CK-12 21st Century Physics: A Compilation of Contemporary and Emerging Technologies Read online

  4. The element with the lightest atom is hydrogen, and its positive part is known as a proton, 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., for the main component of helium, for that of carbon, for nitrogen, for oxygen, and so on, up to for the main variety of uranium, the heaviest atom found in nature.

  Figure 3.1

  The Helium Nucleus

  The nucleus of helium has the positive charge of 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, grams of helium, of carbon etc. all contain atoms, a constant known as Avogadro's number. That too is the number of molecules in grams of hydrogen (molecule ), grams of water (molecule , grams of carbon dioxide (molecule ) 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., for hydrogen, for oxygen, for carbon, for uranium, for sodium (Natrium), for lead (Plumbum), for chlorine, 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 % and % . Hydrogen has known isotopes: Ordinary hydrogen , "heavy" hydrogen (also known as deuterium ) forming of atoms in nature, and tritium , 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 as it emits an electron and one of its neutrons (see 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., in , in . In heavier atoms neutrons have the majority, which increases as atomic weight rises, e.g., has protons and 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 letters of the Greek alphabet— or (alpha, beta, gamma) radiation.

  Alpha 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 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 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 radiation, a family of disturbances propagating through space and including radio waves, microwaves, light (visible, infra-red, and ultra-violet), 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 a constant of nature named Planck's constant after its discoverer. For more about quantum phenomena, see (#5) and the Web files linked from it (Q2 ... Q8 htm).

  A fundamental equation containing 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 (also denoted by lambda the Greek letter ), spreading with velocity (the speed of light, ). As the wave passes a point in (empty) space, a total wave train of length 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 each, so the total number of up-down excursions each second, the frequency of the wave, is: (also denoted by nu , the Greek ). 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 with 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 emitt
ed 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 particles emitted by uranium, thorium, or some of their daughter products. As evidence, helium from the Sun contains a small amount of the isotope one neutron, two protons), but terrestrial helium is almost pure .

  Review Questions

  If chlorine consists of % and % , and is Avogadro's number—what is the mass of atoms of chlorine, i.e., one mole of chlorine? (That would be the molar mass of natural chlorine).

  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

  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?

  A certain radioactive isotope has a half-life of 2 days. How long approximately does it take until only of it remains in a given sample?

  The density of hydrogen (forming molecules) is about grams per cubic meter. How many molecules of hydrogen are in one cubic micron (a micron is one millionth of a meter)?

  Review Answers

  If chlorine consists of % and % , and is Avogadro's number— what is the mass of atoms of chlorine? (That would be the atomic mass of natural chlorine.) (Out of atoms, will have an atomic mass of and one will have . The average is the sum divided by )

  Compile a glossary, defining briefly in alphabetical order in your own words. alpha particle

  Energetic helium nucleus, emitted by radioactive nuclei.

  atom

  Elementary building block in the chemistry of matter.

  atomic mass

  Mass of an atom, in units of one twelfth of the mass of carbon atom.

  Avogadro’s number

  Number of atoms or molecules in a number of grams equal to the atomic or molecular mass.

  beta particle

  Fast electrons emitted by radioactive nuclei.

  electromagnetic radiation

  A family of waves propagating in space, representing oscillating electric and magnetic forces, e.g., light, radio.

  electron

  Light elementary particle, negatively charged, found in all atoms.

  energy level

  One of the energies at which, according to quantum laws, atoms or nuclei may be found.

  excited state of atom

  A state of an atom with more energy than the lowest "ground state."

  excited state of atomic nucleus

  A state of the atomic nucleus with more energy than the stable (or most stable) "ground state."

  frequency of EM wave

  Number of oppositely directed excursions of the electric or magnetic force at a point in space where the wave passes.

  gamma rays

  Electromagnetic radiation of very short waves, emitted by nuclei.

  ground state

  The lowest energy state of an atom or nucleus.

  half life

  For a radioactive element, the time needed for half of it to decay.

  ion

  Atom or molecule which has lost one or more electrons, or attached extra ones.

  isotope

  Variety of a chemical element with a certain number of protons and neutrons.

  molecule

  A chemical combination of two or more atoms.

  molecular weight

  The sum of atomic weights of a molecule.

  neutrino

  Uncharged and nearly massless elementary particle; may carry energy.

  neutron

  Uncharged nucleon, similar to proton.

  nuclear radiation

  Waves or particles emitted by unstable atomic nuclei.

  nucleus (of atom)

  Core of an atom, electrically positive and with most of the mass.

  photon

  Quantity of energy associated with the emission or absorption of an electromagnetic wave.

  Planck's constant

  A physical constant appearing in equations of quantum physics.

  proton

  An elementary positive particle; neutrons and protons form the atom's nucleus.

  quantum mechanic

  Rules of mechanics on the atomic and nuclear scale.

  radiation

  General name for either electromagnetic or nuclear radiation.

  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.]

  A certain radioactive isotope has a half-life of 2 days. How long approximately does it take until only of it remains in a given sample? [About 20 days, or half-lives, because ]

  Hydrogen (forming molecules) weighs about grams per cubic meter. How many molecules of hydrogen are in one cubic micron (a micron is the millionth part of the meter)?

  If is Avogadro's number then grams hydrogen contains

  molecules, and grams contain . A cubic micron is cubic meters, so the number is: [ or about million molecules.]

  Nuclear Binding Energy

  A carbon nucleus of (for instance) contains protons and neutrons. The protons are all positively charged and repel each other: they nevertheless stick together, showing the existence of another force—a nuclear attraction, the strong nuclear force, which overcomes electric repulsion at very close range. Hardly any effect of this force is observed outside the nucleus, so it must have a much stronger dependence on distance—it is a short range force. The same force is also found to pull neutrons together, or neutrons and protons.

  The energy of the nucleus is negative (just like the energy of planets in the solar system #7), for one must do work, or invest, energy to tear a nucleus apart into its individual protons and neutrons (the energy is zero when all particles are infinitely far away). Mass spectrometers have measured the masses of nuclei, which are alw
ays less than the sum of the masses of protons and neutrons that form them, and the difference, e.g., ( is the mass of the carbon atom), is called the "mass defect". The binding energy is then given by Einstein's famous .

  Nuclear Fusion

  The binding energy of helium is appreciable, and seems to be the energy source of the Sun and of most stars. The Sun has plenty of hydrogen, whose nucleus is a single proton, and energy is released when protons combine into a helium nucleus, a process in which two of them are also converted to neutrons.

  The conversion of protons into neutrons is the result of another nuclear force, known as the weak force (the word nuclear is assumed here). The weak force also has a short range, but is much weaker than the strong force. The weak force tries to make the number of neutrons and protons in the nucleus equal; these two particles are closely related and are sometimes collectively known as nucleons.

  The protons combine to helium only if they have enough velocity to overcome each other's repulsion and get within range of the strong nuclear attraction, which means they must form a very hot gas. Hydrogen hot enough for combining to helium requires an enormous pressure to keep it confined, but suitable conditions exist in the central regions of the Sun (core), where such pressure is provided by the enormous weight of the layers above the core, created by the Sun's strong gravity. The process of combining protons to form helium is an example of nuclear fusion.

  Our oceans have plenty of hydrogen, and helium does not harm the environment, so it would be great if physicists could harness nuclear fusion to provide the world with energy. Experiments in that direction have so far come up short. Sufficiently hot hydrogen will also be ionized, and to confine it, very strong magnetic fields have been used, because charged particles (like those trapped in the Earth's radiation belt) are guided by magnetic field lines. Fusion experiments also rely on heavy hydrogen, which fuses more easily, and gas densities have been kept moderate. In spite of all such tricks, though fusion energy has been released, so far more energy is consumed by the apparatus than is yielded by the process.