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- The half-life for the process 238U→206Pb is 4.5 * 10^9 yr. A mineral sample contains 75.0 mg of 238U and 18.0 mg of 206Pb. What is the age of the mineral?
Problem 44
- An analytical laboratory balance typically measures mass to the nearest 0.1 mg. What energy change would accompany the loss of 0.1 mg in mass, according to Einstein's mass-energy equivalence principle (E=mc²)?
Problem 45
Problem 46
The thermite reaction, Fe2O31s2 + 2 Al1s2 ¡2 Fe1s2 + Al2O31s2, H = -851.5 kJ>mol, is one of the most exothermic reactions known. Because the heat released is sufficient to melt the iron product, the reaction is used to weld metal under the ocean. How much heat is released per mole of Al2O3 produced? How does this amount of thermal energy compare with the energy released when 2 mol of protons and 2 mol of neutrons combine to form 1 mol of alpha particles?
Problem 47
How much energy must be supplied to break a single aluminum-27 nucleus into separated protons and neutrons if an aluminum-27 atom has a mass of 26.9815386 amu? How much energy is required for 100.0 g of aluminum-27? (The mass of an electron is given on the inside back cover.)
- How much energy must be supplied to break a single ²¹Ne nucleus into separated protons and neutrons if the nucleus has a mass of 20.98846 amu? What is the nuclear binding energy for 1 mol of ²¹Ne?
Problem 48
Problem 49c
The atomic masses of hydrogen-2 (deuterium), helium-4, and lithium-6 are 2.014102 amu, 4.002602 amu, and 6.0151228 amu, respectively. For each isotope, calculate
(c) the nuclear binding energy per nucleon.
Problem 50a
The atomic masses of nitrogen-14, titanium-48, and xenon-129 are 13.999234 amu, 47.935878 amu, and 128.904779 amu, respectively. For each isotope, calculate (a) the nuclear mass.
- The energy from solar radiation falling on Earth is 1.07 * 10^16 kJ/min. (a) How much loss of mass from the Sun occurs in one day from just the energy falling on Earth? (b) If the energy released in the reaction 235U + 10n → 14156Ba + 9236Kr + 310n (235U nuclear mass, 234.9935 amu; 141Ba nuclear mass, 140.8833 amu; 92Kr nuclear mass, 91.9021 amu) is taken as typical of that occurring in a nuclear reactor, what mass of uranium-235 is required to equal 0.10% of the solar energy that falls on Earth in 1.0 day?
Problem 51
Problem 52
Based on the following atomic mass values: 1H, 1.00782 amu; 2H, 2.01410 amu; 3H, 3.01605 amu; 3He, 3.01603 amu; 4He, 4.00260 amu—and the mass of the neutron given in the text, calculate the energy released per mole in each of the following nuclear reactions, all of which are possibilities for a controlled fusion process:
(a) 21H + 31H → 42He + 10n
(b) 21H + 21H → 32He + 10n
(c) 21H + 32He → 42He + 11H
- The isotope 6228Ni has the largest binding energy per nucleon of any isotope. Calculate this value from the atomic mass of nickel-62 (61.928345 amu) and compare it with the value given for iron-56 in Table 21.7.
Problem 54
Problem 55b
Iodine-131 is a convenient radioisotope to monitor thyroid activity in humans. It is a beta emitter with a half-life of 8.02 days. The thyroid is the only gland in the body that uses iodine. A person undergoing a test of thyroid activity drinks a solution of NaI, in which only a small fraction of the iodide is radioactive. b. A normal thyroid will take up about 12% of the ingested iodide in a few hours. How long will it take for the radioactive iodide taken up and held by the thyroid to decay to 0.01% of the original amount?
Problem 56
Why is it important that radioisotopes used as diagnostic tools in nuclear medicine produce gamma radiation when they decay? Why are alpha emitters not used as diagnostic tools?
- (a) Which of the following are required characteristics of an isotope to be used as a fuel in a nuclear power reactor? (i) It must emit gamma radiation. (ii) On decay, it must release two or more neutrons. (iii) It must have a half-life of less than one hour. (iv) It must undergo fission upon the absorption of a neutron. (b) What is the most common fissionable isotope in a commercial nuclear power reactor?
Problem 57
- Which of the following statements about the uranium used in nuclear reactors is or are true? (i) Natural uranium has too little 235U to be used as a fuel. (ii) 238U cannot be used as a fuel because it forms a supercritical mass too easily. (iii) To be used as fuel, uranium must be enriched so that it is more than 50% 235U in composition. (iv) The neutron-induced fission of 235U releases more neutrons per nucleus than the fission of 238U.
Problem 58
- What is the function of the control rods in a nuclear reactor? What substances are used to construct the control rods? Why are these substances chosen?
Problem 59
Problem 60c
(c) What other substances are used as a moderator in nuclear reactor designs?
Problem 61
Complete and balance the nuclear equations for the following fission or fusion reactions:
(a) 21H + 21H → 32He + _
(b) 23992U + 10n¡ → 13351Sb + 9841Nb + _ 10n
Problem 62
Complete and balance the nuclear equations for the following fission reactions:
(a) 23592U + 10n → 16062Sm + 7230Zn + _ 10n
(b) 23994Pu + 10n → 14458Ce + _ + 2 10n
Problem 64b
The spent fuel elements from a fission reactor are much more intensely radioactive than the original fuel elements. (b) Given that only two or three neutrons are released per fission event and knowing that the nucleus undergoing fission has a neutron-to-proton ratio characteristic of a heavy nucleus, what sorts of decay would you expect to be dominant among the fission products?
- Which type or types of nuclear reactors have these characteristics? (a) Does not use a secondary coolant (b) Creates more fissionable material than it consumes (c) Uses a gas, such as He or CO2, as the primary coolant.
Problem 65
- Which type or types of nuclear reactors have these characteristics? (a) Can use natural uranium as a fuel (b) Does not use a moderator (c) Can be refueled without shutting down
Problem 66
Problem 68
Which are classified as ionizing radiation: X rays, alpha particles, microwaves from a cell phone, and gamma rays?
Problem 69a
A laboratory rat is exposed to an alpha-radiation source whose activity is 14.3 mCi. (a) What is the activity of the radiation in disintegrations per second? In becquerels?
Problem 69b
A laboratory rat is exposed to an alpha-radiation source whose activity is 14.3 mCi. (b) The rat has a mass of 385 g and is exposed to the radiation for 14.0 s, absorbing 35% of the emitted alpha particles, each having an energy of 9.12 * 10-13 J. Calculate the absorbed dose in millirads and grays.
Problem 71a
The table provided gives the number of protons (p) and neutrons (n) for four isotopes, identified only as (i)–(iv). a. Write the symbol for each of the isotopes.
Problem 72
Radon-222 decays to a stable nucleus by a series of three alpha emissions and two beta emissions. What is the stable nucleus that is formed?
- Equation 21.28 is the nuclear reaction responsible for much of the helium-4 production in our Sun. How much energy is released in this reaction?
Problem 73
Problem 74a
Chlorine has two stable nuclides, 35Cl and 37Cl. In contrast, 36Cl is a radioactive nuclide that decays by beta emission. (a) What is the product of decay of 36Cl?
Problem 74b
Chlorine has two stable nuclides, 35Cl and 37Cl. In contrast, 36Cl is a radioactive nuclide that decays by beta emission. (b) Based on the empirical rules about nuclear stability, explain why the nucleus of 36Cl is less stable than either 35Cl or 37Cl.
Problem 76
Nuclear scientists have synthesized approximately 1600 nuclei not known in nature. More might be discovered with heavy-ion bombardment using high-energy particle accelerators. Complete and balance the following reactions, which involve heavy-ion bombardments:
(a) 63Li + 5628Ni → ?
(b) 4020Ca + 24896Cm → 14762Sm + ?
(c) 8838Sr + 8436Kr → 11646Pd + ?
(d) 4020Ca + 23892U → 7030Zn + 4 10n + 2 ?