# 3.1: Introduction

Difficulty Level: At Grade Created by: CK-12

This chapter is a short non-mathematical course introducing high school physics students and interested non-scientists to the physics of the atomic nucleus and to phenomena associated with nuclear fission. You can also access a summary of this chapter on David Stern's website, http://www.phy6.org/stargaze/SnucEnerA-0.htm , as well as the entire chapter at http://www.phy6.org/stargaze/SnucEnerA-1.htm .

## Introduction to Nuclear Energy

Nuclear Energy is the source of the sun's heat, creating sunlight and thus the ultimate source of most energy used by humanity.

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.

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. This is a very condensed overview, and 15\begin{align*}15\end{align*} additional references (marked #1 to #15) are scattered throughout with the chapter and listed at the end. They add relevant additional material at the same level; most are on the World Wide Web, and can be accessed from your computer.

## The Foundations: Atoms and Nuclei

To begin with, certain facts will be assumed. Make sure you understand them—if not, seek material to help you do so! The stories of their discovery are interesting, but take us too far afield (see reference #1 for a quick overview, #14 for a historical overview). The facts (key words in bold face):

1. Matter is composed of tiny atoms. Atoms in nature exist in 92\begin{align*}92\end{align*} 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, which are similar to protons, but without electric charge.

Whole atoms, with equal numbers of both, have zero net electric charge. Certain chemical molecules however (acids, bases, and salts) are formed by some atoms borrowing an electron from others with which they are combined. Because water weakens electrical forces at molecular dimensions, when such compounds are dissolved in water, the electrical components missing an electron or having an extra borrowed one (ions) may sometimes temporarily separate. Such solutions (e.g., sea water) therefore conduct electricity and their ions may sometimes be separated by an electric current (for more, see reference #2). Ionic compounds melted by heat (e.g., molten salt) and compounds dissolved in them may also be separated by electric current.

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 (#3). Other methods allow the creation in a vacuum of free positive or free negative ions (atoms that 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 known as a proton, 1836\begin{align*}1836\end{align*} 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\begin{align*}4\end{align*} for the main component of helium, 12\begin{align*}12\end{align*} for that of carbon, 14\begin{align*}14\end{align*} for nitrogen, 16\begin{align*}16\end{align*} for oxygen, and so on, up to 238\begin{align*}238\end{align*} for the main variety of uranium, the heaviest atom found in nature.

The Helium Nucleus

The nucleus of helium has the positive charge of 2\begin{align*}2\end{align*} protons, although it is 4 times heavier. Similarly carbon has only 6 times the charge. That suggests these nuclei contain 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. One gram of hydrogen, 4\begin{align*}4\end{align*} grams of helium, 12\begin{align*}12\end{align*} of carbon etc. all contain \begin{align*} N_{A} = 6.022 \times 10^{23}\end{align*} atoms, a constant known as Avogadro's number. That too is the number of molecules in \begin{align*}2\end{align*} grams of hydrogen (molecule \begin{align*}\mathrm{H}_2\end{align*}), \begin{align*}18\end{align*} grams of water (molecule \begin{align*}\mathrm{H}_2\mathrm{O}\end{align*}, \begin{align*}44\end{align*} grams of carbon dioxide (molecule \begin{align*}\mathrm{CO}_2\end{align*}) and so forth—numbers formed by adding atomic weights of a component to give the molecular mass.

5. To denote an element in nature, an abbreviated symbol is used, e.g., \begin{align*}H\end{align*} for hydrogen, \begin{align*}O\end{align*} for oxygen, \begin{align*}C\end{align*} for carbon, \begin{align*}U\end{align*} for uranium, \begin{align*}Na\end{align*} for sodium (Natrium), \begin{align*}Pb\end{align*} for lead (Plumbum), \begin{align*}Cl\end{align*} for chlorine, \begin{align*}Fe\end{align*} for iron (Ferrum) etc. Actually, most atoms in nature have several varieties (isotopes), differing in weight by very close to the weight of a nucleon (i.e., proton or neutron). 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 \begin{align*}75\end{align*}% \begin{align*}^{35}\mathrm{Cl}\end{align*} and \begin{align*}25\end{align*}% \begin{align*}^{37}\mathrm{Cl}\end{align*}. Hydrogen \begin{align*}(H)\end{align*} has \begin{align*}3\end{align*} known isotopes: Ordinary hydrogen \begin{align*}^{1}\mathrm{H}\end{align*}, "heavy" hydrogen \begin{align*}^{2}\mathrm{H}\end{align*} (also known as deuterium \begin{align*}D\end{align*}) forming \begin{align*}1/6000\end{align*} of atoms in nature, and tritium \begin{align*}^{3}\mathrm{H}\end{align*}, which is unstable, must be produced artificially, and decays with an average time of 12.5 years (half life, time after which only half its atoms are left). It turns into a helium isotope \begin{align*}^{3}\mathrm{He}\end{align*} as it emits an electron and one of its neutrons (see \begin{align*}7\end{align*} 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 four times the mass. It turns out it contains two protons and two neutrons, particles similar to protons but slightly heavier and with no electric charge. Light atoms have about an equal number of protons and neutrons, e.g., \begin{align*}6+6\end{align*} in \begin{align*}^{12}C\end{align*}, \begin{align*}8+8\end{align*} in \begin{align*}^{16}O\end{align*}. In heavier atoms neutrons have the majority, which increases as atomic weight rises, e.g., \begin{align*}^{238}\mathrm{U}\end{align*} has \begin{align*}92\end{align*} protons and \begin{align*}146\end{align*} 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 \begin{align*}3\end{align*} letters of the Greek alphabet—\begin{align*}(\alpha, \beta, \gamma)\end{align*} or (alpha, beta, gamma) radiation.

Alpha \begin{align*}(\alpha)\end{align*} particles are nuclei of helium, and emitting them changes an atom to one with two fewer protons and two 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 \begin{align*}\alpha -\end{align*}emitting polonium.

Beta particles are fast electrons or positrons (the anti-particle of the electron) emitted when a neutron is converted into a proton or a proton is converted into a neutron, respectively. 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 its twin anti-neutrino, either of which can pass through matter almost unhindered.

Gamma rays are similar to \begin{align*}x-\end{align*}rays, a form of electromagnetic radiation (see next item below) similar to light or 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 \begin{align*}(EM)\end{align*} radiation, a family of disturbances propagating through space and including radio waves, microwaves, light (visible, infra-red, and ultra-violet), \begin{align*}x-\end{align*}rays, gamma rays, and ranges between the named ones. These differ in wavelength and are described qualitatively in (#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).

Some 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 water molecules in the food 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 \begin{align*}h,\end{align*} a constant of nature named Planck's constant after its discoverer. For more about quantum phenomena, see (#5) and the \begin{align*}7\end{align*} Web files linked from it (Q2 ... Q8 htm).

A fundamental equation containing \begin{align*}h\end{align*} 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 \begin{align*}L\end{align*} (also denoted by lambda \begin{align*} \lambda \end{align*} the Greek letter \begin{align*}L\end{align*}), spreading with velocity \begin{align*}c\end{align*} (the speed of light, \begin{align*}300,000 \;\mathrm{km/sec}\end{align*}). As the wave passes a point in (empty) space, a total wave train of length \begin{align*}c\end{align*} 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 \begin{align*} L \end{align*} each, so the total number of up-down excursions each second, the frequency \begin{align*}f\end{align*} of the wave, is: \begin{align*}f = c/L\end{align*} (also denoted by nu \begin{align*} \nu \end{align*}, the Greek \begin{align*}N\end{align*}). The wavelength can be measured, and the wave describes all optical phenomena.

However, when an EM wave interacts with matter and gives up its energy, it was found that it happens only in discrete lumps of energy or "photons," each of which contains energy \begin{align*}E = h f\end{align*} with \begin{align*} h \end{align*} equal to Planck's constant.

Max Planck in Germany (Nobel Prize, 1918) proposed that 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 metal by light of different colors ("photoelectric effect"). That was what earned Einstein his 1921 Nobel Prize—not his 1905 discovery of relativity! Photons are localized to perhaps just the atom which absorbs the energy, and not spread over all space like a wave; however they require a quantum mechanical description. For more, see #4 and the web pages under #5 above.

As mentioned earlier, beta particles are fast electrons or positrons emitted when a neutron is converted into a proton or a proton is converted into a neutron, respectively.

Because of quantum rules, an electron in an individual atom of a gas can only move in certain well-defined orbits and no others—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 higher energy level; then, as it returns to a lower level, it emits well-defined frequencies of light (see #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.

## Tidbits

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 \begin{align*}\alpha -\end{align*}particles emitted by uranium, thorium, or some of their daughter products. As evidence, helium from the Sun contains a small amount of the isotope \begin{align*}^3\mathrm{He}\end{align*} one neutron, two protons), but terrestrial helium is almost pure \begin{align*}^4\mathrm{He}\end{align*}.

## Review Questions

1. If chlorine consists of \begin{align*}25\end{align*}% \begin{align*}^{37}\mathrm{Cl}\end{align*} and \begin{align*}75\end{align*}% \begin{align*}^{35}\mathrm{Cl}\end{align*}, and \begin{align*} N_A \end{align*} is Avogadro's number—what is the mass of \begin{align*} N_A \end{align*} atoms of chlorine, i.e., one mole of chlorine? (That would be the molar mass of 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 \begin{align*}1/1000\end{align*} of it remains in a given sample?
5. The density of hydrogen (forming \begin{align*}\mathrm{H}_2\end{align*} molecules) is about \begin{align*}90\end{align*} grams per cubic meter. How many molecules of hydrogen are in one cubic micron (a micron is one millionth of a meter)?

1. If chlorine consists of \begin{align*}25\end{align*}% \begin{align*}^{37}\mathrm{Cl}\end{align*} and \begin{align*}75\end{align*}% \begin{align*}^{35}\mathrm{Cl}\end{align*}, and \begin{align*} N_A \end{align*} is Avogadro's number— what is the mass of \begin{align*} N_A \end{align*} atoms of chlorine? (That would be the atomic mass of natural chlorine.) (Out of \begin{align*}4\end{align*} atoms, \begin{align*}3\end{align*} will have an atomic mass of \begin{align*}35\end{align*} and one will have \begin{align*}37\end{align*}. The average is the sum divided by \begin{align*}4: (105 + 37)/4 = 142/4 = 35.5.\end{align*})
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. Neutrons do not "feel" magnetic forces, but electrons and protons can get trapped, though those splashed from the atmosphere always return and hit the atmosphere again. Is this a credible explanation to the "radiation belt" trapped in the magnetic field of the Earth? [Yes. Particles from the atmosphere always return and are absorbed by the atmosphere, but neutrons may decay in flight and yield energetic protons (also electrons), which could appear on a magnetically trapped orbit. The original Van Allen belt is believed to originate that way.]
4. A certain radioactive isotope has a half-life of 2 days. How long approximately does it take until only \begin{align*}1/1000\end{align*} of it remains in a given sample? [About 20 days, or \begin{align*}10\end{align*} half-lives, because \begin{align*}(1/2)^{10} = 1/1024\end{align*}]
5. Hydrogen (forming \begin{align*}\mathrm{H}_2\end{align*} molecules) weighs about \begin{align*}90\end{align*} grams per cubic meter. How many molecules of hydrogen are in one cubic micron (a micron is the millionth part of the meter)? If \begin{align*} N_{A}\end{align*} is Avogadro's number \begin{align*}6.022 \times 10^{23}\end{align*} then \begin{align*}2\end{align*} grams hydrogen contains \begin{align*} N_{A} \end{align*} molecules, and \begin{align*}90\end{align*} grams contain \begin{align*} 45 \ N_{A}\end{align*}. A cubic micron is \begin{align*}10^{-18}\end{align*} cubic meters, so the number is: [\begin{align*}N = 45 (6.022 \times 10^{23}) 10^{-18} = 271 \times 10^5 = 2.71 \times 10^7\end{align*} or about \begin{align*}27\end{align*} million molecules.]

### Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes

Show Hide Details
Description
Tags:
Subjects:
{"extraction_info": {"found_math": true, "script_math_tex": 106, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8503748774528503, "perplexity": 1767.3093446977387}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917122739.53/warc/CC-MAIN-20170423031202-00288-ip-10-145-167-34.ec2.internal.warc.gz"}