Why would a fusion reactor produce less radioactive waste than a fission reactor?
> Name at least one conservation law that prevents each of the following reactions from occurring. (a) (b) (c)
> A ∑0 particle traveling through matter strikes a proton. A ∑+, a gamma ray, as well as a third particle, emerge. Use the quark model of each to determine the identity of the third particle.
> What is the electrical charge of the baryons with the quark compositions (a) ūūd- and (b) ūd-d-? What are these baryons called?
> Identify the particles corresponding to the quark states (a) suu, (b) ūd, (c) s-d, and (d) ssd.
> The quark compositions of the K0 and Λ0 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.
> In the theory of quantum chromodynamics, quarks come in three colors. How would you justify the statement, “All baryons and mesons are colorless”?
> Find the number of electrons, and of each species of quark, in 1.00 L of water.
> 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.
> Determine whether or not strangeness is conserved in the following decays and reactions. (a) Λ0 ( p + π- (b) π- + p ( Λ0 + K0 (c) (d) (e) (f)
> (a) Show that baryon number and charge are conserved in the following reactions of a pion with a proton: (b) The first reaction is observed, but the second never occurs. Explain these observations. (c) Could the second reaction happen if it created a th
> If the average energy released in a fission event is 208 MeV, find the total number of fission events required to operate a 100. - W light-bulb for 1.0 h.
> Which of the following processes are allowed by the strong interaction, the electromagnetic interaction, the weak interaction, or no interaction at all? (a) (b) (c) (d) (e)
> Determine which of the reactions below can occur. For those that cannot occur, determine the conservation law (or laws) that each violates. (a) (b) (c) (d) (e)
> Each of the following reactions is forbidden. Determine a conservation law that is violated for each reaction. (a) (b) (c) (d) (e)
> For the following two reactions, the first may occur but the second cannot. Explain. K0 ( π+ + π- (can occur) Λ0 ( π+ + π- (cannot occur)
> (a) Determine the muon - lepton number in the reaction μ- ( e- + v-e + vμ. (b) Determine the value of strangeness in the reaction π- + p ( Λ0 + K0.
> A radioactive sample has an activity R. For each of the following changes, indicate whether the activity would increase, decrease, or remain unchanged. Indicate your answers with I, D, or U. (a) The number of radioactive nuclei in the sample is doubled.
> (a) Determine the baryon number of the reaction p + p- ( 2(. Determine (b) The baryon number and (c) The electron - lepton number of the reaction Ω- ( Λ0 + K-.
> A neutral pion at rest decays into two photons according to π0 ( ( + ( Find the energy, momentum, and frequency of each photon.
> 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 photon produces a proton – antiproton pair according to the reaction ( ( p + p-. What is the minimum possible frequency of the photon? What is its wavelength?
> 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: 11H + 115B ( 3(24He) This reaction is an attractive possibility because boron is easily obtained from Earth’
> A typical uranium - 234 fission event releases 208 MeV of energy. Determine (a) The energy released per event in joules and (b) The change in mass during the event.
> Assume a deuteron and a triton are at rest when they fuse according to the reaction 12H + 13H ( 24He + 01n + 17.6 MeV Neglecting relativistic corrections, determine the kinetic energy acquired by the neutron.
> Another series of nuclear reactions that can produce energy in the interior of stars is the cycle described below. This cycle is most efficient when the central temperature in a star is above 1.6 x 107 K. Because the temperature at the center of the Sun
> Find the energy released in the fusion reaction 12H + 12H ( 13H + 11H
> Find the energy released in the fusion reaction 11H + 12H ( 23He + (
> Particles known as resonances have very short half - lives, on the order of 10-23s. Would you guess that they are hadrons or leptons? Explain.
> When a star has exhausted its hydrogen fuel, it may fuse other nuclear fuels. At temperatures above 1.0 x 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
> The proton – proton cycle responsible for the Sun’s 3.84 x 1026 W power output yields about 26.7 MeV of energy for every four protons that are fused into a helium nucleus. Determine (a) The energy in joules released during each proton – proton cycle fusi
> Suppose a deuterium – deuterium fusion reactor is designed to have a plasma confinement time of 1.50 s. Determine the minimum ion density per cubic cm required to obtain a net power output from the reactor.
> 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 Earth’s surface, estimate the amount of uranium dissolved in the ocean. (b) Estimate how long this uranium could supp
> An all - electric home uses approximately 2.00 x 103 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 efficiency and 208 MeV released per fission.
> According to one estimate, there are 4.4 x 106 metric tons of world uranium reserves extractable at $130/kg or less. About 0.70% of naturally occurring uranium is the fissionable isotope 235U. (a) Calculate the mass of 235U in this reserve in grams. (b)
> Natural uranium ore contains about 0.720% of the fissile uranium - 235 isotope. Suppose a sample of uranium ore contains 2.50 x 1028 uranium nuclei. Determine the number of uranium - 235 nuclei in the sample.
> A piece of charcoal used for cooking is found at the remains of an ancient campsite. A 1.00-kg sample of carbon from the wood has an activity equal to 5.00 x 102 decays per minute. Find the age of the charcoal. Hint: Living material has an activity equal
> After how many half-lives will (a) 10.0%, (b) 5.00%, and (c) 1.00% of a radioactive sample remain?
> A by-product of some fission reactors is the isotope 23994Pu, which is an alpha emitter with a half-life of 24000 years: Consider a sample of 1.0 kg of pure 23994Pu at t = 0. Calculate (a) The number of 23994Pu nuclei present at t = 0 and (b) The initia
> Explain the main differences between alpha, beta, and gamma rays.
> The theory of nuclear astrophysics is that all the heavy elements like uranium are formed in the interior of massive stars. These stars eventually explode, releasing the elements into space. If we assume that at the time of explosion there were equal amo
> After the sudden release of radioactivity from the Chernobyl nuclear reactor accident in 1986, the radioactivity of milk in Poland rose to 2.00 x 103 Bq/L due to iodine - 131, with a half - life of 8.04 days. Radioactive iodine is particularly hazardous
> A medical laboratory stock solution is prepared with an initial activity due to 24Na of 2.5 mCi/mL, and 10.0 mL of the stock solution is diluted at t0 = 0 to a working solution whose total volume is 250 mL. After 48 h, a 5.0 - mL sample of the working so
> Many radioisotopes have important industrial, medical, and research applications. One of these is 60Co, which has a half - life of 5.2 years and decays by the emission of a beta particle (energy 0.31 MeV) and two gamma photons (energies 1.17 MeV and 1.33
> In a piece of rock from the Moon, the 87Rb content is assayed to be 1.82 x 1010 atoms per gram of material and the 87Sr content is found to be 1.07 x 109 atoms per gram. (The relevant decay is 87Rb ( 87Sr + e-. The half - life of the decay is 4.8 x 1010
> The 14C isotope undergoes beta decay according to the process given by Equation 29.15. Find the Q value for this process. Equation 29.15:
> A 200.0 - mCi sample of a radioactive isotope is purchased by a medical supply house. If the sample has a half - life of 14.0 days, how long will it keep before its activity is reduced to 20.0 mCi?
> Find the threshold energy that the incident neutron must have to produce the reaction: 10n + 24He ( 12H + 13H.
> A radioactive sample contains 3.50 μg of pure 11C, which has a half - life of 20.4 min. (a) How many moles of 11C are present initially? (b) Determine the number of nuclei present initially. What is the activity of the sample (c) Initially and (d) After
> A particular radioactive source produces 100. mrad of 2 - MeV gamma rays per hour at a distance of 1.0 m. (a) How long could a person stand at this distance before accumulating an intolerable dose of 1.0 rem? (b) Assuming the gamma radiation is emitted u
> A patient swallows a radiopharmaceutical tagged with phosphorus - 32 (1532P), a β- emitter with a half - life of 14.3 days. The average kinetic energy of the emitted electrons is 7.00 x 102 keV. If the initial activity of the sample is 1.31 MBq, determin
> An x - ray technician works 5 days per week, 50 weeks per year. Assume the technician takes an average of eight x - rays per day and receives a dose of 5.0 rem/yr as a result. (a) Estimate the dose in rem per x - ray taken. (b) How does this result compa
> A “clever” technician decides to heat some water for his coffee with an x - ray machine. If the machine produces 10. rad/s, how long will it take to raise the temperature of a cup of water by 50.8 C? Ignore heat losses during this time.
> A 200. - rad dose of radiation is administered to a patient in an effort to combat a cancerous growth. Assuming all the energy deposited is absorbed by the growth, (a) Calculate the amount of energy delivered per unit mass. (b) Assuming the growth has a
> A person whose mass is 75.0 kg is exposed to a whole - body dose of 25.0 rad. How many joules of energy are deposited in the person’s body?
> In terms of biological damage, how many rad of heavy ions are equivalent to 100 rad of x - rays?
> (a) Determine the product of the reaction 37Li + 24He ( ? + n. (b) What is the Q value of the reaction?
> Complete the following nuclear reactions: (a) ? + 147N ( 11H + 178O (b) 37Li + 11H ( 24He + ?
> Natural gold has only one isotope, 19779Au. If gold is bombarded with slow neutrons, e- particles are emitted. (a) Write the appropriate reaction equation. (b) Calculate the maximum energy of the emitted beta particles. The mass of 19880Hg is 197.96675 u
> Consider two reactions: (1) n + 12H ( 13H (2) 11H + 12H ( 23He (a) Compute the Q values for these reactions. Identify whether each reaction is exothermic or endothermic. (b) Which reaction results in more released energy? Why? (c) Assuming the difference
> Why do nearly all the naturally occurring isotopes lie above the N = Z line in Figure 29.3?
> (a) Suppose 105B is struck by an alpha particle, releasing a proton and a product nucleus in the reaction. What is the product nucleus? (b) An alpha particle and a product nucleus are produced when 136C is struck by a proton. What is the product nucleus?
> One method of producing neutrons for experimental use is to bombard 37Li with protons. The neutrons are emitted according to the reaction (a) Calculate the mass in atomic mass units of the particles on the left side of the equation. (b) Calculate the ma
> Identify the unknown particles X and X’ in the following nuclear reactions: (a) X + 24He ( 1224Mg + 01n (b) 23592U + 01n ( 3890Sr + X + 201n (c) 211H ( 12H + X + X’
> A beam of 6.61 - MeV protons is incident on a target of 1327Al. Those protons that collide with the target produce the reaction (1427Si has a mass of 26.986721 u.) Neglecting any recoil of the product nucleus, determine the kinetic energy of the emergin
> A wooden artifact is found in an ancient tomb. Its carbon - 14 (146C) activity is measured to be 60.0% of that in a fresh sample of wood from the same region. Assuming the same amount of 14C was initially present in the artifact as is now contained in th
> In the decay 23490Th ( AZRa + 42He, identify (a) The mass number (by balancing mass numbers) and (b) The atomic number (by balancing atomic numbers) of the Ra nucleus.
> A 3H (tritium) nucleus beta decays into 3He by creating an electron and an antineutrino according to the reaction Use Appendix B to determine the total energy released in this reaction.
> 6628Ni (mass = 65.9291 u) undergoes beta decay to 2966Cu (mass = 65.9289 u). (a) Write the complete decay formula for this process. (b) Find the maximum kinetic energy of the emerging electrons.
> Determine which of the following suggested decays can occur spontaneously: (a) 2040Ca ( e+ + 1940K (b) 14460Nd ( 24He + 14058Ce
> Find the energy released in the alpha decay of 23892U. The following mass value will be useful: 23490Th has a mass of 234.043583 u.
> 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 conservation law would be violated if they produced one gamma ray with an energy of 1.02 MeV? (a) Energy (b) Momentum
> The mass of 56Fe is 55.9349 u, and the mass of 56Co is 55.9399 u. Which isotope decays into the other and by what process?
> Complete the following radioactive decay formulas: (a) 512B ( ? + e- + v- (b) 23490Th ( 23088Ra + ? (c) ? ( 714N + e- + v-
> Identify the missing nuclides in the following decays: (a) 21283Bi ( ? + 24He (b) 3695Kr ( ? + e- + v- (c) ? ( 24He + 14058Ce
> On March 11, 2011, a magnitude 9.0 earthquake struck northwest Japan. The tsunami that followed left thousands of people dead and triggered a meltdown at the Fukushima Daiichi Nuclear Power Plant, releasing radioactive isotopes 137Cs and 134Cs, among oth
> Chromium’s radioactive isotope 51Cr has a half - life of 27.7 days and is often used in nuclear medicine as a diagnostic tracer in blood studies. Suppose a 51Cr sample has an activity of 2.00 μCi when it is placed on a storage shelf. (a) How many 51Cr nu
> A building has become accidentally contaminated with radioactivity. The longest - lived material in the building is strontium - 90. (The atomic mass of 3890Sr is 89.9077 u.) If the building initially contained 5.0 kg of this substance and the safe level
> A freshly prepared sample of a certain radioactive isotope has an activity of 10.0 mCi. After 4.00 h, the activity is 8.00 mCi. (a) Find the decay constant and half - life of the isotope. (b) How many atoms of the isotope were contained in the freshly pr
> After a plant or animal dies, its 14C content decreases with a half - life of 5730 yr. If an archaeologist finds an ancient fire pit containing partially consumed firewood and the 14C content of the wood is only 12.5% that of an equal carbon sample from
> After 2.00 days, the activity of a sample of an unknown type radioactive material has decreased to 84.2% of the initial activity. What is the half - life of this material?
> Tritium has a half - life of 12.33 years. What fraction of the nuclei in a tritium sample will remain (a) After 5.00 yr? (b) After 10.0 yr? (c) After 123.3 yr? (d) According to Equation 29.4a, an infinite amount of time is required for the entire sample
> A neutral atom is designated as 4018X. How many (a) Protons, (b) Neutrons, and (c) Electrons does the atom have? Answer: By convention, 1840X contains 18 protons and has a mass number of 40 so that 40 = Nprotons + Nneutrons and Nneutrons = 22. By c
> The half - life of 131I is 8.04 days. (a) Convert the half - life to seconds. (b) Calculate the decay constant for this isotope. (c) Convert 0.500 μCi to the SI unit the becquerel. (d) Find the number of 131I nuclei necessary to produce a sample with an
> A drug tagged with 4399Tc (half - life = 6.05 h) is prepared for a patient. If the original activity of the sample was 1.1 x 104 Bq, what is its activity after it has been on the shelf for 2.0 h?
> Radon gas has a half - life of 3.83 days. If 3.00 g of radon gas is present at time t = 0, what mass of radon will remain after 1.50 days have passed?
> Calculate the binding energy of the last neutron in the 2043Ca nucleus. Hint: You should compare the mass of 2043Ca with the mass of 2042Ca plus the mass of a neutron. The mass of 2042Ca = 41.958622 u, whereas the mass of 2043Ca = 42.958770 u.
> Two nuclei having the same mass number are known as isobars. (a) Calculate the difference in binding energy per nucleon for the isobars 1123Na and 1223Mg. (b) How do you account for this difference? (The mass of 1223Mg = 22.994127 u.)
> The peak of the stability curve occurs at 56Fe, which is why iron is prominent in the spectrum of the Sun and stars. Show that 56Fe has a higher binding energy per nucleon than its neighbors 55Mn and 59Co. Compare your results with Figure 29.4. Figure 2
> What fraction of a radioactive sample has decayed after three half - lives have elapsed? (a) 1/8 (b) 3/4 (c) 7/8 (d) None of these
> True or False: A radioactive atom always decays after two half - lives have elapsed.
> Why is a neutron stable inside the nucleus? (In free space, the neutron decays in 900 s.)
> Which of the following reactions cannot occur? (a) p + p- ( 2( (b) ( + p ( n + π0 (c) π0 + n ( K+ + ∑- (d) π+ + p ( K+ + ∑+
> Which of the following reactions cannot occur? (a) p + p ( p + p + p- (b) n ( p + e- + v-e (c) μ+ ( e+ + ve + v-μ (d) π- ( μ- + v-μ
> If the Q value of an endothermic reaction is -2.17 MeV, the minimum kinetic energy needed in the reactant nuclei for the reaction to occur must be (a) Equal to 2.17 MeV, (b) Greater than 2.17 MeV, (c) Less than 2.17 MeV, or (d) Exactly half of 2.17 MeV.
> Which of the following are possible reactions? (a) 01n + 23592U ( 14054Xe + 9438Sr + 2(01n) (b) 01n + 23592U ( 13250Sn + 10142Mo + 3(01n) (c) 01n + 23994Pu ( 12753I + 9341Nb + 3(01n)
> Suppose the decay constant of radioactive substance A is twice the decay constant of radioactive substance B. If substance B has a half - life of 4 h, what’s the half-life of substance A? (a) 8 h (b) 4 h (c) 2 h
> Find the nuclear radii of the following nuclides: (a) 12H (b) 2760Co (c) 19779Au (d) 23994Pu.
> The atomic mass of an oxygen atom is 15.999 u. Convert this mass to units of (a) Kilograms and (b) MeV/c2.
> A pair of nuclei for which Z1 = N2 and Z2 = N1 are called mirror isobars. (The atomic and neutron numbers are interchangeable.) Binding - energy measurements on such pairs can be used to obtain evidence of the charge independence of nuclear forces. Charg
> Calculate the binding energy per nucleon for (a) 2H, (b) 4He, (c) 56Fe, and (d) 238U.
