wave train" of length c must go each second through it, chopped into up-down oscillations (of the electric or magnetic force, but that is not important here) of length L each, so the total number of up-down excursions each second, the frequency f of the wave, is
    

    f = c/L
    (also denoted by ν, the Greek N). The wavelength can be measured, and the wave describes all optical phenomena.

        However, when an EM wave gives up its energy, it was found that happens only in "photons" of energy, each of which contains energy
    

    E = h f
    with h Planck's constant.

        Max Planck in Germany (Nobel Prize 1918) proposed the above equation in 1900 to explain the color distribution emitted from hot objects, but its significance in atomic processes was recognized after Einstein's 1905 explanation of the ejection of electrons from atoms by light of different colors (photo-electric effect). That was what earned Einstein his 1921 Nobel prize--not his 1905 discovery of relativity! Photons are somewhat like particles, localized to perhaps just the atom which absorbs the energy, and not spread over all space like a wave. For more, see reference #4 and the web pages under reference #5 above.

        Because of quantum rules, an electron in an individual atom of a gas can only move in certain well-defined orbits and no other--like a wave with well defined stable patterns, e.g. sound in a musical instrument. When an atom is "excited" (e.g. by electrical forces in fluorescent tubes or in sodium vapor lamps of street lights), an electron may be moved to a more energetic level; then, as it returns to a lower level, it emits well-defined frequencies of light ( see reference #6 for examples), sensed (when visible) as specific colors, and each frequency represents (by the above equation) the energy difference between two states of the atom. All such electrons end in the "ground state" of lowest energy, which is stable. Because of the existence of the ground state (which is determined by quantum laws), the electron is in no danger of moving further and "falling" into the atom's nucleus.
    
    Tidbit: The interior of the Earth is heated by nuclear energy, too, by the radioactivity of elements such as uranium and potassium, mainly in the Earth's crust. While radioactive elements form only a tiny fraction of the Earth's composition, the heat produced when their radiations are absorbed cannot easily escape. Consider the area of one square metre on which you stand: if all the Earth crust had similar chemistry, all radioactive heat produced by a column extending 100 km below you can only escape through this narrow area. (The depth could be greater, but heat production is reduced at great depths). One can therefore say that geothermal power plants, hot springs and volcanoes, all get their heat from atomic nuclei.
    
    And by the way... Practically all helium on Earth (as used in party balloons, for instance) is usually extracted from natural gas, and has originated as α-particles emitted by uranium, thorium or some of their daughter products. As evidence, helium from the Sun contains a small amount of the isotope ³He (1 neutron, two protons), but terrestrial helium is almost pure ⁴He.
    
    

    Problems:

    (answers in section S-8A-5)
    
    
    1.     If chlorine consists of 25% ³⁷Cl and 75% ³⁵Cl, and A is Avogadro's number--what is the mass of A atoms of chlorine? (That would be the effective atomic weight in natural chlorine).
       
       
    2.     Compile a glossary, defining briefly in alphabetical order in your own words:
       
       Alpha particle, Atom, Atomic weight, Avogadro's number, Beta particle Electromagnetic radiation, Electron, Energy level, Excited state of atom, Excited state of atomic nucleus, Frequency of EM wave, Gamma rays, Ground state, Half life, Ion, Isotope, Molecule, Molecular weight, Neutrino, Neutron, Nuclear radiation, Nucleus (of atom),photon, Planck's constant, Proton, Quantum mechanics, Radiation,
       
       
    3.     Very high energy ions from space ("cosmic radiation") arrive at the top of the Earth's magnetosphere, collide with atoms and splash out fragments, some of which are neutrons. A neutron is not deflected by magnetic forces and can escape along a straight path, but electrons and protons are deflected and can get trapped magnetically. Those splashed from the atmosphere are usually guided by the magnetic force back into the atmosphere again.
       
       Are such fragments a credible origin for the "radiation belt" trapped in the magnetic field of the Earth?
       
       
    4.     A certain radioactive isotope has a half-life of 2 days. How long approximately does it take until only 1/1000 of it remains in a given sample?
       
       
    5.     Hydrogen (forming H₂ molecules) weighs about 90 grams per cubic meter. How many molecules of hydrogen are in one cubic micron (a micron is one millionth of a metre)?

Attached next section (S-8A-2)   Nuclear Binding Energy

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Author and Curator:   Dr. David P. Stern
     Mail to Dr.Stern:   stargaze("at" symbol)phy6.org .

Updated 2-11-2009, edited 20 October 2016