The rate of spontaneous fi ssion in 238U is 6.7 decaysper second for each kg of uranium

Rutherford was able to initiate nuclear reactions with particles before 1920. Why wasnt he able to initiate nuclear reactions with protons?

In Example 13.2 we learned that the 12C(, n)15O cross section is much larger than the 12C(, p)15N reaction for E 14.6 MeV. We believe this is evidence of a resonance in 16O. If it is a resonance, why arent both neutron and proton exit channels strongly populated? Why do we conclude the difference must be due to quantum numbers in the exit channel? Can the Coulomb barrier in the exit channels make a difference?

Why do the lifetimes of nuclear excited states decrease for higher excitation energies?

Why is the density of nuclear excited states larger for higher excitation energies?

Both deuterons and alpha particles can cause direct reactions by stripping. Which are more effective? Explain.

Discuss the changes in the cross section for neutroninduced and proton-induced reactions as the initial kinetic energy is decreased from 50 MeV. Ignore resonances.

Think about how a chain reaction could be controlled without delayed neutrons. Is it possible? What would be the diffi culties?

Think carefully about the fi ssion process. Does it seem peculiar that symmetric fi ssion is not the most probable? Does the distribution shown in Figure 13.8 seem reasonable? Explain.

Why is it useful to slow down neutrons produced by fi ssion in a nuclear reactor?

All the moderators mentioned in this chapter to slow down neutrons are light nuclei. Why are light nuclei used for moderators instead of heavy nuclei?

Why is fi ssion fuel placed in 4-m-long rods placed parallel but separated, rather than in one lump of mass?

Discuss how each of the following sources of energy is ultimately derived from the sun: wood, coal, gas, oil, water, and wind.

Why does a stars temperature increase as fusion proceeds? Why are higher temperatures required for the carbon cycle than for the proton-proton chain?

The fusion process continues in a very massive star until its core consists of nuclei near 56Fe. Explain why this occurs.

The fi rst wall of a magnetic fusion containment vessel has been said to contain the most hostile environment yet designed by man. Justify this statement.

Neutron-activation analysis is much more widely used than charged-particle activation. Why do you suppose that is true?

Explain in your own words the origin of the names of elements 97 through 102; that is, who or what the elements were named after and the reasons for doing so.

Explain in your own words the origin of the names of elements 103 through 108that is, who or what the elements were named after and the reasons for doing so.

Explain in your own words the origin of the names of elements 109 through 114that is, who or what the elements were named after and the reasons for doing so. You can skip those elements for which International Union of Pure and Applied Chemistry has not yet offi cially assigned a name.

How many new elements have been discovered that are not mentioned in this textbook? Discuss them.

Small research nuclear reactors, like those mostly used in universities, are often submerged in concrete structures that look like swimming pools. The water serves as a moderator of the neutrons. They often have a blue glow in the swimming pool around the reactor. What is the origin of the blue color? Hint: Look up Cerenkov radiation

A common fi ssion fragment is 90Sr. Why is this isotope considered particularly dangerous to human health?

The fi rst excited state of 17F is at 0.495 MeV. Can the p 16O reaction populate this state? Give your reasons.

239Pu absorbs a thermal neutron, and the resulting nucleus gamma decays to the ground state. (a) What is the energy of the gamma ray? (b) What would be the energy of the gamma ray if a 1.0-MeV neutron is absorbed by 239Pu at rest?

List as many nuclear reactions as you can that use deuterons and alpha particles for projectiles with stable targets that will populate 22Ne as the fi nal state in direct reactions.

Calculate how much energy is released when 239Pu absorbs a thermal neutron and fi ssions in the reaction n 239 94Pu S 240 94Pu* S 95 40Zr 142 54Xe 3n

A sample of shale contains 0.055% 238U by weight. Calculate the number of spontaneous fi ssions in one day in a 106-kg pile of the shale by determining (a) the mass of 238U present, (b) the number of 238U atoms, (c) the fi ssion activity, and fi nally (d) the num- ber of fi ssions. The spontaneous fi ssion activity rate of 238U is 6.7 fi ssions/kg # s.

Calculate the percentage abundance of 235U and 238U 2.0 billion years ago if the abundance today is 0.72% and 99.3%, respectively. The higher percentage of 235U probably allowed natural nuclear reactors to occur. Explain why such a reaction could not occur today.

Use the information in Figure 13.8 to write at least three common sets of fi ssion fragments for the fi ssion products of 236U (that is, the unstable nuclide present after 235U has absorbed a neutron and has undergone fi ssion).

A fi ssion reactor operates at the 1250-MWe level. Assume all this energy comes from the (average) 200 MeV released by fi ssion caused by thermal neutron absorption by 235U. At what daily rate is the mass of 235U used? (In practice, the energy conversion is not 100% effi - cient, nor is all the 235U in a fuel cell used.)

Calculate the energy released in kilowatt hours from the fi ssion of 1.0 kg of 235U. Compare this with the energy released from the combustion of 1.0 kg of coal. The heat of combustion of coal is given in Table 13.1.

In his book Great Ideas in Physics, Alan Lightman estimated that the energy (all forms, not just electrical) needed for a large American city for one day is roughly the same as could be provided by converting 100% of the mass of a golf ball into energy. Check to see whether this estimate is valid within an order of magnitude.

In 2011 one estimate of worldwide proven oil reserves was 2.0  1011 m3. Using the data in Table 13.1, answer the following questions. (a) How much energy would that amount of oil produce? (b) If oil were the sole source of energy for the world, how long would it last, assuming a steady yearly energy consumption of 500 EJ (5.0  1020 J)? (c) How much uranium used to fuel nuclear reactors would be required to supply the amount of energy you found in (a)?

Neutrons in equilibrium with their surroundings at temperature T are called thermal neutrons and have an average kinetic energy 3 2kT. Calculate the thermal neutron energy for (a) room temperature (300 K) and (b) the sun (15  106 K).

Determine the ground-state Q values for each of the reactions in the carbon cycle and show that the overall energy released is the same as for the proton-proton chain (26.7 MeV).

There is a bottleneck in producing masses higher than 4He, because there are no mass-5 or mass-8 stable nuclides. For older stars with high densities and high temperatures (T 100 million K), three alpha particles can form 12C. This occurs by two alpha particles fi rst forming 8Be, and 8Be reacting with another alpha particle to form 12C before 8Be can decay back to two alpha particles. (a) Explain why this has to happen for very hot stars and high density. (b) Calculate how much energy is given up when three alpha particles form 12C.

Following the triple-alpha process to form 12C (see the previous problem), a variety of nuclear reactions can form heavier nuclide masses. In one of them, 16O 16O S 32S , the temperature must be greater than about 3 billion K. (a) Why does the temperature have to be so high? (b) Calculate how much energy is released in the reaction. It is reactions like this that allow nuclei in the iron region to be formed.

One of the fusion reactions that goes on in massive stars is silicon burning, 28Si 28Si S 56Ni . This reaction is how fusion reactions eventually reach the most stable iron/nickel region. It is also a precursor to the end of a stars life and may lead to a supernova, if the stars mass is suffi cient. (a) Calculate the ignition temperature required for this reaction. (b) How much energy is expended in this reaction?

One of the fusion reactions that goes on in massive stars is carbon burning, 12C 12C S 24Mg . (a) Calculate the ignition temperature required for this reaction. (b) How much energy is expended in this reaction?

Assume that two thirds of Earths surface is covered with water to an average depth of 3 km. Calculate how many nuclei of deuterium exist (2H is 0.015% abundant). Estimate using reaction (13.22) how much energy is available through fusion.

The ignition temperature of fusion reactions is referred to in both temperature and kinetic energy. (a) Explain why this is done. (b) What is the relation between the two? (c) At what temperature is the energy 6.0 keV?

The following reactions may be useful in producing energy for fusion reactions. Find their Q values. 4He(3He, )7Be, 2H(d, p)3H, 2H(p, )3He, 12C(p, ) 13N, 3He(3He, pp)4He, 7Li(p, )4He, 3H(d, n)4He, 3He(d, p)4He.

Determine how hot the environment must be for the fi rst reaction of the CNO cycle to occur. (Hint: First fi nd the threshold kinetic energy for the proton and the Coulomb barrier. After determining the kinetic energy, determine the temperature.)

One of the possibilities for producing energy in a star after the hydrogen has burned to helium is 3 S 12C (that is, three alpha particles react to form 12C). How much energy is released in this process?

For a thermal neutron (300 K), fi nd its (a) energy, (b) speed, and (c) de Broglie wavelength.

To determine the wear of an automobile engine, a steel compression ring is placed in a nuclear reactor, where it becomes neutron activated because of the formation of 59Fe(t1/2 44.5 days, ). The activity of the ring when placed in the engine is 4.0  105 Bq. Over the next 60 days, the car is driven 100,000 km on a test track. The engine oil is extracted, and the activity rate of the oil is measured to be 512 /min. What fraction of the ring was worn off during the test?

(a) Why does a 99mTc generator need to be shipped once a week to hospitals? (b) What is the activity of a 1011-Bq 99mTc generator source 9 days after it was produced? (c) If the activity is 0.9  1011 Bq on Monday morning when it arrives, what will be the activity at the same time on Friday morning, the last day of the working week?

The Los Angeles County Police want to use neutron activation analysis to look for a tiny residue of barium in gunpowder. The suspected residue is placed in a nuclear reactor, where it is activated by the neutron fl ux. Natural barium contains 71.7% 138Ba. The  emitter 139Ba is produced in the 138Ba(n, )139Ba reaction. The half-life of 139Ba is 83.1 min. 139Ba beta decays to 139La, 72% going to the ground state and 27% going to the fi rst excited state at 0.166 MeV. Scientists think they need a count rate for the 166-keV  ray (decay to the ground state) of at least 1000 Bq 30 min after the residue is removed from the reactor in order to make a positive identifi cation of barium. (a) How many 139Ba nuclei must be present at the end of the activation? (Remember the decay and fraction going to the fi rst excited state.) (b) How many grams of 139Ba must be produced? If the original amount of barium was 0.01 g, what fraction of the 138Ba was activated?

A 5.0  105 Bq 241Am alpha source is used in a smoke alarm. The device is arranged so that 15% of the decay alphas are detected. (a) What current is detected? (b) If the introduction of smoke causes a 10% change in the intensity of the alpha particles, what sensitivity must the electronic circuit have to cause an alarm?

Consider a spacecrafts power source consisting of 210Po, which emits a 5.3-MeV alpha particle, t1/2 138 days. (a) How many kg of 210Po are needed to initially produce a power source of 5.0 kW? (b) If the power source must produce 7.0 kW after 2.0 years in space, how much 210Po is needed?

A hospital has a 3.0  1014 Bq 60Co source for cancer therapy. What is the rate of  rays incident on a patient of area 0.30 m2 located 4.0 m from the source? 60Co emits a 1.1- and a 1.3-MeV  ray for each disintegration.

Rework Example 13.10 if the neutron is to probe the diameter of a 238U nucleus. Could neutrons from a nuclear reactor be used? Explain.

Assume that a 10.0-kg sample of 239Pu is used to produce electrical power from its decay. If your device is 60% effi cient in producing electrical power, how much power can be produced?

We mentioned several superheavy elements that had been observed but not yet confi rmed or offi cially approved by the International Union of Pure and Applied Chemistry (IUPAC). (a) List those elements. (b) Research and discuss their status: Have they been confi rmed? Has IUPAC approved them?

An infl ated catheter is used in balloon angioplasty to open up arteries that are occluded with plaque formation. Stents are placed in the arteries to support the arterial wall. Radioisotopes have been incorporated into the stents to inhibit the reclosing of the artery (called restenosis). Almost a half million patients in the United States receive intravascular therapy each year. (a) Research the current status of using radioisotopes in this process. How many patients are treated in the United States each year using it? (b) Which radioisotopes are primarily used? Are they beta or gamma emitters? Why would one be favored over the other?

In a nuclear reactor, the effective cross section for thermal neutrons in uranium is the weighted average of the cross sections for the 235 and 238 isotopes present. The thermal neutron cross section is zero for 238U and 580 barns for 235U. Find the effective cross section for thermal neutrons in a reactor that contains (a) natural uranium and (b) uranium enriched to 2.0% 235U.

A thermal neutron induces fi ssion in a 235U nucleus. One of the fi ssion products is 132Sn, and three free neutrons are released. (a) Write the entire fi ssion reaction. (b) How much energy is released?

Compare the following: (a) total atomic binding energy of 1.0 kg of hydrogen atoms, (b) nuclear binding energy of 1.0 kg of deuterons, and (c) annihilation energy of 0.50 kg of protons with 0.50 kg of antiprotons. (d) Comment on the relative orders of magnitudes of the energies you computed in (a), (b), and (c).

One method used to determine unknown atomic masses consists of precisely measuring the kinetic energies of the particles involved in a nuclear reaction and using known atomic masses. The mass of 34Si is determined by the 30Si(18O, 14O)34Si reaction initiated by 100-MeV 18O particles. The outgoing particles have 86.63 MeV of energy, which can be determined only by measuring the 14O energy and using the conserva- tion of momentum and energy. (a) What is the Q value of the reaction? (b) What is the mass of 34Si assuming the other three masses involved are known (see Appendix 8)?

90Sr is one of the most deadly products of nuclear fi ssion. Assume that 4% of the fi ssion fragment yield from a 235U atomic bomb is 90Sr. In a nuclear interchange on the planet Inhospitable, 1000 atomic bombs, each corresponding to the fi ssion of 100 kg of 235U, are detonated. (a) How many atoms of 90Sr are released? (b) Assuming the 90Sr is spread evenly over the planet of diameter 12,000 km, what is the resulting activity for each m2? The half-life of 90Sr is 28.8 y.

Assume a temperature of 2.0  108 K in a controlled thermonuclear reactor. (a) Calculate the most probable energy of deuterons at this temperature. (b) Use the Maxwell-Boltzmann distribution from Chapter 9 to determine the fraction of deuterons having an energy that is 2, 5, and 10 times the most probable energy.

A PuBe source has a neutron activity of 1.6  105 Bq. The neutrons are produced by the 9Be(, n)12C reaction with an effective cross section of 90 mb and thickness of 3.2 cm. (a) What is the probability of an incident alpha particle interacting with a 9Be nucleus? (b) What must be the rate of alpha particles incident on 9Be? (c) What must be the amount of mass of the 239Pu producing the alpha particles?

A typical person of mass 65 kg contains 0.35% potassium, by weight. Of the potassium, 0.012% is 40K, an unstable nucleus that decays through  (89.3%) and electron capture (10.7%) with a t1/2 1.28  109y. What is the 40K activity due to  decay in a typical persons body?

The yields of nuclear fi ssion bomb weapons are measured in terms of the equivalent amount of energy produced by 1 kiloton of TNT (1 kiloton TNT 4.2  1012J). The bomb dropped on Hiroshima, Japan, on August 6, 1945, was believed to yield 1520 kilotons. Assume that the bomb yield was 15 kilotons of TNT and that each fi ssion reaction yields 200 MeV. What is the minimum mass of 235U that this bomb (called Little Boy) could have contained?

The rate of spontaneous fi ssion in 238U is 6.7 decays per second for each kg of uranium present. The remaining decays of the 238U nuclide are alpha decays. What is the probability that decay will occur by spontaneous fi ssion?