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- Each statement that follows refers to a comparison between two radioisotopes, A and X. Indicate whether each of the following statements is true or false. (a) If the half-life for A is shorter than the half-life for X, A has a larger decay rate constant.
문제 33
- It has been suggested that strontium-90 (generated by nuclear testing) deposited in the hot desert will undergo radioactive decay more rapidly because it will be exposed to much higher average temperatures. (a) Is this a reasonable suggestion? (Section 14.5) (b) Does the process of radioactive decay have an activation energy, like the Arrhenius behavior of many chemical reactions (Section 14.5)?
문제 34
문제 35
Some watch dials are coated with a phosphor, like ZnS, and a polymer in which some of the 1H atoms have been replaced by 3H atoms, tritium. The phosphor emits light when struck by the beta particle from the tritium decay, causing the dials to glow in the dark. The half-life of tritium is 12.3 yr. If the light given off is assumed to be directly proportional to the amount of tritium, by how much will a dial be dimmed in a watch that is 50 yr old?
문제 36
It takes 4 h 39 min for a 2.00-mg sample of radium-230 to decay to 0.25 mg. What is the half-life of radium-230?
문제 37
Cobalt-60 is a strong gamma emitter that has a half-life of 5.26 yr. The cobalt-60 in a radiotherapy unit must be replaced when its radioactivity falls to 75% of the original sample. If an original sample was purchased in June 2016, when will it be necessary to replace the cobalt-60?
- How much time is required for a 6.25-mg sample of 51Cr to decay to 0.75 mg if it has a half-life of 27.8 days?
문제 38
- Radium-226, which undergoes alpha decay, has a half-life of 1600 yr. (a) How many alpha particles are emitted in 5.0 min by a 10.0-mg sample of 226Ra?
문제 39
문제 41
The cloth shroud from around a mummy is found to have a 14C activity of 9.7 disintegrations per minute per gram of carbon as compared with living organisms that undergo 16.3 disintegrations per minute per gram of carbon. From the half-life for 14C decay, 5715 yr, calculate the age of the shroud.
- A wooden artifact from a Chinese temple has a 14C activity of 38.0 counts per minute as compared with an activity of 58.2 counts per minute for a standard of zero age. From the half-life for 14C decay, 5715 years, determine the age of the artifact.
문제 42
문제 43
Potassium-40 decays to argon-40 with a half-life of 1.27 * 109 yr. What is the age of a rock in which the mass ratio of 40Ar to 40K is 4.2?
- 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?
문제 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)?
문제 45
문제 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?
문제 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?
문제 48
문제 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.
문제 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?
문제 51
문제 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.
문제 54
- 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. (a) Why is NaI a good choice for the source of iodine? (b) If a Geiger counter is placed near the person’s thyroid (which is near the neck) right after the sodium iodide solution is taken, what will the data look like as a function of time?
문제 55
문제 55c
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. (c) 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?
문제 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?
문제 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.
문제 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?
문제 59
문제 60c
(c) What other substances are used as a moderator in nuclear reactor designs?
문제 61
Complete and balance the nuclear equations for the following fission or fusion reactions:
(a) 21H + 21H → 32He + _
(b) 23992U + 10n¡ → 13351Sb + 9841Nb + _ 10n
문제 62
Complete and balance the nuclear equations for the following fission reactions:
(a) 23592U + 10n → 16062Sm + 7230Zn + _ 10n
(b) 23994Pu + 10n → 14458Ce + _ + 2 10n
- A portion of the Sun’s energy comes from the reaction 4 11H → 42He + 2 0-1e, which requires a temperature of 106 to 107 K. Use the mass of the helium-4 nucleus given in Table 21.7 to determine how much energy is released per mol of hydrogen atoms.
문제 63