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physics
modern physics

College Physics 7th edition Jerry D. Wilson, Anthony J. Buffa, Bo Lou - Solutions

What are the (a) Half-life (b) Decay constant for a stable isotope?
Nuclide A has a half-life that is one-third that of nuclide B. The type A sample starts with twice the number of undecayed nuclei as in the sample of type B. Compare the initial sample activities expressed as a ratio of the activity of sample A to that of B.
Using the general guidelines for nuclear stability, explain why aluminum has only one stable isotope (27Al). In other words, why aren’t isotopes of aluminum, such as 28Al or 26Al, stable?
A Rutherford scattering experiment uses a beam of alpha particles of a known kinetic energy. Qualitatively compare the distance of closest approach (rmin) to a target consisting of lead atoms to that to a target made up of uranium atoms. Give a numerical answer as a ratio of the closest approach
Compared to 3He, the probability of absorbing a neutron is much less likely for 4He. Explain this using what you know about odd– even proton and neutron numbers.
Explain how the fusing of very light nuclei and the split-ting of very heavy nuclei can both release energy.
If one nucleus has a larger average binding energy than another nucleus, does this mean that it takes more total energy to break the former into its constituent nucleons? Explain your answer.
If X- rays and slow neutrons give the same effective dose, how will their doses compare?
PET scans require extremely fast computers coupled with gamma- ray detectors capable of accurate energy measurements. Explain why both energy accuracy and comparison of arrival times are crucial to the success of a PET scan.
A Geiger counter is not efficient. That is, the number of events it records is always smaller than the amount of ionizing radiation that enters it. Explain why the efficiency is not 100%.
Theoretically, the tumor- killing efficiency of particle beams is much greater than that of a beam of X- rays or gamma rays. Explain why this is true.
A Rutherford scattering experiment is performed on a gold foil target with alpha beams of two different kinetic energies, one of 3.00MeV, the second of 6.00 MeV. Qualitatively compare the distance of closest approach (rmin) for the two different energy alpha beams. Give a numerical answer as a
Determine the number of protons, neutrons, and electrons in a neutral atom with the following nuclei: (a) 90Zr and (b) 208Pb.
Write the nuclear equations expressing (a) The beta decay of 60Co and (b) The alpha decay of 222Rn.
Write the nuclear equations for (a) The alpha decay of 237Np, (b) The decay of 32P, (c) The decay of 56Co, (d) Electron capture in 56Co, and (e) The decay of 42K from an excited nuclear state to the ground state (not excited).
Polonium-214 can decay by alpha decay. (a) The product of its decay has how many fewer protons than polonium-214: (1) zero, (2) one, (3) two, or (4) four? (b) Write the nuclear equation for this decay and determine the daughter nucleus.
A lead-209 nucleus results from both alpha–beta sequential decays and beta–alpha sequential decays. What was the grandparent nucleus? Show this result for both decay routes by writing the nuclear equations for both sequential decay processes.
Complete the following nuclear decay equations by filling in the blanks:
Complete the following nuclear-decay equations by filling in the blanks:
Actinium-227 decays by alpha decay or beta decay and is part of a long decay sequence, shown in Fig. 29.8. Write all the possible nuclear decays for the decay series from 227Ac to 215Po. Identify the daughter nucleus at the end of each decay.
The decay series for neptunium-237 is shown in Fig. 29.20.(a) What is the decay mode of each of the sequential decays? (b) Determine the daughter nucleus at the end of each decay.
A particular radioactive sample undergoes 2.50 x 106 decays/s. What is the activity of the sample in (a) Curies and (b) Becquerel’s?
At present, a radioactive beta source with a long half-life has an activity of 20 mCi. (a) What is the present decay rate in decays per second? (b) Assuming that one beta particle is emitted per decay, how many are currently emitted per minute?
The half-life of a radioactive isotope is known to be exactly 1 h. (a) What fraction of a sample would be left after exactly 3 h: (1) one-third, (2) one-eighth, or (3) one-ninth? (b) What fraction of a sample would be left after exactly 1 day?
A alpha source gives off alpha particles each with a kinetic energy of 2.78 MeV. At what rate (in watts) is kinetic energy being produced?
A sample of technetium-104, which has a half-lfe of 18.0 min, has an initial activity of 10.0 mCi. Determine the activity of the sample after exactly 1 h has elapsed.
Calculate the time required for a sample of radioactive tritium to lose of its activity. (Tritium has a half-life of 12.3 years.)
131I is given to a patient for use in a diagnostic procedure on her thyroid. What percentage of the 131I sample remains after exactly one day, assuming that all of the 131I is retained in the patient’s thyroid gland? (Answer to three significant figures.)
Carbon-14 dating is used to determine the age of some unearthed bones. (a) If the activity of bone A is higher than that of bone B, then bone A is (1) older than, (2) younger than, (3) the same age as bone B. Explain your reasoning. (b) A sample of bone A is found to have 4.0 beta per gram of
Prove that the number N of radioactive nuclei remaining in a sample after an integer number (n) of half-lives has elapsed is N –No/2n = (1/2)n No. Here No stands for the initial number of nuclei.
Suppose that some ancient writings on parchment are found sealed in a jar in a cave. If carbon-14 dating shows the parchment to be 28 650 years old, what percentage of the original carbon-14 atoms still remains in the sample?
(a) What is the decay constant of fluorine-17 if its half-life is known to be 66.0 s? (b) How long will it take for the activity of a sample of 17F to decrease to of its initial value? (c) Repeat part (b), but instead determine the time to decrease to an additional to of its initial value. Does
Francium-223 (22387FR) has a half-life of 21.8 min. (a) How many nuclei are initially present in a 25.0-mg sample of 22387FR? (b) What is its initial activity? (c) How many nuclei will be present 1 h and 49 min later? (d) What will be the sample’s activity at this later time?
An isotope of potassium has the same number of neutrons as argon-40. Write this potassium isotope in nuclear notation.
A basement room containing radon gas (t1/2 = 3.82days) is sealed to be airtight. (a) If 7.50 x 1010 radon atoms are trapped in the room, estimate how many radon atoms remain in the room after one week. (b) Radon undergoes alpha decay. After 30 days, is the number of its daughter nuclei equal to,
In 1898, Pierre and Marie Curie isolated about 10 mg of radium-226 from eight tons of uranium ore. If this sample had been placed in a museum, (a) How much of the radium would remain in the year 2109? (b) How many radium nuclei would have decayed during this time?
An ancient artifact is found to contain 250 g of carbon and has an activity of 475 decays/min. (a) What is the approximate age of the artifact, to the nearest thousand years? (b) What would its initial activity have been?
The recoverable U. S. reserves of high-grade uranium-238 ore (high-grade ore contains about 10 kg of 238U3O8 per ton) are estimated to be about 500,000 tons. Neglecting any geological changes, what mass of 238U existed in this high-grade ore when the Earth was formed, about 4.8 billion years ago?
Nitrogen-13, with a half-life of 10.0 min, decays by beta emission. (a) Write down the decay equation to determine the daughter product and whether the beta particle is a positron or electron. (b) If a sample of pure 13N has a mass of 1.50 g at a certain time, what is the activity 35.0 min later?
Which one of each of the following pairs of nuclei would you expect it to be easier to remove a neutron from: (a) 168O or 178O; (b) 4020Ca or 4220Ca; (c) 105B or 115B; (d) 20882Pb or 20983Bi? State your reasoning for your choice in each case.
The total binding energy of 21H is 2.224 MeV. Use this information to compute the mass (in u) of a 2H nucleus from the known mass of the proton and the neutron.
Use Avogadro’s number (Section 10.3) to show that 1u = 1.66 x 10-27kg.
(a) What is the total binding energy of the 12C nucleus? (b) What is its average binding energy per nucleon?
35Cl and 37Cl are two isotopes of chlorine. What are the numbers of protons, neutrons, and electrons in each if (a) The atom is electrically neutral, (b) The ion has a –2 charge, and (c) The ion has a +1 charge?
(a) The mass of the nuclide 168O is 15.994 915 u. What is the total binding energy for this nucleus? (b) Determine its average binding energy per nucleon.
Which isotope of hydrogen has (a) The highest total binding energy and (b) The lowest average binding energy per nucleon, deuterium or tritium? Justify your answer mathematically.
Near high-neutron areas, such as a nuclear reactor, neutrons will be absorbed by protons (the hydrogen nucleus in water molecules) and will give off a gamma ray of a characteristic energy in the process. (a) Write the equation for the neutron absorption process and the sub-sequent gamma decay of
(a) How much energy (to four significant figures) would be required to completely separate all the nucleons of a nitrogen-14 nucleus, the atom of which has a mass of 14.003 074 u? (b) Compute the average binding energy per nucleon of this nuclide.
Calculate the binding energy of the last neutron in the 4019K nucleus.
Suppose an alpha particle could be removed intact from an aluminum-27 nucleus (m = 26.981 541 u). (a) Write the equation that represents this process and determine the daughter nuclide. (b) If the daughter nuclide has mass of 22.989 770 u, how much energy would be required to perform this
On average, determine whether the nucleons are more tightly bound in a 27Al nucleus or in a 23Na nucleus.
The atomic mass of 23692U is 235.043 925 u. Find the average binding energy per nucleon for this isotope.
The mass of 84Be is 8.005 305 u. (a) Which is less, the total mass of two alpha particles or the mass of the 8Be nucleus? (b) Which is greater, the total binding energy of the 8Be nucleus or the total binding energy of two alpha particles? (c) On the basis of your answers to parts (a) and (b)
In a diagnostic procedure, a patient in a hospital ingests 80 mCi of gold-198 (t1/2 = 2.7 days). What is the activity at the end of one month, assuming none of the gold is eliminated from the body by biological functions?
One isotope of uranium has a mass number of 235, and another has a mass number of 238. What are the numbers of protons, neutrons, and electrons in a neutral atom of each isotope?
A technician working at a nuclear reactor facility is exposed to a slow neutron radiation and receives a dose of 1.25 rad. (a) How much energy is absorbed by 200 g of the worker’s tissue? (b) Was the maximum permissible radiation dosage exceeded?
A person working with several nuclear isotope separation processes for a two-month period receives a 0.50-rad dose from a gamma source, a 0.30-rad dose from a slow-neutron source, and a 0.10-rad dose from an alpha source. Was the maximum permissible radiation dosage exceeded?
Neutron activation analysis was performed on small pieces of hair that had been taken from the exiled Napoleon after he died on the island of St. Helena in 1821. This procedure involves exposing the samples to a source of neutrons. Some (stable) arsenic nuclei, if present in the sample, will absorb
A cancer treatment called the gamma knife (see Insight 29.1, Biological and Medical Application of Radiation) uses focused 60Co sources to treat tumors. Each 60Co nucleus emits two gamma rays, of energy 1.33 MeV and 1.17 MeV, in quick succession. Assume that of the total gamma-ray energy is
The radioactive source in most smoke detectors is 241Am, which has a half-life of 432 years. In a typical detector, only about 0.100 mg of this material is needed. (a) Write down its alpha decay equation and predict the product nucleus. (b) What is the initial source activity? (c) What would be
A sample of 215Bi, which beta decays (t1/2 = 2.4 min), initially contains one-hundreth of Avogadro’s number of nuclei. (a) What is the sample’s mass? (b) Write down the beta decay equation and predict the product nucleus. (c) How many bismuth nuclei are present after 10 min? (d) After 1.0
High-energy gamma ray photons can remove nucleons from nuclei in a process called the photonuclear effect. This is a process analogous to the photoelectric effect in atoms (see Section 27.2). (a) If you wanted to remove a single neutron from a nucleus, which of the following nuclei would likely
Avery slow neutron with negligible kinetic energy is captured by a 10B nucleus, which ends up in its ground state. Calculate the (a) Energy and (b) Wavelength of the photon given off. (Neglect the recoil kinetic energy of the daughter nucleus.)
The experimental expression for the (approximate) radius (R) of a nucleus is R = RoA1/3, where and A is the mass number of the nucleus. Assuming that nuclei are spherical (they are approximately so in many cases), (a) Determine the average nucleon density in a nucleus in units of and (b) Estimate
Figure 29.21 shows the decay series for plutonium-239. Use the information in the figure to(a) Determine the two different decay schemes by which the isotope of radon associated with this chain can be formed, and (b) Determine the subsequent decay scheme for that isotope of radon.
(a) Isotopes of an element must have the same (1) atomic number, (2) neutron number, (3) mass number. (b) Write two possible isotopes for gold-197.
(a) Use Fig. 29.21 to explain why there is essentially no naturally occurring 239Pu in or on the Earth at present.(b) Use the information in the figure to explain why there is very little (but not zero) 235U naturally occurring in or on the Earth. (c) For every 1000 kg of 239P that might have been
Determine which of the following isotopes are likely to be stable and explain clearly and fully how you came to your conclusion, based on the “ rules of stability”: (a) 15O, (b) 8Li, (c) 222Rn, (d) 27Mg, (e) 41Ca. (f) For the unstable isotopes, write down the most likely nuclear decay
31H (tritium) can be produced in water surrounding a strong source of neutrons, such as that occuring in nuclear reactors. One of the ways tritium can form is via neutron capture by deuterium. (a) Write down the equation for this capture reaction. (b) Tritium has a half-life of 12.33 years. What
(a) Estimate the activity due to the 40K in a gallon of whole milk. Typically, a gallon contains about 6.4 g of potassium, which includes all the isotopes of potassium that exist naturally. Assume the same percentages for each isotope as given in the Pulling It Together Example at the end of this
An approximate experimental expression for the radius (R) of a nucleus is R = RoA1/3, where Ro = 1.2 x 10-15 and A is the mass number of the nucleus. (a) Find the nuclear radii of atoms of the noble gases: He, Ne, Ar, Kr, Xe, and Rn. (b) Determine the density of the nuclei associated with each of
Assume Rutherford used alpha particles with a kinetic energy of 5.25 MeV. (a) To which of the following nuclei would the alpha particle come closest in a head-on collision: (1) aluminum, (2) iron, or (3) lead? (b) Determine the distance of closest approach for the three nuclei in part (a) and
Tritium is radioactive. (a) Would you expect it to (1) β+, (2) β-, or (3) alpha decay? Why? (b) Write the nuclear equation for the correct decay and identify the daughter nucleus. Is it stable?
Using the law of conservation of momentum, explain how a colliding beam reaction (in which both particles move toward a head-on collision) requires less incident kinetic energy than a reaction in which one particle is at rest.
Would it take a higher temperature to fuse two protons or to fuse two carbon-12 nuclei? Explain.
A v-bare can interact with a proton in a target of water (although this is very rare). The reaction is essentially the inverse of β–decay; that is, the proton is converted into a neutron. Neutrino experimenters can detect this reaction by using detectors. The neutrino “signature” occurs when
In beta decay, explain why the beta particle kinetic energy must be less than the Q value of the decay.
(a) In beta decay, if the daughter nucleus is stationary, what can you say about the directions of the beta particle and the neutrino? Explain. (b) In a decay with a Q value of 1.5 MeV, suppose the is emitted with very little kinetic energy. How would the momenta of the daughter nucleus and
Compare the effective range of the strong nuclear force with that of the weak nuclear force. What does that tell you about the relative masses of the exchange particle(s) associated with these two forces? What should be the approximate (numerical) ratio of their masses (weak exchange particle to
Explain how you can distinguish between a hadron and a lepton based on their interactions and exchange particles.
Which of the leptons are stable? Which of the hadrons are stable?
For a given Q value and incident particle (called a), how does the threshold energy required to initiate a specific nuclear reaction vary as the mass of the target (called A) changes? Sketch a graph of threshold energy versus tar-get mass ranging from target masses on the order of the incident mass
What are some of the important differences and distinctions between baryons and mesons?
Theoretical physicists often assert that at the extremely high energies thought to have existed in the first moments of the universe, the W particle (which is known to have a mass several hundred times that of the proton) would behave, mass-wise, similarly to the (massless) photon. Explain this
Successful unification of the electromagnetic force with the weak force led physicists to what surprising conclusion about the proton? Describe how you might experimentally detect this prediction.
A 3He particle initiates a reaction when incident on a target nucleus. (a) Find a reaction scenario that would yield a product nucleus that is of the same species as the target nucleus. (b) Find a reaction scenario that would yield a product nucleus that has the same number of nucleons as the
As world oil prices generally rise there has been a call to move electric generation from fossil fuel plants to nuclear fission plants. Discuss some of the pros and cons involved in replacing fossil fuel plants with nuclear versions. Military, terrorism, global warming, and environmental concerns
Explain why there are both density and temperature requirements to sustain a viable fusion energy plant. Why are these requirements at odds with one another?
Complete the following nuclear reactions:
Determine the Q value of the following reaction:
What is the minimum kinetic energy a proton must have in order to initiate the reaction ? (“d” stands for a deuterium nucleus and is called the deuteron.)
226Ra decays and emits a 4.706-MeV alpha particle. Find the kinetic energy of the recoiling daughter nucleus from the decay of a stationary radium-226 nucleus.
The same type of incident particle is used for two endoergic reactions. In one reaction, the mass of the tar-get nucleus is 15 times that of the incident particle, and in the other reaction, it is 20 times the incident particle’s mass. The Q value of the first reaction is known to be three times
Find the approximate energy released in the following fission reactions: (a) 23592U + In ( fission products Plus five neutrons, (b) 23594Pu + In ( fission products Plus three neutrons.
(a) In power reactors, using water as a moderator (“neutron slower”) works well, because the proton and neutron have nearly the same mass. Explain why this is true. (b) From your reasoning in part (a), it follows that in a head-on elastic collision, we might expect a neutron to lose all of its
Fill in the blank: (a) 11H + _____(, 21H + y, (b) _____+ 32He ( 42He + 211H,. (c) Find the energy released in each.
Fill in the missing blank: (a) 21H + 21 H ( 32 He + _____, (b) 21 H + 31 H ( _____+ in. (c) Find the energy released in each.
A neutrino created in a beta decay process has an energy of 2.65 MeV. What is the maximum possible kinetic energy of the beta particle if the disintegration energy is 5.35 MeV: (a) (1) zero, (2) less than 5.35 MeV but not zero, (3) 5.35 MeV, or (4) greater than 5.35 MeV? (b) Under these
(a) Consider the reactionDetermine whether it is endoergic or exoergic. (b) If it is exoergic, find the amount of energy released; if it is endoergic, find the threshold energy.
Show that the disintegration energy for decay is Q = (mp – mD – me)c2 = (Mp – MD)c2, where the m’s represent the masses of the parent and daughter nuclei and the M’s represent the masses of the neutral atoms.

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