Unit 12: Part 5Nuclear Reactions and Elementary Particles

Overview

Nuclear Reactions

Nuclear Fission

Nuclear Fusion

Beta Decay and the Neutrino

Fundamental Forces and Exchange Particles

Elementary Particles

The Quark Model

Overview Continued

Force Unification Theories, the Standard Model, and the Early Universe

Nuclear ReactionsIn nuclear reactions, one pair of nuclei becomes a pair of different nuclei.

Example:

Or, more accurately,

The intermediate state is usually omitted from the equation.

Nuclear ReactionsEnergy is always conserved in nuclear reactions, although it is necessary to take mass energy into account.

The Q value is the change in kinetic energy from the initial nuclei to the final ones.

In the reaction

If Q is positive, the reaction may proceed spontaneously; if Q is negative, energy must be added before the reaction can occur.

Nuclear Reactions

When Q < 0, the minimum kinetic energy needed is:

Nuclear Reactions

The reaction cross-section is a measure of the probability of a particular reaction to occur.

Nuclear Fission

In a fission reaction, a heavy nucleus splits into two lighter nuclei. Fission may be either spontaneous or induced.

Example:

This is induced fission; the incoming neutron excites the uranium nucleus into fissioning.

Nuclear Fission

Fission is reasonably well described by the liquid-drop model, which models the nucleus as an oscillating liquid drop that eventually splits.

Nuclear Fission

The daughter nuclei from fission are not unique; many different decay modes are possible.

Examples:

Note that in each case there are more outgoing neutrons than incoming ones.

Nuclear FissionIf the outgoing neutrons have the correct energy to induce further fission, a chain reaction can take place. There is a minimum mass required, called the critical mass, in order to sustain a chain reaction.

Nuclear Fission

If the chain reaction is uncontrolled, an enormous explosion takes place. This is the operating principle behind nuclear weapons.

Controlling the chain reaction allows the production of energy; if the reaction can be sustained indefinitely, commercial power generation is possible.

Nuclear Fission

A nuclear reactor contains a complex set of fuel rods, control rods, and moderator.

The control rods (which absorb neutrons) are movable; they are positioned so that the chain reaction is stable. A considerable amount of heat is produced, so the rods are usually submerged in flowing water, called cooling water. If the control rods are completely inserted, the chain reaction stops.

The water also acts as a moderator, slowing the neutrons so they are more likely to induce fission.

Nuclear Fission

Schematic diagram of a reactor vessel and fuel assembly

Nuclear FissionThis diagram illustrates how the heat created in the reactor vessel is used to generate electricity.

Nuclear Fission

If the flow of coolant stops, the reactor can become very hot and even melt. This could lead to the release of some radioactive material. The accidents at Three Mile Island and Chernobyl were of this type, although the Chernobyl accident was complicated by a poor design that allowed the chain reaction to go out of control.

Nuclear Fusion

Energy can be produced through the fusion of very light elements.

Example, deuterium–tritium fusion:

Nuclear Fusion

Proton–proton fusion powers the Sun:

The net effect is that four protons fuse to make a helium nucleus.

Nuclear Fusion

Attempts have been made to establish a controlled fusion reaction. The nuclei must be very energetic to overcome the Coulomb repulsion—the temperature in the core of the Sun is about 15 million degrees—and it is extremely hard to confine enough nuclei to create a critical mass.

Beta Decay and the Neutrino

Beta decay appears to be a two-body process:

Since the initial nucleus is at rest, the daughter nucleus and the beta particle should have equal and opposite momenta, and the beta particle should have an energy characteristic of the particular reaction.

Beta Decay and the Neutrino

But the measured energy of the beta particle is always less than the expected value!

This would appear to violate conservation of energy.

Beta Decay and the NeutrinoThe solution: a neutral, near-massless particle called the neutrino (Italian for little neutral one-Enrico Fermi). Its existence was postulated in order to “fix” the beta decay problem; it was first observed about 20 years later (Wolfgang Pauli).

The correct form for beta decay:

The last particle is the neutrino; an antineutrino in the first case and a neutrino in the second.

Fundamental Forces and Exchange Particles

Looking at the fundamental interactions between elementary particles, we find there are four:

Gravitational force

Electromagnetic force

Strong nuclear force

Weak nuclear force

Fundamental Forces and Exchange Particles

The gravitational and electromagnetic forces are familiar; their range is essentially infinite.

The complete quantum mechanical description of these forces does not use the concept of a field; rather, there are “virtual” particles exchanged when one elementary particle interacts with another.

Fundamental Forces and Exchange Particles

These virtual particles are extremely short-lived and cannot be observed; according to the uncertainty principle the conservation of energy can be violated during this brief time. These virtual particles transmit energy and momentum from one interacting particle to the other.

Forces with infinite range must have massless exchange particles; the range of short-range forces is limited by their massive exchange particles.

Fundamental Forces and Exchange Particles

The exchange particle for the electromagnetic force is the photon.

This diagram, called a Feynman diagram, helps illustrate the process.

Fundamental Forces and Exchange Particles

The existence of an exchange particle between nucleons was proposed in the 1930s. Calculations showed that its mass should be about 270 times that of the electron.

Such particles were discovered about 10 years later, and are called pions.

Pions may be positively charged, negatively charged, or neutral.

Fundamental Forces and Exchange Particles

This Feynman diagram shows a strong interaction with an exchanged pion.

Fundamental Forces and Exchange Particles

The strong nuclear force cannot account for beta decay, which can be seen in its simplest form in the decay of a free neutron:

This must be the result of a new force, called the weak nuclear force. The exchange particle for the weak force is called the W; its existence was postulated for some time before it was actually observed.

Fundamental Forces and Exchange Particles

Attempts to create a successful quantum theory of gravity have so far been unsuccessful, as have attempts to detect the graviton.

This table summarizes the four forces.

Elementary Particles

Two types of elementary particle have been identified—leptons, such as the electron and neutrino, and hadrons, such as the proton and neutron.

There is no evidence that the electron has any internal structure; it appears to be truly fundamental (not made of anything else). A heavier lepton, called the muon, was discovered in cosmic rays. It is unstable.

Elementary ParticlesA third charged lepton, called the tau, is about twice as massive as the proton. It is produced in accelerators.

Each lepton type has its own neutrino associated with it—the electron neutrino, the muon neutrino, and the tau neutrino.

Hadrons consist of baryons, such as the proton and neutron, and mesons, such as the pion. The lightest baryon (the proton) is stable; the lightest meson is not.

The following table summarizes the properties of some elementary particles.

30.6 Elementary ParticlesThe full list fills an entire book!

The Quark Model

There is such a wide variety of hadrons that it seems impossible that each one could be a different elementary particle. It turns out that they can all be made from a combination of six different fractionally charged particles called quarks.

The Quark Model

Hadrons can be made from a combination of three quarks; mesons are a quark–antiquark combination.

The Quark Model

Quarks are confined—attempting to separate quarks takes more and more energy as the separation grows, until finally a quark–antiquark pair is created.

Interactions between quarks are mediated by massless particles called gluons.

The Quark Model

The interaction between hadrons, then, is really an interaction between quarks.

Force Unification Theories, the Standard Model, and the Early

Universe

For almost a century, efforts to unify the descriptions of the four forces, so that they are different manifestations of the same ultimate force, have been ongoing.

The electromagnetic and weak nuclear forces have been successfully unified into a force called the electroweak force. This unification becomes relevant only when the reaction energies are large enough to dwarf the W mass.

Force Unification Theories, the Standard Model, and the Early

UniverseThese Feynman diagrams depict weak interactions.

Force Unification Theories, the Standard Model, and the Early

Universe

Promising attempts have been made to unify the strong nuclear force with the electroweak force, creating a Grand Unified Theory (GUT). More work remains to be done, but success seems quite likely.

Less likely is a unification that includes gravity; efforts along these lines, although extensive, have not yet been fruitful.

Force Unification Theories, the Standard Model, and the Early

Universe

The Standard Model of elementary particles consists of the electroweak theory plus the strong interaction theory, called quantum chromodynamics (QCD). Deviations from standard model predictions have been sought for some time; so far, none have been found.

Force Unification Theories, the Standard Model, and the Early

Universe

Exploring unification means exploring higher and higher energies, which cannot be done experimentally. However, the universe did experience those energies shortly after the Big Bang; predictions from unified theories can be made for the early development of the universe and checked for consistency.

Summary

A nuclear reaction involves nuclei and particles.

The Q value of a nuclear reaction is the energy released or absorbed.

An unstable nucleus can fission into two lighter nuclei, releasing energy.

A chain reaction occurs when one fission triggers two others, and so forth.

Summary

A nuclear reactor uses a controlled chain reaction to produce energy.

Two light nuclei can, if the Coulomb barrier can be overcome, fuse into a heavier nucleus, with the release of energy.

Beta decay produces a beta particle and a neutrino along with the daughter nucleus.

Fundamental forces are carried by exchange particles.

Summary

The weak nuclear force is responsible for beta decay.

Leptons—electrons, neutrinos, and the muon and tau—interact weakly.

Hadrons interact strongly. Hadrons include baryons and mesons.

Hadrons are made of quarks—three quarks for a baryon, and a quark–antiquark pair for a meson.

Summary

The force between quarks is carried by gluons; quarks are confined and are never observed singly.

The electroweak force unites the electromagnetic and weak forces.

Grand unified theories would unify the strong force with the electroweak force. The electroweak force plus QCD comprise the standard model.