Solved: Each of the following reactions is forbidden.

In the fi rst atomic bomb, a test carried out in New Mexico called Trinity, the energy released was equivalent to approximately 17 kilotons of TNT. Estimate the mass converted into energy in this event. Note: One ton of TNT has an energy equivalent of 4.0 _ 109 J. (a) 20 kilotons (b) 0.1 kilotons (c) 1 kg (d) 1 g (e) 1 mg

When a neutron decays to a proton, electron, and neutrino, how much energy is released? (Neglect the energy of the neutrino.) (a) 0.784 MeV (b) 0.352 MeV (c) 4.31 MeV (d) 2.22 MeV (e) 1.70 MeV

Why cant a proton decay into a positron and a neutrino? (a) Charge conservation is violated. (b) Baryon number conservation is violated. (c) Conservation of energy is violated. (d) Lepton number conservation is violated. (e) Conservation of strangeness is violated.

The __ particle is a baryon with spin 32 . Which of the following is true of this particle? (a) It has three possible spin states in a magnetic fi eld. (b) It has four possible spin states. (c) It has three times the charge of a spin-12 particle. (d) It has three times the mass of a spin-12 particle. (e) It cant decay to a spin-12 particle.

When an electron and a positron meet at low speed in empty space, they annihilate each other to produce two 0.511-MeV gamma rays. What law would be violated if they produced one gamma ray with an energy of 1.02 MeV? (a) conservation of energy (b) conservation of momentum (c) conservation of charge (d) conservation of baryon number (e) conservation of electronlepton number.

If the moderator were suddenly removed from a nuclear reactor in an electric generating station, what go supercritical, and a runaway reaction would occur. (b) The nuclear reactions would proceed as before, but the reactor would overheat. (c) The reactor would become subcritical, and the rate at which reactions occurred would diminish. (d) No change would occur in the reactors operation. (e) The rate at which reactions occurred would increase, but the reactor wouldnt go supercritical.

Which particle is most likely to be captured by a 235U nucleus and cause it to undergo fi ssion? (a) an energetic proton (b) an energetic neutron (c) a slow- moving alpha particle (d) a slow-moving neutron (e) a fastmoving electron

In a fi ssion reaction a 235U nucleus captures a neutron, splitting the nucleus into 137I and 96Y. How many free neutrons result from this process? (a) 1 (b) 2 (c) 3 (d) 4 (e) 5

Which of the following particle reactions cant occur? (a) p 1 n S p 1 p 1 p (b) n S p 1 e2 1 ne (c) m2 S e2 1 ne 1 nm (d) p2 S m2 1 nm (e) t2 S e2 1 nt 1 ne

Which of the following particle reactions cant occur? (a) p 1 p S 2g (b) p0 1 n S K0 s 1 S0 (c) g 1 p S n 1 p0 (d) V2 S 2J2 1 e1 1 ne (e) p1 1 p S K1 1 S1

If high-energy electrons with de Broglie wavelengths smaller than the size of the nucleus are scattered from nuclei, the behavior of the electrons is consistent with scattering from very massive structures much smaller in size than the nucleus, namely, quarks. How is this behavior similar to a classic experiment that detected small structures in an atom?

What factors make a fusion reaction diffi cult to achieve?

Doubly charged baryons are known to exist. Why are there no doubly charged mesons?

Why would a fusion reactor produce less radioactive waste than a fi ssion reactor?

Why didnt atoms exist until hundreds of thousands of years after the Big Bang?

Particles known as resonances have very short half-lives, on the order of 10_23 s. Would you guess that they are hadrons or leptons?

Describe the quark model of hadrons, including the properties of quarks.

In the theory of quantum chromodynamics, quarks come in three colors. How would you justify the statement, All baryons and mesons are colorless?

Describe the properties of baryons and mesons and the important differences between them.

Identify the particle decays in Table 30.2 that occur by the electromagnetic interaction. Justify your answer.

Kaons all decay into fi nal states that contain no protons or neutrons. What is the baryon number of kaons?

Why is a neutron stable inside the nucleus? (In free space the neutron decays in 900 s.)

Burning 1 metric ton (1 000 kg) of coal can yield an energy of 3.30 _ 1010 J. Fission of one nucleus of uranium- 235 yields an average energy of approximately 208 MeV. What mass of uranium produces the same energy as 1 metric ton of coal?

Find the energy released in the fi ssion reaction n 1 235 92U S 98 40Zr 1 135 52Te 1 3n The atomic masses of the fi ssion products are 97.912 0 u for 9 40 8Zr and 134.908 7 u for 13 52 5Te.

Find the energy released in the fi ssion reaction 10 n 1 235 92U S 88 38Sr 1 136 54Xe 1 1210 n

The radioactive isotope strontium-90 is a particularly dangerous fi ssion product of 235U because it substitutes for calcium in bones. What other direct fi ssion products would accompany it in the neutron-induced fi ssion of 235U? Note: This reaction may release two, three, or four free neutrons.

Assume ordinary soil contains natural uranium in amounts of 1 part per million by mass. (a) How much uranium is in the top 1.00 m of soil on a 1-acre (43 560-ft2) plot of ground, assuming the specifi c gravity of soil is 4.00? (b) How much of the isotope 235U, appropriate for nuclear reactor fuel, is in this soil? Hint: See Appendix B for the percent abundance of 23 92 5U.

A typical nuclear fi ssion power plant produces about 1.00 GW of electrical power. Assume the plant has an overall effi ciency of 40.0% and each fi ssion produces 200 MeV of thermal energy. Calculate the mass of 235U consumed each day.

Suppose the water exerts an average frictional drag of 1.0 _ 105 N on a nuclear-powered ship. How far can the ship travel per kilogram of fuel if the fuel consists of enriched uranium containing 1.7% of the fi ssionable isotope 235U and the ships engine has an effi ciency of 20%? Assume 208 MeV is released per fi ssion event.

According to one estimate, there are 4.4 _ 106 metric tons of world uranium reserves extractable at $130/kg or less. About 0.7% of naturally occurring uranium is the fi ssionable isotope 235U. (a) Calculate the mass of 235U in this reserve in grams. (b) Find the number of moles of 235U and convert to a number of atoms. (c) Assuming 208 MeV is obtained from each reaction and all this energy is captured, calculate the total energy that can be extracted from the reserve in joules. (d) Assuming world power consumption to be constant at 1.5 _ 1013 J/s, how many years could the uranium reserves provide for all the worlds energy needs? (e) What conclusion can be drawn?

An all-electric home uses approximately 2 000 kWh of electric energy per month. How much uranium-235 would be required to provide this house with its energy needs for one year? Assume 100% conversion effi ciency and 208 MeV released per fi ssion.

Seawater contains 3 mg of uranium per cubic meter. (a) Given that the average ocean depth is about 4 km and water covers two-thirds of Earths surface, estimate the amount of uranium dissolved in the ocean. (b) Estimate how long this uranium could supply the worlds energy needs at the current usage of 1.5 _ 1013 J/s. (c) Where does the dissolved uranium come from? Is it a renewable energy source? Can uranium from the ocean satisfy our energy requirements? Discuss. Note: Breeder reactors increase the effi ciency of nuclear fuel use by approximately two orders of magnitude.

When a star has exhausted its hydrogen fuel, it may fuse other nuclear fuels. At temperatures above 1.0 _ 108 K, helium fusion can occur. Write the equations for the following processes. (a) Two alpha particles fuse to produce a nucleus A and a gamma ray. What is nucleus A? (b) Nucleus A absorbs an alpha particle to produce a nucleus B and a gamma ray. What is nucleus B? (c) Find the total energy released in the reactions given in parts (a) and (b). Note: The mass of 8 4Be _ 8.005 305 u.

Find the energy released in the fusion reaction 1 1H _ 2 1H 3 2He _ _

If an all-electric home uses approximately 2 000 kWh of electric energy per month, how many fusion events described by the reaction 2 1H _ 3 1H 4 2He _ 1 0n would be required to keep this home running for one year?

Another series of nuclear reactions that can produce energy in the interior of stars is the cycle described below. This cycle is most effi cient when the central temperature in a star is above 1.6 _ 107 K. Because the temperature at the center of the Sun is only 1.5 _ 107 K, the following cycle produces less than 10% of the Suns energy. (a) A high-energy proton is absorbed by 12C. Another nucleus, A, is produced in the reaction, along with a gamma ray. Identify nucleus A. (b) Nucleus A decays through positron emission to form nucleus B. Identify nucleus B. (c) Nucleus B absorbs a proton to produce nucleus C and a gamma ray. Identify nucleus C. (d) Nucleus C absorbs a proton to produce nucleus D and a gamma ray. Identify nucleus D. (e) Nucleus D decays through positron emission to produce nucleus E. Identify nucleus E. (f) Nucleus E absorbs a proton to produce nucleus F plus an alpha particle. What is nucleus F ? Note: If nucleus F is not 12C that is, the nucleus you started withyou have made an error and should review the sequence of events.

Assume a deuteron and a triton are at rest when they fuse according to the reaction 21 H 1 31 H S 42 He 1 10 n 1 17.6 MeV Neglecting relativistic corrections, determine the kinetic energy acquired by the neutron.

A reaction that has been considered as a source of energy is the absorption of a proton by a boron-11 nucleus to produce three alpha particles: 11 H 1 11 5B S 3142 He2 This reaction is an attractive possibility because boron is easily obtained from Earths crust. A disadvantage is that the protons and boron nuclei must have large kinetic energies for the reaction to take place. This requirement contrasts to the initiation of uranium fi ssion by slow neutrons. (a) How much energy is released in each reaction? (b) Why must the reactant particles have high kinetic energies?

A photon produces a protonantiproton pair according to the reaction g p _ p. What is the minimum possible frequency of the photon? What is its wavelength?

A photon with an energy of 2.09 GeV creates a proton antiproton pair in which the proton has a kinetic energy of 95.0 MeV. What is the kinetic energy of the antiproton?

A neutral pion at rest decays into two photons according to p0 S g 1 g Find the energy, momentum, and frequency of each photon.

For the following two reactions, the fi rst may occur but the second cannot. Explain. K0 p_ _ p_ (can occur) 0 p_ _ p_ (cannot occur)

Each of the following reactions is forbidden. Determine a conservation law that is violated for each reaction. (a) p _ p m_ _ e_ (b) p_ _ p p _ p_ (c) p _ p p _ p_ (d) p _ p p _ p _ n (e) g _ p n _ p0

Determine the type of neutrino or antineutrino involved in each of the following processes. (a) p_ p0 _ e_ _ ? (b) ? _ p m_ _ p _ p_ (c) 0 p _ m_ _ ? (d) t_ m_ _ ? _ ?

Identify the unknown particle on the left side of the reaction ? _ p n _ m_

(a) Show that baryon number and charge are conserved in the following reactions of a pion with a proton: (1) p1 1 p S K1 1 S1 (2) p1 1 p S p1 1 S1 (b) The fi rst reaction is observed, but the second never occurs. Explain these observations. (c) Could the second reaction happen if it created a third particle? If so, which particles in Table 30.2 might make it possible? Would the reaction require less energy or more energy than the reaction of Equation (1)? Why?

Identify the conserved quantities in the following processes. (a) __ 0 _ m_ _ _m (b) K0 2p0 (c) K_ _ p 0 _ n (d) 0 0 _ _ (e) e_ _ e_ m_ _ m_ (f) p _ n L0 _ _

The quark composition of the proton is uud, whereas that of the neutron is udd. Show that the charge, baryon number, and strangeness of these particles equal the sums of these numbers for their quark constituents.

Find the number of electrons, and of each species of quark, in 1 L of water.

The quark compositions of the K0 and 0 particles are ds and uds, respectively. Show that the charge, baryon number, and strangeness of these particles equal the sums of these numbers for their quark constituents.

Identify the particles corresponding to the quark states (a) suu, (b) ud, (c) sd, and (d) ssd.

What is the electrical charge of the baryons with the quark compositions (a) uud and (b) udd? What are these baryons called? ADDITIONAL PROBLEMS

A 0 particle traveling through matter strikes a proton and a _, and a gamma ray, as well as a third particle, emerges. Use the quark model of each to determine the identity of the third particle.

Name at least one conservation law that prevents each of the following reactions from occurring. (a) p_ _ p _ _ p0 (b) m_ p_ _ _e (c) p p_ _ p_ _ p_

Find the energy released in the fusion reaction H _ 3 2H 4 2He _ e_ _ _

Occasionally, high-energy muons collide with electrons and produce two neutrinos according to the reaction m_ _ e_ 2n. What kind of neutrinos are they?

Each of the following decays is forbidden. For each process, determine a conservation law that is violated. (a) m_ e_ _ _ (b) n p _ e_ _ _e (c) 0 p _ p0 (d) p e_ _ p0 (e) _0 n _ p0

Two protons approach each other with 70.4 MeV of kinetic energy and engage in a reaction in which a proton and a positive pion emerge at rest. What third particle, obviously uncharged and therefore diffi cult to detect, must have been created?

A 2.0-MeV neutron is emitted in a fi ssion reactor. If it loses one-half its kinetic energy in each collision with a moderator atom, how many collisions must it undergo to reach an energy associated with a gas at a room temperature of 20.0C?

The fusion reaction 2 1D _ 2 1D 3 2He _ 1 0n releases 3.27 MeV of energy. If a fusion reactor operates strictly on the basis of this reaction, (a) how much energy could it produce by completely reacting 1 kg of deuterium? (b) At eight cents a kilowatt-hour, how much would the produced energy be worth? (c) Heavy water (D2O) costs about $300 per kilogram. Neglecting the cost of separating the deuterium from the oxygen via electrolysis, how much does 1 kg of deuterium cost, if derived from D2O? (d) Would it be cost-effective to use deuterium as a source of energy? Discuss, assuming the cost of energy production is nine-tenths the value of energy produced.

(a) Show that about 1.0 _ 1010 J would be released by the fusion of the deuterons in 1.0 gal of water. Note that 1 of every 6 500 hydrogen atoms is a deuteron. (b) The average energy consumption rate of a person living in the United States is about 1.0 _ 104 J/s (an average power of 10 kW). At this rate, how long would the energy needs of one person be supplied by the fusion of the deuterons in 1.0 gal of water? Assume the energy released per deuteron is 1.64 MeV.

Calculate the mass of 235U required to provide the total energy requirements of a nuclear submarine during a 100-day patrol, assuming a constant power demand of 100 000 kW, a conversion effi ciency of 30%, and an average energy released per fi ssion of 208 MeV.

A p-meson at rest decays according to p2 S m2 1 nm What is the energy carried off by the neutrino? Assume the neutrino has no mass and moves off with the speed of light. Take mpc 2 _ 139.6 MeV and mmc 2 _ 105.7 MeV. Note : Use relativity; see Equation 26.10.

The reaction p_ _ p _0 _ 0 occurs with high probability, whereas the reaction p_ _ p _0 _ n never occurs. Analyze these reactions at the quark level. Show that the fi rst reaction conserves the total number of each type of quark and the second reaction does not.

The Sun radiates energy at the rate of 3.85 _ 1026 W. Suppose the net reaction 4p _ 2e_ a _ 2ne _ 6g accounts for all the energy released. Calculate the number of protons fused per second. Note: recall that an alpha particle is a helium-4 nucleus.