Chapter 14: Nuclear and Particle Physics — Review and Exercises

What characteristics of radioactivity show it to be nuclear in origin and not atomic?

(a) Identify the particles emitted as $\alpha$ radiation, ${\beta }^{-}$ radiation, ${\beta }^{+}$ radiation, and $\gamma$ radiation.

(b) An $\alpha$ particle of a given energy has a quoted range of 2.0 mm in a material. Does every such particle stop at exactly 2.0 mm? Explain.

Match each description to $\alpha$, ${\beta }^{-}$, ${\beta }^{+}$, or $\gamma$ radiation: (a) a helium-4 nucleus, (b) an electron, (c) a positron, and (d) a high-energy photon. Give the electric charge of each in units of the positive elementary charge.

$\alpha$ particles, ${\beta }^{-}$ particles, ${\beta }^{+}$ particles, and $\gamma$ rays travel horizontally between two plates. The upper plate is positively charged and the lower plate is negatively charged. Which beams deflect upward, which deflect downward, and which continue straight? Explain using their charges.

What is the difference between $\gamma$ rays and characteristic X-rays? Is either necessarily more energetic than the other? Which can be the most energetic?

For typical radioactive-source energies, explain why paper can stop $\alpha$ particles, a suitable thickness of plastic can stop beta particles, and much thicker shielding is usually needed to substantially reduce $\gamma$ radiation. Why does “reducing the $\gamma$ intensity” describe shielding more accurately than “stopping every $\gamma$ photon”?

For each source below, suggest a suitable shielding material and explain your choice: (a) a source of $\alpha$ particles, (b) a source of ${\beta }^{-}$ particles, and (c) a source of $\gamma$ rays. Why must the particle energy and shield thickness also be considered?

In an idealized narrow-beam measurement, each 1.50-cm layer of lead transmits 10.0% of the $\gamma$ rays incident on that layer. What percentage of the original beam remains after two layers? After three? What total thickness leaves 0.100%?

Workers handling radioactive contamination may wear disposable coveralls and gloves. Explain what these prevent. Why do such garments provide little shielding against penetrating $\gamma$ rays?

Where does the energy released in radioactive decay come from? Explain how the total rest mass of the products can be smaller than that of the parent while total energy is conserved.

What does it mean to ionize an atom or molecule? Explain how ionizing radiation can damage living cells even when the incident radiation is electrically neutral.

Explain why ionizing radiation can damage living cells. In your answer, describe what ionization does to an atom or molecule and how this can affect DNA or other cell structures. Does the radiation itself need to carry an electric charge to cause this damage?

A gas detector requires an average of 30 eV of deposited energy per ion pair produced. A particle deposits 0.60 MeV in the gas. Estimate the number of ion pairs produced. Use $1\text{MeV}={10}^6\text{eV}$.

Is it possible for light emitted by a scintillator to be too low in frequency to be used in a photomultiplier tube? Explain.

Explain the relationships among the terms nucleus, nucleon, proton, neutron, and nuclide. Is a neutrino a nucleon? Explain.

For helium-4 ($Z=2$), carbon-14 ($Z=6$), cobalt-60 ($Z=27$), and uranium-235 ($Z=92$), give the numbers of protons, neutrons, and total nucleons. Which number identifies the element?

Give the numbers of protons and neutrons in carbon-12, carbon-14, cobalt-60, cesium-137, and uranium-238. The atomic numbers are 6 for carbon, 27 for cobalt, 55 for cesium, and 92 for uranium. Which two listed nuclides are isotopes of the same element, and how do you know?

What are isotopes? Why do different isotopes of the same element have similar chemistries?

Protons repel one another electrically. What interaction helps bind protons and neutrons into nuclei, and why does its short range matter? Which interaction is responsible for beta decay?

Which statements correctly describe the interaction that binds protons and neutrons in ordinary nuclei? Explain each choice.

(a) It is effective only over very short distances.

(b) It acts only between protons.

(c) It can overcome electric repulsion between neighboring protons.

(d) It is the same inverse-square force that binds electrons to nuclei.

Polonium-210 ($Z=84$) undergoes $\alpha$ decay. Write the complete decay equation and identify the daughter; lead has $Z=82$. Check the total charge and number of nucleons.

Tritium, hydrogen-3 ($Z=1$), undergoes ${\beta }^{-}$ decay. Write the complete decay equation, including the electron and electron antineutrino. Identify the daughter; helium has $Z=2$.

A free neutron undergoes ${\beta }^{-}$ decay: $n\to p+e^{-}+{\overline{\nu }}_e$. Check electric charge and nucleon number before and after the decay. Using $L_e=+1$ for the electron and −1 for the electron antineutrino, check electron-family number as well.

An electron and a positron initially at rest annihilate into two photons. Explain why the photons travel in opposite directions and have equal energies. What supplies their energy?

Manganese-50 ($Z=25$) undergoes ${\beta }^{+}$ decay. Write the complete decay equation, including the positron and electron neutrino. Identify the daughter; chromium has $Z=24$.

Beryllium-7 ($Z=4$) captures an electron. Write the complete reaction equation, including the electron neutrino. Identify the daughter; lithium has $Z=3$.

In electron capture, a proton in a nucleus and an electron become a neutron and an electron neutrino. Show that electric charge is conserved. Using $L_e=+1$ for an electron and for an electron neutrino, explain why the emitted neutrino is consistent with electron-family-number conservation in this reaction.

For ${\beta }^{-}$ decay, ${\beta }^{+}$ decay, and electron capture, describe how a neutron or proton changes and how $Z$ and $A$ change. How do those changes differ from $\alpha$ decay? What happens to $Z$ and $A$ in $\gamma$ emission?

Many samples each initially contain 100 nuclei of the same radioactive isotope. After one half-life, the remaining radioactive nuclei in each sample are counted. Describe what you would expect to find when comparing the samples. How would the results change if each sample initially contained one million radioactive nuclei? Discuss the fraction remaining as well as the number.

In a $3\times {\text{10}}^9$-year-old rock that originally contained some ${}^{\text{238}}\text{U}$, which has a half-life of $4.5\times {10}^9$ years, we expect to find some ${}^{\text{238}}\text{U}$ remaining in it. Why are ${}^{\text{226}}\text{Ra}$, ${}^{\text{222}}\text{Rn}$, and ${}^{\text{210}}\text{Po}$ also found in such a rock, even though they have much shorter half-lives (1600 years, 3.8 days, and 138 days, respectively)?

Carbon-14 has a half-life of 5700 years. Assume a closed sample initially contained 8000 carbon-14 atoms and now contains about 1000. How many half-lives have passed, and what age does this suggest? Explain why this is an estimate rather than an exact clock for each atom.

Carbon-14 has a half-life of 5700 years. Assume that a closed sample initially contains 1600 carbon-14 atoms.

(a) About how many remain after 11,400 years?

(b) If about 200 remain, how much time has passed?

A sealed source has an initial activity of 800 Bq and a half-life of 5.0 years.

(a) What activity is expected after 15 years?

(b) How long until the expected activity is 50 Bq? Assume the daughter contributes no measured activity and the measurement conditions remain unchanged.

Which of these imaging methods use ionizing radiation: conventional X-ray imaging, CT, PET, MRI, and ultrasound? For each, identify the kind of radiation or physical signal used. Explain why “does not use ionizing radiation” does not mean that an imaging method has no safety considerations.

Consider a conventional X-ray image, a CT scan, a PET scan, an MRI scan, and an ultrasound image.

(a) Which use ionizing radiation?

(b) Which of these uses a radioactive substance administered to the patient?

(c) Does receiving an X-ray image ordinarily make the patient radioactive? Explain.

In terms of radiation dose, what is the major difference between medical diagnostic uses of radiation and medical therapeutic uses?

Why can a short physical half-life help limit the time a diagnostic radiopharmaceutical remains radioactive? Why must its half-life still be long enough for preparation and imaging?

Molybdenum-99 ($Z=42$) undergoes ${\beta }^{-}$ decay to technetium-99, often in the metastable state technetium-99m. Write the ${\beta }^{-}$ equation including the electron antineutrino. When technetium-99m emits a $\gamma$ photon, do its proton and neutron counts change?

In PET imaging, a positron emitted by a radiopharmaceutical annihilates with an electron. Explain why detecting two photons at nearly the same time on opposite sides of the patient helps locate the event. What does the location of the two detectors tell you about where the annihilation occurred, and what remains undetermined?

Why can an $\alpha$-emitting material be much more hazardous when inhaled or swallowed than when it is outside intact skin? Explain why $\gamma$ radiation can contribute to exposure even when its source remains outside the body.

Why is radon more closely associated with inducing lung cancer than other types of cancer?

Suppose a person swallows some radioactive material by accident. What information is needed to be able to assess possible damage?

Describe how each change can reduce exposure to a radiation source: (a) spending less time near it, (b) working farther away, and (c) placing suitable shielding between it and the worker. Why must the shielding material and thickness be chosen for the radiation involved?

A worker must briefly handle equipment near a sealed $\gamma$-ray source. Suggest one change involving time, one involving distance, and one involving shielding that could reduce exposure. Explain why a pair of ordinary disposable gloves cannot substitute for these measures against the $\gamma$ rays.

Why does the fusion of light nuclei into heavier nuclei release energy?

Energy input is required to fuse medium-mass nuclei, such as iron or cobalt, into more massive nuclei. Explain why.

The net conversion in the proton–proton chain, including positron annihilation, can be written $4p+2e^{-}\to {}^4\text{He}+2{\nu }_e+Q$, where $Q$ is the released energy. Check electric charge and nucleon number. If $L_e$ is +1 for an electron and an electron neutrino, check electron-family number too.

Light nuclei can release energy when they fuse. Why is it nevertheless difficult to start and sustain fusion? Explain the roles of electric repulsion, high temperature, and keeping the reacting nuclei together long enough.

Explain why the fission of heavy nuclei releases energy. Similarly, why is it that energy input is required to fission light nuclei?

A heavy nucleus splits into two smaller nuclei in one reaction; two light nuclei combine in another.

(a) Name the two processes.

(b) Which powers the Sun?

(c) Can both release energy?

(d) When either releases energy, how does the total rest mass of the products compare with that of the reactants?

In the fission reaction $n+{}^{235}\text{U}\to {}^{92}\text{Kr}+{}^{142}\text{Ba}+xn$, determine x by conserving nucleon number. Check electric charge using $Z=92$ for U, 36 for Kr, and 56 for Ba. How can the emitted neutrons help sustain a chain reaction?

Radioactivity depends on the nucleus and not the atom or its chemical state. Why, then, is one kilogram of uranium more radioactive than one kilogram of uranium hexafluoride containing uranium of the same isotopic composition?

In a steady fission chain reaction, about how many neutrons from each fission must, on average, cause another fission? Explain how neutron absorption and leakage affect whether the chain reaction dies away, stays steady, or grows. How do control rods help regulate it?

Fission commonly leaves radioactive fission products. Does that mean a fusion facility would necessarily produce no radioactive material? Discuss how neutrons from some fusion reactions can affect surrounding materials.

Control rods stop the self-sustaining fission chain reaction in a nuclear reactor, but the reactor still requires cooling. Explain the source of the continuing energy release and why inserting the control rods does not stop it.

Why is a commercial power reactor not a nuclear bomb? Distinguish an explosive nuclear-weapon chain reaction from steam or chemical explosions that can occur in a reactor accident.

An event releases $5.0\times {10}^{13}\text{J}$ of nuclear energy—an amount comparable to the electrical energy used throughout the city of Alameda in the San Francisco Bay Area in about two weeks. Using $E=\mathrm{\Delta }m{c}^2$ and $c=3.0\times {10}^8\text{m/s}$, find the corresponding decrease in rest mass in grams.

The measured activity of a radioactive contaminant at a particular site can fall faster than radioactive decay alone predicts. Give two physical processes that could cause this. Does a fall in activity at that site necessarily mean the radioactive nuclei have decayed?

Identify the interaction chiefly responsible for each: (a) Earth’s orbit around the Sun, (b) the attraction between an electron and a nucleus, (c) binding protons and neutrons into a nucleus, and (d) beta decay. Which of these interactions have a short range at nuclear or subnuclear scales?

An antihydrogen atom contains an antiproton and a positron. How could annihilation when it encounters ordinary matter help distinguish antihydrogen from hydrogen? If its positron annihilates with an electron, with both initially approximately at rest, two photons are emitted. Explain why the photons have equal energies and calculate the energy of each in MeV. Use $m_e{c}^2=0.511\text{MeV}$.

What lifetime do you expect for an antineutron isolated from normal matter?

In ${\mu }^{-}\to e^{-}+{\overline{\nu }}_e+{\nu }_{\mu }$, check electric charge, electron-family number, and muon-family number. Use +1 for a lepton in its family, −1 for its antiparticle, and zero for particles outside that family.

Early solar-neutrino experiments detected fewer electron neutrinos than solar models predicted. Explain how neutrino flavor change resolves this discrepancy. Why was a measurement sensitive to all three active neutrino flavors an important test?

In ordinary nuclear reactions without baryon–antibaryon production, how does baryon-number conservation account for conservation of the total number of nucleons? Why does this not require the total rest mass to remain unchanged?

(a) Classify the electron, muon, electron neutrino, pion, kaon, proton, neutron, photon, and gluon as leptons, mesons, baryons, or gauge bosons. You may use the particle table.

(b) Which categories in this list contain hadrons?

(c) Describe the valence-quark content of an ordinary meson and an ordinary baryon. Why does mass alone not determine these categories?

Using the particle table and the quark model, classify each of these as a lepton, meson, baryon, or gauge boson: electron, tau, muon neutrino, pion, kaon, proton, neutron, photon, and gluon. Which of these are composite particles? Explain why “heavier particle” is not a reliable definition of baryon.

Measurements of beta decay showed that the daughter nucleus and emitted electron did not account for all the initial energy and momentum. Explain how an additional, electrically neutral particle could account for these observations. Why was the missing energy and momentum evidence for such a particle, but not by itself conclusive proof of its existence?

Which interactions are described by the Standard Model? Which is left out? How does a proposed grand unified theory differ from the already established electroweak theory?

Does the discovery of the Higgs boson mean that it replaces the W and Z bosons as the carrier of the weak interaction? Explain your response.

If a deeper theory successfully unifies all four forces, it will still be correct to say that the orbit of the moon is determined by the gravitational force. Explain why.