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- Which statement best explains why nuclear transmutations involving neutrons are generally easier to accomplish than those involving protons or alpha particles? (a) Neutrons are not a magic number particle. (b) Neutrons do not have an electrical charge. (c) Neutrons are smaller than protons or alpha particles. (d) Neutrons are attracted to the nucleus even at long distances, whereas protons and alpha particles are repelled.
Problem 27
- In 1930, the American physicist Ernest Lawrence designed the first cyclotron in Berkeley, California. In 1937, Lawrence bombarded a molybdenum target with deuterium ions, producing for the first time an element not found in nature. What was this element? Starting with molybdenum-96 as your reactant, write a nuclear equation to represent this process.
Problem 28
Problem 29b
Complete and balance the following nuclear equations by supplying the missing particle: (b) 21H + 32He → 42He + ?
Problem 29d
Complete and balance the following nuclear equations by supplying the missing particle: (d) 12253I → 12254Xe + ?
Problem 29e
Complete and balance the following nuclear equations by supplying the missing particle: (e) 5926Fe → 0-1e + ?
Problem 30a
Complete and balance the following nuclear equations by supplying the missing particle: (a) 147N + 42He¡? + 11H
Problem 30d
Complete and balance the following nuclear equations by supplying the missing particle: (d) 5826Fe + 2 10n¡6027Co + ?
Problem 30e
Complete and balance the following nuclear equations by supplying the missing particle: (e) 23592U + 10n¡13554Xe + 2 10n + ?
- Write balanced equations for (a) 238922U + 1n -> 224194Pu. (b) 147N + 1a -> 1p + 178O. (c) 5626Fe + 1a -> 1b + 6029Cu.
Problem 31
- Write balanced equations for each of the following nuclear reactions: (a) 23892U + 10n → g + 23992U. (b) 168O + 11p → a + 179N. (c) 188O + 10n → b- + 199F.
Problem 32
- 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)?
Problem 34
Problem 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Some watch dials are coated with a phosphor, like ZnS, and a polymer in which some of the 1H atoms have been replaced by 3H atoms, tritium.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?
Problem 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?
Problem 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 2021, 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?
Problem 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?
Problem 39
Problem 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, 5730 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.
Problem 42
Problem 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?
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?