Solved: Uranium-238 undergoes a slow decay step (t1/2 4.5

How do chemical and nuclear reactions differ in (a) Magnitude of the energy change? (b) Effect on rate of increasing temperature? (c) Effect on rate of higher reactant concentration? (d) Effect on yield of higher reactant concentration?

2 Sulfur has four naturally occurring stable isotopes. The one with the lowest mass number is sulfur- 32, which is also the most abundant (95.02%). (a) What percentage of the S atoms in a matchhead are 32S? (b) The isotopic mass of 32S is 31.972070 amu. Is the atomic mass of S larger, smaller, or equal to this mass? Explain.

What led Marie Curie to draw the following conclusions? (a) Radioactivity is a property of the element and not the compound in which it is found. (b) A highly radioactive element, aside from uranium, occurs in pitchblende?

Which of the following produce an atom of a different element: (a) ? decay; (b) ? decay; (c) ? emission; (d) ? emission; (e) e capture? Show how Z and N change, if at all, with each process. 2

Why is 3 2He stable, but 2 2He has never been detected?

How do the modes of decay differ for a neutron-rich nuclide and a proton-rich nuclide?

Why might it be difficult to use only a nuclides N/Z ratio to predict whether it will decay by ? emission or by e capture? What other factor is important?

Write balanced nuclear equations for the following: (a) Alpha decay of 234 92U (b) Electron capture by neptunium-232 (c) Positron emission by 12 7N

Write balanced nuclear equations for the following: (a) ? decay of sodium-26 (b) ? decay of francium-223 (c) Alpha decay of 212 83Bi

Write balanced nuclear equations for the following: (a) ? emission by magnesium-27 (b) ? emission by 23 12Mg (c) Electron capture by 103 46Pd

Write balanced nuclear equations for the following: (a) ? decay of silicon-32 (b) Alpha decay of polonium-218 (c) Electron capture by 110 49In

Write balanced nuclear equations for the following: (a) Formation of 48 22Ti through positron emission (b) Formation of silver-107 through electron capture (c) Formation of polonium-206 through ? decay

Write balanced nuclear equations for the following: (a) Formation of 241 95Am through ? decay (b) Formation of 228 89Ac through ? decay (c) Formation of 203 83Bi through ? decay

Write balanced nuclear equations for the following: (a) Formation of 186Ir through electron capture (b) Formation of francium-221 through ? decay (c) Formation of iodine-129 through ? decay

Write balanced nuclear equations for the following: (a) Formation of 52Mn through positron emission (b) Formation of polonium-215 through ? decay (c) Formation of 81Kr through electron capture

Which nuclide(s) would you predict to be stable? Why? (a) 20 8O (b) 59 27Co (c) 9 3Li

Which nuclide(s) would you predict to be stable? Why? (a) 146 60Nd (b) 114 48Cd (c) 88 42Mo

Which nuclide(s) would you predict to be stable? Why? (a) 127I (b) tin-106 (c) 68As

Which nuclide(s) would you predict to be stable? Why? (a) 48K (b) 79Br (c) argon-32

What is the most likely mode of decay for each? (a) 238 92U (b) 48 24Cr (c) 50 25Mn

What is the most likely mode of decay for each? (a) 111 47Ag (b) 41 17Cl (c) 110 44Ru

What is the most likely mode of decay for each? (a) 15C (b) 120Xe (c) 224Th

What is the most likely mode of decay for each? (a) 106In (b) 141Eu (c) 241Am

Why is 52 24Cr the most stable isotope of chromium?

Why is 40 20Ca the most stable isotope of calcium?

Np is the parent nuclide of a decay series that starts with ? emission, followed by ? emission, and then two more ? emissions. Write a balanced nuclear equation for each step.

Why is helium found in deposits of uranium and thorium ores? What kind of radioactive emission produces it?

In a natural decay series, how many ? and ? emissions per atom of uranium-235 result in an atom of lead-207?

What electronic process is the basis for detecting radioactivity in (a) a scintillation counter; (b) a Geiger-Mller counter?

What is the reaction order of radioactive decay? Explain.

After 1 minute, three radioactive nuclei remain from an original sample of six. Is it valid to conclude that t1/2 equals 1 minute? Is this conclusion valid if the original sample contained 6 1012 nuclei and 3 1012 remain after 1 minute? Explain.

Radioisotopic dating depends on the constant rate of decay and formation of various nuclides in a sample. How is the proportion of 14C kept relatively constant in living organisms?

What is the specific activity (in Ci/g) if 1.65 mg of an isotope emits 1.56 106 ? particles per second?

What is the specific activity (in Ci/g) if 2.6 g of an isotope emits 4.13 108 ? particles per hour?

What is the specific activity (in Bq/g) if 8.58 g of an isotope emits 7.4 104 ? particles per minute?

What is the specific activity (in Bq/g) if 1.07 kg of an isotope emits 3.77 107 ? particles per minute?

If one-trillionth of the atoms of a radioactive isotope disintegrate each day, what is the decay constant of the process?

If 2.8 1010% of the atoms of a radioactive isotope disintegrate in 1.0 yr, what is the decay constant of the process?

If 1.00 1012 mol of 135Cs emits 1.39 105 ? particles in 1.00 yr, what is the decay constant?

If 6.40 109 mol of 176W emits 1.07 1015 ? in 1.00 h, what is the decay constant?

The isotope 212 83Bi has a half-life of 1.01 yr. What mass (in mg) of a 2.00-mg sample will remain after 3.75 103 h?

The half-life of radium-226 is 1.60 103 yr. How many hours will it take for a 2.50-g sample to decay to the point where 0.185 g of the isotope remains?

A rock contains 270 mol of 238U (t1/2 ? 4.5 109 yr) and 110 mol of 206Pb. Assuming that all the 206Pb comes from decay of the 238U, estimate the rocks age.

A fabric remnant from a burial site has a 14C/12C ratio of 0.735 of the original value. How old is the fabric?

Due to decay of 40K, cows milk has a specific activity of about 6 1011 mCi per milliliter. How many disintegrations of 40K nuclei are there per minute in an 8.0-oz glass of milk?

Plutonium-239 (t1/2 ? 2.41 104 yr) represents a serious nuclear waste hazard. If seven half-lives are required to reach a tolerable level of radioactivity, how long must 239Pu be stored?

A rock that contains 3.1 1015 mol of 232Th (t1/2 ? 1.4 1010 yr) has 9.5 104 fission tracks, each track representing the fission of one atom of 232Th. How old is the rock?

A volcanic eruption melts a large area of rock, and all gases are expelled. After cooling, 40 18Ar accumulates from the ongoing decay of 40 19K in the rock (t1/2 ? 1.25 109 yr). When a piece of rock is analyzed, it is found to contain 1.38 mmol of 40K and 1.14 mmol of 40Ar. How long ago did the rock cool?

Irene and Frederic Joliot-Curie converted 27 13Al to 30 15P in 1933. Why was this transmutation significant?

Early workers mistakenly thought neutron beams were ? radiation. Why? What evidence led to the correct conclusion?

Why must the electrical polarity of the tubes in a linear accelerator be reversed at very short time intervals?

Why does bombardment with protons usually require higher energies than bombardment with neutrons?

Determine the missing species in these transmutations, and write a full nuclear equation from the shorthand notation: (a) 10B (?,n) __ (b) 28Si (d,__) 29P (where d is a deuteron, 2 H) (c) __ (?,2n) 244Cf

Name the unidentified species, and write each transmutation process in shorthand notation: (a) gamma irradiation of a nuclide yields a proton, a neutron, and 29Si; (b) bombardment of 252Cf with 10B yields five neutrons and a nuclide; (c) bombardment of 238U with a particle yields three neutrons and 239Pu.

Elements 104, 105, and 106 have been named rutherfordium (Rf), dubnium (Db), and seaborgium (Sg), respectively. These elements are synthesized from californium-249 by bombarding with carbon- 12, nitrogen-15, and oxygen-18 nuclei, respectively. Four neutrons are formed in each reaction as well. (a) Write balanced nuclear equations for the formation of these elements. (b) Write the equations in shorthand notation.

The effects on matter of ? rays and ? particles differ. Explain.

What is a cation-electron pair, and how does it form?

Why is ionizing radiation more harmful to children than adults?

Why is .OH more dangerous than OH in an organism?

A 135-lb person absorbs 3.3 107 J of energy from radioactive emissions. (a) How many rads does she receive? (b) How many grays (Gy) does she receive?

A 3.6-kg laboratory animal receives a single dose of 8.92 104 Gy. (a) How many rads did the animal receive? (b) How many joules did the animal absorb?

A 70.-kg person exposed to 90Sr absorbs 6.0 105 ? particles, each with an energy of 8.74 1014 J. (a) How many grays does the person receive? (b) If the RBE is 1.0, how many millirems is this? (c) What is the equivalent dose in sieverts (Sv)?

A laboratory rat weighs 265 g and absorbs 1.77 1010 ? particles, each with an energy of 2.20 1013 J. (a) How many rads does the animal receive? (b) What is this dose in Gy? (c) If the RBE is 0.75, what is the equivalent dose in Sv?

If 2.50 pCi [1 pCi (picocurie) ? 1 1012 Ci] of radioactivity from 239Pu is emitted in a 95-kg human for 65 h, and each disintegration has an energy of 8.25 1013 J, how many grays does the person receive?

A small region of a cancer patients brain is exposed for 24.0 min to 475 Bq of radioactivity from 60Co for treatment of a tumor. If the brain mass exposed is 1.858 g and each ? particle emitted has an energy of 5.05 1014 J, what is the dose in rads?

What two ways are radioactive tracers used in organisms?

Why is neutron activation analysis (NAA) useful to art historians and criminologists?

Positrons cannot penetrate matter more than a few atomic diameters, but positron emission of radiotracers can be monitored in medical diagnosis. Explain

A steel part is treated to form some iron-59. Oil used to lubricate the part emits 298 ? particles (with the energy characsiL48593_ch24_1064-1108 29:11:07 02:51pm Page 1104 Apago PDF Enhancer Problems 1105 teristic of 59Fe) per minute per milliliter of oil. What other information would you need to calculate the rate of removal of the steel from the part during use?

The oxidation of methanol to formaldehyde can be accomplished by reaction with chromic acid: 6H(aq) 3CH3OH(aq) 2H2CrO4(aq) 3CH2O(aq) 2Cr3(aq) 8H2O(l) The reaction can be studied with the stable isotope tracer 18O and mass spectrometry. When a small amount of CH3 18OH is present in the alcohol reactant, CH2 18O forms. When a small amount of H2Cr18O4 is present, H2 18O forms. Does chromic acid or methanol supply the O atom to the aldehyde? Explain. The

Many scientists at first reacted skeptically to Einsteins equation, E ? mc2 . Why?

How does a change in mass arise when a nuclide forms from nucleons?

When a nucleus forms from nucleons, is energy absorbed or released? Why?

What is the binding energy per nucleon? Why is the binding energy per nucleon, rather than per nuclide, used to compare nuclide stability?

A 3 H nucleus decays with an energy of 0.01861 MeV. Convert this energy into (a) electron volts; (b) joules.

Arsenic-84 decays with an energy of 1.57 1015 kJ per nucleus. Convert this energy into (a) eV; (b) MeV.

How many joules are released when 1.5 mol of 239Pu decays, if each nucleus releases 5.243 MeV?

How many MeV are released per nucleus when 3.2 103 mol of chromium-49 releases 8.11 105 kJ?

Oxygen-16 is one of the most stable nuclides. The mass of a 16O atom is 15.994915 amu. Calculate the binding energy (a) per nucleon in MeV; (b) per atom in MeV; (c) per mole in kJ.

Lead-206 is the end product of 238U decay. One 206Pb atom has a mass of 205.974440 amu. Calculate the binding energy (a) per nucleon in MeV; (b) per atom in MeV; (c) per mole in kJ

Cobalt-59 is the only stable isotope of this transition metal. One 59Co atom has a mass of 58.933198 amu. Calculate the binding energy (a) per nucleon in MeV; (b) per atom in MeV; (c) per mole in kJ

Iodine-131 is one of the most important isotopes used in the diagnosis of thyroid cancer. One atom has a mass of 130.906114 amu. Calculate the binding energy (a) per nucleon in MeV; (b) per atom in MeV; (c) per mole in kJ.

The 80Br nuclide decays either by ? decay or by electron capture. (a) What is the product of each process? (b) Which process releases more energy? (Masses of atoms: 80Br ? 79.918528 amu; 80Kr ? 79.916380 amu; 80Se79.916520 amu; neglect the mass of electrons involved because these are atomic, not nuclear, masses.)

What is the minimum number of neutrons from each fission event that must be absorbed by other nuclei for a chain reaction to be sustained?

In what main way is fission different from radioactive decay? Are all fission events in a chain reaction identical? Explain

What is the purpose of enrichment in the preparation of fuel rods? How is it accomplished?

Describe the nature and purpose of these components of a nuclear reactor: (a) control rods; (b) moderator; (c) reflector.

State an advantage and a disadvantage of heavy-water reactors compared to light-water reactors.

What are the expected advantages of fusion reactors over fission reactors?

Why is iron the most abundant element in Earths core?

Compare the s- and r-processes in stellar nucleosynthesis.

What is the cosmic importance of unstable 8 Be?

The reaction that will probably power the first commercial fusion reactor is 3 1H 2 1H 4 2He 1 0n How much energy would be produced per mole of reaction? (Masses of atoms: 3 1H ? 3.01605 amu; 2 1H ? 2.0140 amu; 4 2He ? 4.00260 amu; mass of 1 0n ? 1.008665 amu.)

Some 243 95Am was present when Earth formed, but it all decayed in the next billion years. The first three steps in this decay series are emission of an ? particle, a ? particle, and another ? particle. What other isotopes were present on the young Earth in a rock that contained some 243 95Am?

Curium-243 undergoes ? decay to plutonium-239: 243Cm 239Pu ? (a) Find the change in mass, ?m (in kg). (Masses: 243Cm ? 243.0614 amu; 239Pu ? 239.0522 amu; 4 He ? 4.0026 amu; 1 amu ? 1.661 1024 g.) (b) Find the energy released in joules. (c) Find the energy released in kJ/mol of reaction, and comment on the difference between this value and a typical heat of reaction for a chemical change, which is a few hundred kJ/mol.

Plutonium triggers for nuclear weapons were manufactured at the Rocky Flats plant in Colorado. An 85-kg worker inhaled a dust particle containing 1.00 g of 239 94Pu, which resided in his body for 16 h (t1/2 of 239Pu ? 2.41 104 yr; each disintegration released 5.15 MeV). (a) How many rads did he receive? (b) How many grays?

Archeologists removed some charcoal from a Native American campfire, burned it in O2, and bubbled the CO2 formed into Ca(OH)2 solution (limewater). The CaCO3 that precipitated was filtered and dried. If 4.58 g of the CaCO3 had a radioactivity of 3.2 d/min, how long ago was the campfire?

A 5.4- g sample of 226RaCl2 has a radioactivity of 1.5 105 Bq. Calculate t1/2 of 226Ra

How many rads does a 65-kg human receive each year from the approximately 108 g of 14 6C naturally present in her body (t1/2 ? 5730 yr; each disintegration releases 0.156 MeV)?

The overall reaction taking place during hydrogen burning in a young star is 41 1H 4 2He 21 0 ? 2? energy How much energy (in MeV) is released per He nucleus formed? Per mole of He? (Masses: 1 1H atom ? 1.007825 amu; 4 2He atom ? 4.00260 amu; positron ? 5.48580 104 amu.) 24

A sample of AgCl emits 175 nCi/g. A saturated solution prepared from the solid emits 1.25 102 Bq/mL due to radioactive Ag ions. What is the molar solubility of AgCl?

The scene below depicts a neutron bombarding 235U: (a) Is this an example of fission or of fusion? (b) Identify the other nuclide formed. (c) What is the most likely mode of decay of the nuclide with Z ? 55?

3 What fraction of the 235U (t1/2 ? 7.0 108 yr) created when Earth was formed would remain after 2.8 109 yr?

238U (t1/2 ? 4.5 109 yr) begins a decay series that ultimately forms 206Pb. The scene below depicts the relative number of 238U atoms (red) and 206Pb atoms (green) in a mineral. If all the Pb comes from 238U, calculate the age of the sample.

Cosmologists modeling the origin of the elements postulate nuclides with very short half-lives. One of these nuclides, 8 Be (t1/2 ? 7 1017 s), plays a key role in stellar nucleosynthesis (p. 1099) because it must fuse with 4 He to form 12C before decaying. Another explanation involves the simultaneous fusion of three 4 He nuclei to form 12C. Comment on the validity of this alternative mechanism.

Technetium-99m is a metastable nuclide used in numerous cancer diagnostic and treatment programs. It is prepared just before use because it decays rapidly through ? emission: 99mTc 99Tc ? Use the data below to determine (a) the half-life of 99mTc; (b) the percentage of the isotope that is lost if it takes 2.0 h to

How many curies are produced by 1.0 mol of 40K (t1/2 ? 1.25 109 yr)? How many becquerels?

The fraction of a radioactive isotope remaining at time t is , where t1/2 is the half-life. If the half-life of carbon-14 is 5730 yr, what fraction of carbon-14 in a piece of charcoal remains after (a) 10.0 yr; (b) 10.0 103 yr; (c) 10.0 104 yr? (d) Why is radiocarbon dating more reliable for the fraction remaining in part (b) than that in part (a) or in part (c)?

The isotopic mass of 210 86Rn is 209.989669 amu. When this nuclide decays by electron capture, it emits 2.368 MeV. What is the isotopic mass of the resulting nuclide?

Exactly 0.1 of the radioactive nuclei in a sample decay per hour. Thus, after n hours, the fraction of nuclei remaining is (0.900)n . Find the value of n equal to one half-life

In neutron activation analysis (NAA), stable isotopes are bombarded with neutrons. Depending on the isotope and the energy of the neutron, various emissions are observed. What are the products when the following neutron-activated species decay? Write an overall equation in shorthand notation for the reaction starting with the stable isotope before neutron activation. (a) 52 23V* [? emission] (b) 64 29Cu* [? emission] (c) 28 13Al* [? emission] 2

In the 1950s, radioactive material was spread over the land from aboveground nuclear tests. A woman drinks some contaminated milk and ingests 0.0500 g of 90Sr, which is taken up by bones and teeth and not eliminated. (a) How much 90Sr (t1/2 ? 29 yr) is present in her body after 10 yr? (b) How long will it take for 99.9% of the 90Sr to decay?

The scene below represents a reaction (with neutrons gray and protons purple) that occurs during the lifetime of a star. (a) Write a balanced nuclear equation for the reaction. (b) If the mass difference is 7.7 102 amu, find the energy (kJ) released.

What volume of radon will be produced per hour at STP from 1.000 g of 226Ra (t1/2 ? 1599 yr; 1 yr ? 8766 h; mass of one 226Ra atom ? 226.025402 amu)?

90Kr (t1/2 ? 32 s) is used to study respiration. How soon after being made must a sample be administered to the patient if the activity must be at least 90% of the original activity?

Which isotope in each pair is more stable? Why? (a) 140 55Cs or 133 55Cs (b) 79 35Br or 78 35Br (c) 28 12Mg or 24 12Mg (d) 14 7N or 18 7N

A bone sample containing strontium-90 (t1/2 ? 29 yr) emits 7.0 104 ? particles per month. How long will it take for the emission to decrease to 1.0 104 particles per month?

The 23rd-century starship Enterprise uses a substance called dilithium crystals as its fuel. (a) Assuming this material is the result of fusion, what is the product of the fusion of two 6 Li nuclei? (b) How much energy is released per kilogram of dilithium formed? (Mass of one 6 Li atom is 6.015121 amu.) (c) When four 1 H atoms fuse to form 4 He, how many positrons are released? (d) To determine the energy potential of the fusion processes in parts (b) and (c), compare the changes in mass per kilogram of dilithium and of 4 He. (e) Compare the change in mass per kilogram in part (b) to that for the formation of 4 He by the method used in current fusion reactors (see p. 1098). (For masses, see Problem 24.93.) (f) Using early 21st-century fusion technology, how much tritium can be produced per kilogram of 6 Li in the following reaction: 6 3Li 1 0n 4 2He 3 1H? When this amount of tritium is siL48593_ch24_1064-1108 29:11:07 02:51pm Page 1106 Apago PDF Enhancer fused with deuterium, what is the change in mass? How does this quantity compare with the use of dilithium in part (b)?

Uranium and radium are found in many rocky soils throughout the world. Both undergo radioactive decay, and one of the products is radon-222, the heaviest noble gas (t1/2 ? 3.82 days). Inhalation of this gas contributes to many lung cancers. According to Environmental Protection Agency recommendations, the level of radioactivity from radon in homes should not exceed 4.0 pCi/L of air. (a) What is the safe level of radon in Bq/L of air? (b) A home has a radon measurement of 41.5 pCi/L. The owner vents the basement in such a way that no more radon enters the living area. What is the activity of the radon remaining in the room air (in Bq/L) after 9.5 days? (c) How many more days does it take to reach the EPA recommended level?

Nuclear disarmament could be accomplished if weapons were not replenished. The tritium in warheads decays to helium with a half-life of 12.26 yr and must be replaced or the weapon is useless. What fraction of the tritium is lost in 5.50 yr?

A decay series starts with the synthetic isotope 239 92U. The first four steps are emissions of a ? particle, another ?, an ? particle, and another ?. Write a balanced nuclear equation for each step. Which natural series could start by this sequence?

How long can a 54-lb child be exposed to 1.0 mCi of radiation from 222Rn before accumulating 1.0 mrad if the energy of each disintegration is 5.59 MeV?

An earthquake in the area of present-day San Francisco is to be dated by measuring the 14C activity (t1/2 ? 5730 yr) of parts of a tree uprooted during the event. The tree parts have an activity of 12.9 d/min?g C, and a living tree has an activity of 15.3 d/min?g C. How long ago did the earthquake occur?

Were organisms a billion years ago exposed to more or less ionizing radiation than similar organisms today? Explain.

Tritium (3 H; t1/2 ? 12.26 yr) is continually formed in the upper troposphere by interaction of solar particles with nitrogen. As a result, natural waters contain a small amount of tritium. Two samples of wine are analyzed, one known to be made in 1941 and another made earlier. The water in the 1941 wine has 2.23 times as much tritium as the water in the other. When was the other wine produced?

Even though plutonium-239 (t1/2 ? 2.41 104 yr) is one of the main fission fuels, it is still a radiation hazard present in spent uranium fuel from nuclear power plants. How many years does it take for 99% of the plutonium-239 in spent fuel to decay?

Carbon from the remains of an extinct Australian marsupial, called Diprotodon, has a specific activity of 0.61 pCi/g. Modern carbon has a specific activity of 6.89 pCi/g. How long ago did the Diprotodon apparently become extinct?

The reaction that allows for radiocarbon dating is the continual formation of carbon-14 in the upper atmosphere: 14 7N 1 0n 14 6C 1 1H What is the energy change associated with this process in eV/reaction and in kJ/mol reaction? (Masses of atoms: 14 7N ? 14.003074 amu; 14 6C ? 14.003241 amu; 1 1H ? 1.007825 amu; mass of 1 0n ? 1.008665 amu.)

9 What is the nuclear binding energy of a lithium-7 nucleus in units of kJ/mol and eV/nucleus? (Mass of a lithium-7 atom ? 7.016003 amu.)

Gadolinium-146 undergoes electron capture. Identify the product, and use Figure 24.2 to find the modes of decay and the other two nuclides in the series below:

Using 21st-century technology, hydrogen fusion requires temperatures around 108 K. But, lower initial temperatures are used if the hydrogen is compressed. In the late 24th century, the starship Leinad uses such methods to fuse hydrogen at 106 K. (a) What is the kinetic energy of an H atom at 1.00 106 K? (b) How many H atoms are heated to 1.00 106 K from the energy of one H and one anti-H atom annihilating each other? (c) If these H atoms fuse into 4 He atoms (with the loss of two positrons per 4 He formed), how much energy (in J) is generated? (d) How much more energy is generated by the fusion in (c) than by the hydrogen-antihydrogen collision in (b)? (e) Should the captain of the Leinad change the technology and produce 3 He (mass ? 3.01603 amu) instead of 4 He

A metastable (excited) form of 50Sc changes to its stable form by emitting ? radiation with a wavelength of 8.73 pm. What is the change in mass of 1 mol of the isotope when it undergoes this change?

A sample of cobalt-60 (t1/2 ? 5.27 yr), a powerful ? emitter used to treat cancer, was purchased by a hospital on March 1, 2007. The sample must be replaced when its activity reaches 70.% of the original value. On what date must it be replaced?

Uranium-233 decays to thorium-229 by ? decay, but the emissions have different energies and products: 83% emit an ? particle with energy of 4.816 MeV and give 229Th in its ground state; 15% emit an ? particle of 4.773 MeV and give 229Th in excited state I; and 2% emit a lower energy ? particle and give 229Th in the higher excited state II. Excited state II emits a ? ray of 0.060 MeV to reach excited state I. (a) Find the ?-ray energy and wavelength that would convert excited state I to the ground state. (b) Find the energy of the ? particle that would convert 233U to excited state II.

Uranium-238 undergoes a slow decay step (t1/2 ? 4.5 109 yr) followed by a series of fast steps to form the stable isotope 206Pb. Thus, on a time scale of billions of years, 238U effectively decays directly to 206Pb, and the relative amounts of these isotopes are used to find the age of some rocks (see margin note, p. 1079). Two students derive equations relating number of halflives (n) since the rock formed to the amounts of the isotopes: Student 1: Student 2: (a) Which equation is correct, and why? (b) If a rock contains exactly twice as much 238U as 206Pb, what is its age in years?

In the naturally occurring thorium-232 decay series, the steps emit this sequence of particles: ?, ?, ?, ?, ?, ?, ?, ?,? and ?. Write a balanced equation for each step. 2

At death, a nobleman in ancient Egypt was mummified and his body contained 1.4 103 g of 40K (t1/2 ? 1.25 109 yr), 1.2 108 g of 14C (t1/2 ? 5730 yr), and 4.8 1014 g of 3 H ((t1/2 ? 12.26 yr). Which nuclide would give the most accurate estimate of the mummys age? Explain.

Assuming that many radioactive nuclides can be considered safe after 20 half-lives, how long will it take for each of the following nuclides to be safe: (a) 242Cm (t1/2 ? 163 days); (b) 214Po (t1/2 ? 1.6 104 s); (c) 232Th (t1/2 ? 1.39 1010 yr)?

An ancient sword has a blade from the early Roman Empire, around 100 AD, but the wooden handle, inlaid wooden decorations, leather ribbon, and leather sheath have different styles. Given the following activities, estimate the age of each part. Which part was made near the time of the blade (t1/2 of 14C ? 5730 yr; 0 ? 15.3 d/min? )?

The starship Voyager, like many other vessels of the newly designed 24th-century fleet, uses antimatter as fuel. (a) How much energy is released when 1.00 kg each of antimatter and matter annihilate each other? (b) When the antimatter is atomic antihydrogen, a small amount of it is mixed with excess atomic hydrogen (gathered from interstellar space during flight). The annihilation releases so much heat that the remaining hydrogen nuclei fuse to form 4 He. If each hydrogen-antihydrogen collision releases enough heat to fuse 1.00 105 hydrogen atoms, how much energy (in kJ) is released per kilogram of antihydrogen? (c) Which produces more energy per kilogram of antihydrogen, the procedure in part (a) or that in part (b)?

Use Einsteins equation, the mass in grams of 1 amu, and the relation between electron volts and joules to find the energy equivalent (in MeV) of a mass difference of 1 amu.

Determine the age of a rock containing 0.065 g of uranium- 238 (t1/2 ? 4.5 109 yr) and 0.023 g of lead- 206. (Assume all the lead-206 came from 238U decay.)

Plutonium-242 decays to uranium-238 by emission of an ? particle with an energy of 4.853 MeV. The 238U that forms is unstable and emits a ? ray (? ? 0.02757 nm). (a) Write balanced equations for these reactions. (b) What would be the energy of the ? particle if 242Pu decayed directly to the more stable 238U?

Seaborgium-263 (Sg), the first isotope of element 106 synthesized, was made, together with four neutrons, by bombarding californium-249 with oxygen-18. It then underwent a series of decays starting with three ? emissions. Write balanced equations for the synthesis and the three ? emissions of 263Sg

Some nuclear power plants use plutonium-239, which is produced in breeder reactors (see margin note, p. 1097). The rate-determining step is the second ? emission. How long does it take to make 1.00 kg of 239Pu if the reaction is complete when the product is 90.% 239Pu?

A random-number generator can be used to simulate the probability of a given atom decaying over a given time. For example, the formula ?RAND() in the Excel spreadsheet returns a random number between 0 and 1; thus, for one radioactive atom and a time of one half-life, a number less than 0.5 means the atom decays and a number greater than 0.5 means it doesnt. (a) Place the ?RAND() formula in cells A1 to A10 of an Excel spreadsheet. In cell B1, place ?IF(A1<0.5, 0, 1). This formula returns 0 if A1 is <0.5 (the atom decays) and 1 if A1 is >0.5 (the atom does not decay). Place analogous formulas in cells B2 to B10 (using the Fill Down procedure in Excel). To determine the number of atoms remaining after one half-life, sum cells B1 to B10 by placing ?SUM(B1:B10) in cell B12. To create a new set of random numbers, click on an empty cell (e.g., B13) and hit Delete. Perform 10 simulations, each time recording the total number of atoms remaining. Do half of the atoms remain after each half-life? If not, why not? (b) Increase the number of atoms to 100 by placing suitable formulas in cells A1 to A100, B1 to B100, and B102. Perform 10 simulations, and record the number of atoms remaining each time. Are these results more realistic for radioactive decay? Explain.

In the following Excel-based simulation, the fate of 256 atoms is followed over five half-lives. Set up formulas in columns A and B, as in Problem 24.146, and simulate the fate of the sample of 256 atoms over one half-life. Cells B1 to B256 should contain 1 or 0. In cell C1, enter ?IF(B1?0, 0, RAND()). This returns 0 if the original atom decayed in the previous half-life or a random number between 0 and 1 if it did not. Fill the formula in C1 down to cell C256. Column D should have formulas similar to those in B, but with modified references, as should columns F, H, and J. Columns E, G, and I should have formulas similar to those in C, but with modi- fied references. In cell B258, enter ?SUM(B1:B256). This records the number of atoms remaining after the first half-life. Put formulas in cells D258, F258, H258, and J258 to record atoms remaining after subsequent half-lives. (a) Ideally, how many atoms should remain after each half-life? (b) Make a table of the atoms remaining after each half-life in four separate simulations. Compare these outcomes to the ideal outcome. How would you make the results more realistic?

Representations of three nuclei (with neutrons gray and protons purple) are shown below. Nucleus 1 is stable, but 2 and 3 are not. (a) Write the symbol for each isotope. (b) What is (are) the most likely mode(s) of decay for 2 and 3?

A metastable (excited) form of 50Sc changes to its stable form by emitting  radiation with a wavelength of 8.73 pm. What is the change in mass of 1 mol of the isotope when it undergoes this change?

A sample of cobalt-60 (t1/2  5.27 yr), a powerful  emitter used to treat cancer, was purchased by a hospital on March 1, 2007. The sample must be replaced when its activity reaches 70.% of the original value. On what date must it be replaced?

Uranium-233 decays to thorium-229 by  decay, but the emissions have different energies and products: 83% emit an  particle with energy of 4.816 MeV and give 229Th in its ground state; 15% emit an  particle of 4.773 MeV and give 229Th in excited state I; and 2% emit a lower energy  particle and give 229Th in the higher excited state II. Excited state II emits a  ray of 0.060 MeV to reach excited state I. (a) Find the -ray energy and wavelength that would convert excited state I to the ground state. (b) Find the energy of the  particle that would convert 233U to excited state II.

Uranium-238 undergoes a slow decay step (t1/2  4.5 109 yr) followed by a series of fast steps to form the stable isotope 206Pb. Thus, on a time scale of billions of years, 238U effectively decays directly to 206Pb, and the relative amounts of these isotopes are used to find the age of some rocks (see margin note, p. 1079). Two students derive equations relating number of halflives (n) since the rock formed to the amounts of the isotopes: Student 1: Student 2: (a) Which equation is correct, and why? (b) If a rock contains exactly twice as much 238U as 206Pb, what is its age in years?

In the naturally occurring thorium-232 decay series, the steps emit this sequence of particles: , , , , , , , , , and . Write a balanced equation for each step. 2

At death, a nobleman in ancient Egypt was mummified and his body contained 1.4 103 g of 40K (t1/2  1.25 109 yr), 1.2 108 g of 14C (t1/2  5730 yr), and 4.8 1014 g of 3 H ((t1/2  12.26 yr). Which nuclide would give the most accurate estimate of the mummys age? Explain.

Assuming that many radioactive nuclides can be considered safe after 20 half-lives, how long will it take for each of the following nuclides to be safe: (a) 242Cm (t1/2  163 days); (b) 214Po (t1/2  1.6 104 s); (c) 232Th (t1/2  1.39 1010 yr)?

An ancient sword has a blade from the early Roman Empire, around 100 AD, but the wooden handle, inlaid wooden decorations, leather ribbon, and leather sheath have different styles. Given the following activities, estimate the age of each part. Which part was made near the time of the blade (t1/2 of 14C  5730 yr; 0  15.3 d/ming)?

The starship Voyager, like many other vessels of the newly designed 24th-century fleet, uses antimatter as fuel. (a) How much energy is released when 1.00 kg each of antimatter and matter annihilate each other? (b) When the antimatter is atomic antihydrogen, a small amount of it is mixed with excess atomic hydrogen (gathered from interstellar space during flight). The annihilation releases so much heat that the remaining hydrogen nuclei fuse to form 4 He. If each hydrogen-antihydrogen collision releases enough heat to fuse 1.00 105 hydrogen atoms, how much energy (in kJ) is released per kilogram of antihydrogen? (c) Which produces more energy per kilogram of antihydrogen, the procedure in part (a) or that in part (b)?

Determine the age of a rock containing 0.065 g of uranium- 238 (t1/2  4.5 109 yr) and 0.023 g of lead-206. (Assume all the lead-206 came from 238U decay.)

Plutonium-242 decays to uranium-238 by emission of an  particle with an energy of 4.853 MeV. The 238U that forms is unstable and emits a  ray (  0.02757 nm). (a) Write balanced equations for these reactions. (b) What would be the energy of the  particle if 242Pu decayed directly to the more stable 238U?

Seaborgium-263 (Sg), the first isotope of element 106 synthesized, was made, together with four neutrons, by bombarding californium-249 with oxygen-18. It then underwent a series of decays starting with three  emissions. Write balanced equations for the synthesis and the three  emissions of 263Sg

Some nuclear power plants use plutonium-239, which is produced in breeder reactors (see margin note, p. 1097). The rate-determining step is the second  emission. How long does it take to make 1.00 kg of 239Pu if the reaction is complete when the product is 90.% 239Pu?

A random-number generator can be used to simulate the probability of a given atom decaying over a given time. For example, the formula RAND() in the Excel spreadsheet returns a random number between 0 and 1; thus, for one radioactive atom and a time of one half-life, a number less than 0.5 means the atom decays and a number greater than 0.5 means it doesnt. (a) Place the RAND() formula in cells A1 to A10 of an Excel spreadsheet. In cell B1, place IF(A1<0.5, 0, 1). This formula returns 0 if A1 is <0.5 (the atom decays) and 1 if A1 is >0.5 (the atom does not decay). Place analogous formulas in cells B2 to B10 (using the Fill Down procedure in Excel). To determine the number of atoms remaining after one half-life, sum cells B1 to B10 by placing SUM(B1:B10) in cell B12. To create a new set of random numbers, click on an empty cell (e.g., B13) and hit Delete. Perform 10 simulations, each time recording the total number of atoms remaining. Do half of the atoms remain after each half-life? If not, why not? (b) Increase the number of atoms to 100 by placing suitable formulas in cells A1 to A100, B1 to B100, and B102. Perform 10 simulations, and record the number of atoms remaining each time. Are these results more realistic for radioactive decay? Explain.

In the following Excel-based simulation, the fate of 256 atoms is followed over five half-lives. Set up formulas in columns A and B, as in Problem 24.146, and simulate the fate of the sample of 256 atoms over one half-life. Cells B1 to B256 should contain 1 or 0. In cell C1, enter IF(B10, 0, RAND()). This returns 0 if the original atom decayed in the previous half-life or a random number between 0 and 1 if it did not. Fill the formula in C1 down to cell C256. Column D should have formulas similar to those in B, but with modified references, as should columns F, H, and J. Columns E, G, and I should have formulas similar to those in C, but with modi- fied references. In cell B258, enter SUM(B1:B256). This records the number of atoms remaining after the first half-life. Put formulas in cells D258, F258, H258, and J258 to record atoms remaining after subsequent half-lives. (a) Ideally, how many atoms should remain after each half-life? (b) Make a table of the atoms remaining after each half-life in four separate simulations. Compare these outcomes to the ideal outcome. How would you make the results more realistic?