?55PE from the appendices and the periodic table may be

83PE Problem Construct Your Own Problem Consider the decay of radioactive substances in the Earth’s interior. The energy emitted is converted to thermal energy that reaches the earth’s surface and is radiated away into cold dark space. Construct a problem in which you estimate the activity in a cubic meter of earth rock? And then calculate the power generated. Calculate how much power must cross each square meter of the Earth’s surface if the power is dissipated at the same rate as it is generated. Among the things to consider are the activity per cubic meter, the energy per decay, and the size of the Earth.

Problem 1CQ Suppose the range for 5.0 MeV? ray is known to be 2.0 mm in a certain material. Does this mean that every 5.0 MeV? a ray that strikes this material travels 2.0 mm, or does the range have an average value with some statistical fluctuations in the distances traveled? Explain.

Problem 2CQ What is the difference between ? rays and characteristic x rays? Is either necessarily more energetic than the other? Which can be the most energetic?

Problem 2PE A particle of ionizing radiation creates 4000 ion pairs in the gas inside a Geiger tube as it passes through. What minimum energy was deposited, if 30.0 eV is required to create each ion pair?

Problem 3CQ Ionizing radiation interacts with matter by scattering from electrons and nuclei in the substance. Based on the law of conservation of momentum and energy, explain why electrons tend to absorb more energy than nuclei in these interactions.

Problem 1PE The energy of 30.0 eV is required to ionize a molecule of the gas inside a Geiger tube, thereby producing an ion pair. Suppose a particle of ionizing radiation deposits 0.500 MeV of energy in this Geiger tube. What maximum number of ion pairs can it create?

Problem 3PE (a) Repeat Exercise 31.2, and convert the energy to joules or calories. (b) If all of this energy is converted to thermal energy in the gas, what is its temperature increase, assuming 50.0 cm3 of ideal gas at 0.250-atm pressure? (The small answer is consistent with the fact that the energy is large on a quantum mechanical scale but small on a macroscopic scale.) Reference Exercise 31.2: A particle of ionizing radiation creates 4000 ion pairs in the gas inside a Geiger tube as it passes through. What minimum energy was deposited, if 30.0 eV is required to create each ion pair?

Problem 4CQ What characteristics of radioactivity show it to be nuclear in origin and not atomic?

Problem 6PE Find the length of a side of a cube having a mass of 1.0 kg and the density of nuclear matter, taking this to be 2.3×1017 kg/m3 .

Problem 4PE Suppose a particle of ionizing radiation deposits 1.0 MeV in the gas of a Geiger tube, all of which goes to creating ion pairs. Each ion pair requires 30.0 eV of energy. (a) The applied voltage sweeps the ions out of the gas in 1.00 µs . What is the current? (b) This current is smaller than the actual current since the applied voltage in the Geiger tube accelerates the separated ions, which then create other ion pairs in subsequent collisions. What is the current if this last effect multiplies the number of ion pairs by 900?

Problem 5CQ What is the source of the energy emitted in radioactive decay? Identify an earlier conservation law, and describe how it was modified to take such processes into account.

Problem 5PE Verify that a 2.3×1017 kg mass of water at normal density would make a cube 60 km on a side, as claimed in Example 31.1. (This mass at nuclear density would make a cube 1.0 m on a side.) Example 31.1: How Small and Dense Is a Nucleus? (a) Find the radius of an iron-56 nucleus. (b) Find its approximate density in kg / m 3 , approximating the mass of 56Fe to be 56 u.

Problem 7CQ Explain how an ? particle can have a larger range in air than a ? particle with the same energy in lead.

Problem 7PE What is the radius of an ? particle?

Problem 8CQ Arrange the following according to their ability to act as radiation shields, with the best first and worst last. Explain your ordering in terms of how radiation loses its energy in matter. (a) A solid material with low density composed of low-mass atoms. (b) A gas composed of high-mass atoms. (c) A gas composed of low-mass atoms. (d) A solid with high density composed of high-mass atoms.

Problem 9CQ Often, when people have to work around radioactive materials spills, we see them wearing white coveralls (usually a plastic material). What types of radiation (if any) do you think these suits protect the worker from, and how?

Problem 8PE Find the radius of a 238 Pu nucleus. 238 Pu is a manufactured nuclide that is used as a power source on some space probes.

Problem 9PE (a) Calculate the radius of 58 Ni, one of the most tightly bound stable nuclei. (b) What is the ratio of the radius of 58 Ni to that of 258 Ha , one of the largest nuclei ever made? Note that the radius of the largest nucleus is still much smaller than the size of an atom.

Problem 10CQ Is it possible for light emitted by a scintillator to be too low in frequency to be used in a photomultiplier tube? Explain.

Problem 10PE The unified atomic mass unit is defined to be 1 u = 1.6605×10?27 kg . Verify that this amount of mass converted to energy yields 931.5 MeV. Note that you must use four-digit or better values for c and |qe|.

11CQ Problem The weak and strong nuclear forces are basic to the structure of matter. Why we do not experience them directly?

12CQ Problem Define and make clear distinctions between the terms neutron, nucleon, nucleus, nuclide, and neutrino.

13CQ Problem What are isotopes? Why do different isotopes of the same element have similar chemistries?

11PE Problem What is the ratio of the velocity of a ? particle to that of an ? particle, if they have the same nonrelativistic kinetic energy?

13PE Problem The detail observable using a probe is limited by its wavelength. Calculate the energy of a ? -ray photon that has a wavelength of 1×10?16 m , small enough to detect details about one-tenth the size of a nucleon. Note that a photon having this energy is difficult to produce and interacts poorly with the nucleus, limiting the practicability of this probe.

12PE Problem If a 1.50-cm-thick piece of lead can absorb 90.0% of the ? rays from a radioactive source, how many centimeters of lead are needed to absorb all but 0.100% of the ? rays?

14PE Problem (a) Show that if you assume the average nucleus is spherical with a radius r = r0A 1 / 3 , and with a mass of A u, then its density is independent of A . (b) Calculate that density in u/fm3 and kg/m3 , and compare your results with those found in Example 31.1 for 56Fe . Example 31.1: How Small and Dense Is a Nucleus? (a) Find the radius of an iron-56 nucleus. (b) Find its approximate density in kg / m 3 , approximating the mass of 56Fe to be 56 u.

15CQ Problem What conservation law requires an electron’s neutrino to be produced in electron capture? Note that the electron no longer exists after it is captured by the nucleus.

14CQ Problem Star Trek fans have often heard the term “antimatter drive.” Describe how you could use a magnetic field to trap antimatter, such as produced by nuclear decay, and later combine it with matter to produce energy. Be specific about the type of antimatter, the need for vacuum storage, and the fraction of matter converted into energy.

15PE Problem What is the ratio of the velocity of a 5.00-MeV ? ray to that of an ? particle with the same kinetic energy? This should confirm that ? s travel much faster than ? s even when relativity is taken into consideration. (See also Exercise 31.11.) Reference Exercise 31.11: What is the ratio of the velocity of a ? particle to that of an ? particle, if they have the same nonrelativistic kinetic energy?

17CQ Problem What do the three types of beta decay have in common that is distinctly different from alpha decay?

16CQ Problem Neutrinos are experimentally determined to have an extremely small mass. Huge numbers of neutrinos are created in a supernova at the same time as massive amounts of light are first produced. When the 1987A supernova occurred in the Large Magellanic Cloud, visible primarily in the Southern Hemisphere and some 100,000 light-years away from Earth, neutrinos from the explosion were observed at about the same time as the light from the blast. How could the relative arrival times of neutrinos and light be used to place limits on the mass of neutrinos?

16PE Problem (a) What is the kinetic energy in MeV of a ? ray that is traveling at 0.998c ? This gives some idea of how energetic a ? ray must be to travel at nearly the same speed as a ? ray. (b) What is the velocity of the ? ray relative to the ? ray?

In the following eight problems, write the complete decay equation for the given nuclide in the complete \({ }_{Z}^{A} \mathrm{X}_{N}\) notation. Refer to the periodic table for values of \(Z\) \(\beta^{-}\) decay of \({ }^{40} K\), a naturally occurring rare isotope of potassium responsible for some of our exposure to background radiation. Equation Transcription: Text Transcription: _Z ^A X_N Z beta^- ^40 K

In the following eight problems, write the complete decay equation for the given nuclide in the complete \({ }_{Z}^{A} \mathrm{X}_{N}\) notation. Refer to the periodic table for values of \(Z\) \(\beta^{-}\) decay of \({ }^{3} H\) (tritium), a manufactured isotope of hydrogen used in some digital watch displays, and manufactured primarily for use in hydrogen bombs. Equation Transcription: Text Transcription: _Z ^A X_N Z beta^- ^3 H

18CQ Problem In a 3 × 109 -year-old rock that originally contained some 238 U , which has a half-life of 4.5 × 109 years, we expect to find some 238 U remaining in it. Why are 226Ra , 222Rn , and 210 Po also found in such a rock, even though they have much shorter half-lives (1600 years, 3.8 days, and 138 days, respectively)?

19CQ Problem Does the number of radioactive nuclei in a sample decrease to exactly half its original value in one half-life? Explain in terms of the statistical nature of radioactive decay.

In the following eight problems, write the complete decay equation for the given nuclide in the complete \({ }_{Z}^{A} \mathrm{X}_{N}\) notation. Refer to the periodic table for values of \(Z\) \(\beta^{+}\) decay of \({ }^{50} Mn\). Equation Transcription: Text Transcription: _Z ^A X_N Z beta^+ ^50 Mn

In the following eight problems, write the complete decay equation for the given nuclide in the complete \({ }_{Z}^{A} \mathrm{X}_{N}\) notation. Refer to the periodic table for values of \(Z\) Electron capture by \({ }^{7} Be\). Equation Transcription: Text Transcription: _Z ^A X_N Z ^7 Be

20CQ Problem Radioactivity depends on the nucleus and not the atom or its chemical state. Why, then, is one kilogram of uranium more radioactive than one kilogram of uranium hexafluoride?

23CQ Problem To obtain the most precise value of BE from the equation BE = [ZM ( 1H) + Nmn ]c 2 – m (AX)c 2 , we should take into account the binding energy of the electrons in the neutral atoms. Will doing this produce a larger or smaller value for BE? Why is this effect usually negligible?

In the following eight problems, write the complete decay equation for the given nuclide in the complete \({ }_{Z}^{A} \mathrm{X}_{N}\) notation. Refer to the periodic table for values of \(Z\) Electron capture by \({ }^{106} In\). Equation Transcription: Text Transcription: _Z ^A X_N Z ^106 In

21CQ Problem Explain how a bound system can have less mass than its components. Why is this not observed classically, say for a building made of bricks?

In the following eight problems, write the complete decay equation for the given nuclide in the complete \({ }_{Z}^{A} \mathrm{X}_{N}\) notation. Refer to the periodic table for values of \(Z\) \(\alpha\) decay of \({ }^{210} Po\), the isotope of polonium in the decay series of \({ }^{238} U\) that was discovered by the Curies. A favorite isotope in physics labs, since it has a short half-life and decays to a stable nuclide. Equation Transcription: Text Transcription: _Z ^A X_N Z alpha ^210 Po ^238 U

In the following eight problems, write the complete decay equation for the given nuclide in the complete \({ }_{Z}^{A} \mathrm{X}_{N}\) notation. Refer to the periodic table for values of \(Z\) \(\beta^{+}\) decay of \({ }^{52} Fe\). Equation Transcription: Text Transcription: _Z ^A X_N Z beta^+ ^52 Fe

24CQ Problem How does the finite range of the nuclear force relate to the fact that BE / A is greatest for A near 60?

26CQ Problem A physics student caught breaking conservation laws is imprisoned. She leans against the cell wall hoping to tunnel out quantum mechanically. Explain why her chances are negligible. (This is so in any classical situation.)

25CQ Problem Why is the number of neutrons greater than the number of protons in stable nuclei having A greater than about 40, and why is this effect more pronounced for the heaviest nuclei?

25PE Problem ? ? decay producing 137Ba . The parent nuclide is a major waste product of reactors and has chemistry similar to potassium and sodium, resulting in its concentration in your cells if ingested.

In the following eight problems, write the complete decay equation for the given nuclide in the complete \({ }_{Z}^{A} \mathrm{X}_{N}\) notation. Refer to the periodic table for values of \(Z\) \(\alpha\) decay of \({ }^{226} Ra\), another isotope in the decay series of \({ }^{238} U\), first recognized as a new element by the Curies. Poses special problems because its daughter is a radioactive noble gas. In the following four problems, identify the parent nuclide and write the complete decay equation in the \({ }_{Z}^{A} \mathrm{X}_{N}\) notation. Refer to the periodic table for values of \(Z\). Equation Transcription: Text Transcription: _Z ^A X_N Z alpha ^226 Ra ^238 U _Z ^A X_N Z

27CQ Problem When a nucleus ? decays, does the ? particle move continuously from inside the nucleus to outside? That is, does it travel each point along an imaginary line from inside to out? Explain.

22CQ Problem Spontaneous radioactive decay occurs only when the decay products have less mass than the parent, and it tends to produce a daughter that is more stable than the parent. Explain how this is related to the fact that more tightly bound nuclei are more stable. (Consider the binding energy per nucleon.)

27PE Problem ? decay producing 228Ra . The parent nuclide is nearly 100% of the natural element and is found in gas lantern mantles and in metal alloys used in jets ( 228Ra is also radioactive).

28PE Problem ? decay producing 208 Pb . The parent nuclide is in the decay series produced by 232Th , the only naturally occurring isotope of thorium.

Confirm that charge, electron family number, and the total number of nucleons are all conserved by the rule for \(\alpha\) decay given in the equation \(_Z^A\mathrm{X}_N\ \rightarrow_{\ Z-2}^{\ A-4}\mathrm{Y}_{N-2}+_2^4\mathrm{He}_2\). To do this, identify the values of each before and after the decay. Equation Transcription: Text Transcription: alpha _Z ^A X_N rightarrow _Z-2 ^A-4 Y_N-2 + _2 ^4 He_2

Confirm that charge, electron family number, and the total number of nucleons are all conserved by the rule for \(\beta^{-}\) decay given in the equation \(_Z^A\mathrm{X}_N\ \rightarrow_{\ Z-1}^{\ A}\mathrm{Y}_{N-1}+\beta^-+\nu_e\). To do this, identify the values of each before and after the decay. Equation Transcription: Text Transcription: beta^- _Z ^A X_N rightarrow _Z-1 ^A Y_N-1 + beta^- + nu_e

29PE Problem When an electron and positron annihilate, both their masses are destroyed, creating two equal energy photons to preserve momentum. (a) Confirm that the annihilation equation e + + e ? ? ? + ? conserves charge, electron family number, and total number of nucleons. To do this, identify the values of each before and after the annihilation. (b) Find the energy of each ? ray, assuming the electron and positron are initially nearly at rest. (c) Explain why the two ? rays travel in exactly opposite directions if the center of mass of the electron-positron system is initially at rest.

Confirm that charge, electron family number, and the total number of nucleons are all conserved by the rule for \(\beta^{-}\) decay given in the equation \(_Z^A\mathrm{X}_N\ \rightarrow_{\ Z}^{\ A}+1\mathrm{Y}_{N-1}+\beta^-+\overline{\nu}_e\). To do this, identify the values of each before and after the decay. Equation Transcription: Text Transcription: beta^- _Z ^A X_N rightarrow _Z+1 ^A Y_N-1 + beta^- + nu_e ^-

Confirm that charge, electron family number, and the total number of nucleons are all conserved by the rule for electron capture given in the equation \(_Z^A\mathrm{X}_N+e^-\ \rightarrow\ _{Z-1}^A\mathrm{Y}_{N+1}+\nu_e\). To do this, identify the values of each before and after the capture. Equation Transcription: Text Transcription: _Z ^A X_N + e^- rightarrow _Z-1 ^A Y_N+1 + nu_e

34PE Problem A rare decay mode has been observed in which 222Ra emits a 14C nucleus. (a) The decay equation is 222Ra ?A X+14C . Identify the nuclide A X . (b) Find the energy emitted in the decay. The mass of 222Ra is 222.015353 u.

36PE Problem (a) Write the complete ? decay equation for 249Cf . (b) Find the energy released in the decay.

35PE Problem (a) Write the complete ? decay equation for 226Ra . (b) Find the energy released in the decay. (a) Write the complete ? decay equation for 226Ra . (b) Find the energy released in the decay.

Problem 37PE (a) Write the complete ? ? decay equation for the neutron. (b) Find the energy released in the decay.

38PE Problem (a) Write the complete ? ? decay equation for 90Sr , a major waste product of nuclear reactors. (b) Find the energy released in the decay.

40PE Problem (a) Write the complete ? + decay equation for 11C . (b) Calculate the energy released in the decay. The masses of 11C and 11B are 11.011433 and 11.009305 u, respectively.

41PE Problem (a) Calculate the energy released in the ? decay of 238 U . (b) What fraction of the mass of a single 238 U is destroyed in the decay? The mass of 234Th is 234.043593 u. (c) Although the fractional mass loss is large for a single nucleus, it is difficult to observe for an entire macroscopic sample of uranium. Why is this?

43PE Problem (a) Write the complete reaction equation for electron capture by 15 O . (b) Calculate the energy released.

42PE Problem (a) Write the complete reaction equation for electron capture by 7Be. (b) Calculate the energy released.

39PE Problem Calculate the energy released in the ? + decay of 22 Na , the equation for which is given in the text. The masses of 22 Na and 22 Ne are 21.994434 and 21.991383 u, respectively.

44PE Problem Data from the appendices and the periodic table may be needed for these problems. An old campfire is uncovered during an archaeological dig. Its charcoal is found to contain less than 1/1000 the normal amount of 14C . Estimate the minimum age of the charcoal, noting that 2 10 = 1024 .

45PE Problem Data from the appendices and the periodic table may be needed for these problems. A 60Co source is labeled 4.00 mCi, but its present activity is found to be 1.85×107 Bq. (a) What is the present activity in mCi? (b) How long ago did it actually have a 4.00-mCi activity?

47PE Problem Data from the appendices and the periodic table may be needed for these problems. Show that the activity of the 14C in 1.00 g of 12C found in living tissue is 0.250 Bq.

46PE Problem Data from the appendices and the periodic table may be needed for these problems. (a) Calculate the activity R in curies of 1.00 g of 226Ra . (b) Discuss why your answer is not exactly 1.00 Ci, given that the curie was originally supposed to be exactly the activity of a gram of radium.

Problem 48PE Data from the appendices and the periodic table may be needed for these problems. Mantles for gas lanterns contain thorium, because it forms an oxide that can survive being heated to incandescence for long periods of time. Natural thorium is almost 100% 232Th , with a half-life of 1.405×1010 y . If an average lantern mantle contains 300 mg of thorium, what is its activity?

51PE Problem Data from the appendices and the periodic table may be needed for these problems. There is more than one isotope of natural uranium. If a researcher isolates 1.00 mg of the relatively scarce 235 U and finds this mass to have an activity of 80.0 Bq, what is its half-life in years?

50PE Problem Data from the appendices and the periodic table may be needed for these problems. (a) Natural potassium contains 40 K , which has a halflife of 1.277×109 y. What mass of 40 K in a person would have a decay rate of 4140 Bq? (b) What is the fraction of 40 K in natural potassium, given that the person has 140 g in his body? (These numbers are typical for a 70-kg adult.)

52PE Problem Data from the appendices and the periodic table may be needed for these problems. 50 V has one of the longest known radioactive half-lives. In a difficult experiment, a researcher found that the activity of 1.00 kg of 50 V is 1.75 Bq. What is the half-life in years?

53PE Problem Data from the appendices and the periodic table may be needed for these problems. You can sometimes find deep red crystal vases in antique stores, called uranium glass because their color was produced by doping the glass with uranium. Look up the natural isotopes of uranium and their half-lives, and calculate the activity of such a vase assuming it has 2.00 g of uranium in it. Neglect the activity of any daughter nuclides.

54PE Problem Data from the appendices and the periodic table may be needed for these problems. A tree falls in a forest. How many years must pass before the 14C activity in 1.00 g of the tree’s carbon drops to 1.00 decay per hour?

49PE Problem Data from the appendices and the periodic table may be needed for these problems. Cow’s milk produced near nuclear reactors can be tested for as little as 1.00 pCi of 131 I per liter, to check for possible reactor leakage. What mass of 131 I has this activity?

57PE Problem Data from the appendices and the periodic table may be needed for these problems. Natural uranium is 0.7200% 235 U and 99.27% 238 U . What were the percentages of 235 U and 238 U in natural uranium when Earth formed 4.5×109 years ago?

58PE Problem Data from the appendices and the periodic table may be needed for these problems. The ? ? particles emitted in the decay of 3 H (tritium) interact with matter to create light in a glow-in-the-dark exit sign. At the time of manufacture, such a sign contains 15.0 Ci of 3 H . (a) What is the mass of the tritium? (b) What is its activity 5.00 y after manufacture?

56PE Problem Data from the appendices and the periodic table may be needed for these problems. A 5000-Ci 60Co source used for cancer therapy is considered too weak to be useful when its activity falls to 3500 Ci. How long after its manufacture does this happen?

55PE Problem Data from the appendices and the periodic table may be needed for these problems. What fraction of the 40 K that was on Earth when it formed 4.5×109 years ago is left today?

61PE Problem Data from the appendices and the periodic table may be needed for these problems. Armor-piercing shells with depleted uranium cores are fired by aircraft at tanks. (The high density of the uranium makes them effective.) The uranium is called depleted because it has had its 235 U removed for reactor use and is nearly pure 238 U . Depleted uranium has been erroneously called non-radioactive. To demonstrate that this is wrong: (a) Calculate the activity of 60.0 g of pure 238 U . (b) Calculate the activity of 60.0 g of natural uranium, neglecting the 234 U and all daughter nuclides.

World War II aircraft had instruments with glowing radium-painted dials (see Figure 31.2). The activity of one such instrument was \(1.0\times10^5\mathrm{\ Bq}\) when new. (a) What mass of \({ }^{226} \mathrm{Ra}\) was present? (b) After some years, the phosphors on the dials deteriorated chemically, but the radium did not escape. What is the activity of this instrument \(57.0\) years after it was made? Equation Transcription: Text Transcription: 1.0 x 10^5 Bq ^226 Ra 57.0

60PE Problem Data from the appendices and the periodic table may be needed for these problems. (a) The 210 Po source used in a physics laboratory is labeled as having an activity of 1.0 µCi on the date it was prepared. A student measures the radioactivity of this source with a Geiger counter and observes 1500 counts per minute. She notices that the source was prepared 120 days before her lab. What fraction of the decays is she observing with her apparatus? (b) Identify some of the reasons that only a fraction of the ? s emitted are observed by the detector.

63PE Problem Data from the appendices and the periodic table may be needed for these problems. Large amounts of depleted uranium ( 238 U ) are available as a by-product of uranium processing for reactor fuel and weapons. Uranium is very dense and makes good counter weights for aircraft. Suppose you have a 4000-kg block of 238 U . (a) Find its activity. (b) How many calories per day are generated by thermalization of the decay energy? (c) Do you think you could detect this as heat? Explain.

65PE Problem Data from the appendices and the periodic table may be needed for these problems. Construct Your Own Problem Consider the generation of electricity by a radioactive isotope in a space probe, such as described in Exercise 31.64. Construct a problem in which you calculate the mass of a radioactive isotope you need in order to supply power for a long space flight. Among the things to consider are the isotope chosen, its half-life and decay energy, the power needs of the probe and the length of the flight. Reference Exercise 31.64: The Galileo space probe was launched on its long journey past several planets in 1989, with an ultimate goal of Jupiter. Its power source is 11.0 kg of 238 Pu , a by-product of nuclear weapons plutonium production. Electrical energy is generated thermoelectrically from the heat produced when the 5.59-MeV ? particles emitted in each decay crash to a halt inside the plutonium and its shielding. The half-life of 238 Pu is 87.7 years. (a) What was the original activity of the 238 Pu in becquerel? (b) What power was emitted in kilowatts? (c) What power was emitted 12.0 y after launch? You may neglect any extra energy from daughter nuclides and any losses from escaping ? rays.

64PE Problem Data from the appendices and the periodic table may be needed for these problems. The Galileo space probe was launched on its long journey past several planets in 1989, with an ultimate goal of Jupiter. Its power source is 11.0 kg of 238 Pu , a by-product of nuclear weapons plutonium production. Electrical energy is generated thermoelectrically from the heat produced when the 5.59-MeV ? particles emitted in each decay crash to a halt inside the plutonium and its shielding. The half-life of 238 Pu is 87.7 years. (a) What was the original activity of the 238 Pu in becquerel? (b) What power was emitted in kilowatts? (c) What power was emitted 12.0 y after launch? You may neglect any extra energy from daughter nuclides and any losses from escaping ? rays.

66PE Problem Data from the appendices and the periodic table may be needed for these problems. Unreasonable Results A nuclear physicist finds 1.0 µg of 236 U in a piece of uranium ore and assumes it is primordial since its half-life is 2.3×107 y . (a) Calculate the amount of 236 U that would had to have been on Earth when it formed 4.5×109 y ago for 1.0 µg to be left today. (b) What is unreasonable about this result? (c) What assumption is responsible?

67PE Problem Data from the appendices and the periodic table may be needed for these problems. Unreasonable Results (a) Repeat Exercise 31.57 but include the 0.0055% natural abundance of 234 U with its 2.45×105 y half-life. (b) What is unreasonable about this result? (c) What assumption is responsible? (d) Where does the 234 U come from if it is not primordial? Reference Exercise 31.57: Natural uranium is 0.7200% 235 U and 99.27% 238 U . What were the percentages of 235 U and 238 U in natural uranium when Earth formed 4.5×109 years ago?

62PE Problem Data from the appendices and the periodic table may be needed for these problems. The ceramic glaze on a red-orange Fiestaware plate is U2 O3 and contains 50.0 grams of 238 U , but very little 235 U . (a) What is the activity of the plate? (b) Calculate the total energy that will be released by the 238 U decay. (c) If energy is worth 12.0 cents per kW ? h , what is the monetary value of the energy emitted? (These plates went out of production some 30 years ago, but are still available as collectibles.)

68PE Problem Data from the appendices and the periodic table may be needed for these problems. Unreasonable Results The manufacturer of a smoke alarm decides that the smallest current of ? radiation he can detect is 1.00 µA . (a) Find the activity in curies of an ? emitter that produces a 1.00 µA current of ? particles. (b) What is unreasonable about this result? (c) What assumption is responsible?

\({ }^{2} \mathrm{H}\) is a loosely bound isotope of hydrogen. Called deuterium or heavy hydrogen, it is stable but relatively rare - it is \(0.015 \%\) of natural hydrogen. Note that deuterium has \(Z=N\), which should tend to make it more tightly bound, but both are odd numbers. Calculate \(BE/A\), the binding energy per nucleon, for \({ }^{2} \mathrm{H}\) and compare it with the approximate value obtained from the graph in Figure 31.27. Equation Transcription: Text Transcription: ^2 H 0.015% Z = N BE/A ^2 H

74PE Problem (a) Calculate BE / A for 12C . Stable and relatively tightly bound, this nuclide is most of natural carbon. (b) Calculate BE / A for 14C . Is the difference in BE / A between 12C and 14C significant? One is stable and common, and the other is unstable and rare.

72PE Problem (a) Calculate BE / A for 235 U , the rarer of the two most common uranium isotopes. (b) Calculate BE / A for 238 U . (Most of uranium is 238 U .) Note that 238 U has even numbers of both protons and neutrons. Is the BE / A of 238 U significantly different from that of 235 U ?

\({ }^{209} \mathrm{Bi}\) is the heaviest stable nuclide, and its \(BE/A\) is low compared with medium-mass nuclides. Calculate \(BE/A\), the binding energy per nucleon, for \({ }^{209} \mathrm{Bi}\) and compare it with the approximate value obtained from the graph in Figure 31.27. Equation Transcription: Text Transcription: ^209 Bi BE/A BE/A ^209 Bi

\({ }^{56} \mathrm{Fe}\) is among the most tightly bound of all nuclides. It is more than \(90 \%\) of natural iron. Note that \({ }^{56} \mathrm{Fe}\) has even numbers of both protons and neutrons. Calculate \(BE/A\), the binding energy per nucleon, for \({ }^{56} \mathrm{Fe}\) and compare it with the approximate value obtained from the graph in Figure 31.27. Equation Transcription: Text Transcription: ^56 Fe 90% ^56 Fe BE/A ^56 Fe

74PE Problem The fact that BE / A is greatest for A near 60 implies that the range of the nuclear force is about the diameter of such nuclides. (a) Calculate the diameter of an A = 60 nucleus. (b) Compare BE / A for 58 Ni and 90Sr . The first is one of the most tightly bound nuclides, while the second is larger and less tightly bound.

The purpose of this problem is to show in three ways that the binding energy of the electron in a hydrogen atom is negligible compared with the masses of the proton and electron. (a) Calculate the mass equivalent in u of the \(13.6-eV\) binding energy of an electron in a hydrogen atom, and compare this with the mass of the hydrogen atom obtained from Appendix A. (b) Subtract the mass of the proton given in Table 31.2 from the mass of the hydrogen atom given in Appendix A. You will find the difference is equal to the electron’s mass to three digits, implying the binding energy is small in comparison. (c) Take the ratio of the binding energy of the electron \((13.6 \ eV)\) to the energy equivalent of the electron’s mass \((0.511 \ MeV)\). (d) Discuss how your answers confirm the stated purpose of this problem. Equation Transcription: Text Transcription: 13.6-eV (13.6 eV) (0.511 MeV)

77PE Problem Derive an approximate relationship between the energy of ? decay and half-life using the following data. It may be useful to graph the log of t1/2 against E? to find some straight-line relationship.

76PE Problem Unreasonable Results A particle physicist discovers a neutral particle with a mass of 2.02733 u that he assumes is two neutrons bound together. (a) Find the binding energy. (b) What is unreasonable about this result? (c) What assumptions are unreasonable or inconsistent?

Integrated Concepts A \(2.00-T\) magnetic field is applied perpendicular to the path of charged particles in a bubble chamber. What is the radius of curvature of the path of a \(10 \ MeV\) proton in this field? Neglect any slowing along its path. Equation Transcription: Text Transcription: 2.00-T 10 MeV

80PE Problem Unreasonable Results The relatively scarce naturally occurring calcium isotope 48Ca has a half-life of about 2×1016 y . (a) A small sample of this isotope is labeled as having an activity of 1.0 Ci. What is the mass of the 48Ca in the sample? (b) What is unreasonable about this result? (c) What assumption is responsible?

81PE Problem Unreasonable Results A physicist scatters ? rays from a substance and sees evidence of a nucleus 7.5×10–13 m in radius. (a) Find the atomic mass of such a nucleus. (b) What is unreasonable about this result? (c) What is unreasonable about the assumption?

79PE Problem (a) Write the decay equation for the ? decay of 235 U . (b) What energy is released in this decay? The mass of the daughter nuclide is 231.036298 u. (c) Assuming the residual nucleus is formed in its ground state, how much energy goes to the ? particle?

82PE Problem Unreasonable Results A frazzled theoretical physicist reckons that all conservation laws are obeyed in the decay of a proton into a neutron, positron, and neutrino (as in ? + decay of a nucleus) and sends a paper to a journal to announce the reaction as a possible end of the universe due to the spontaneous decay of protons. (a) What energy is released in this decay? (b) What is unreasonable about this result? (c) What assumption is responsible?

26PE Problem ? ? decay producing 90 Y . The parent nuclide is a major waste product of reactors and has chemistry similar to calcium, so that it is concentrated in bones if ingested ( 90 Y is also radioactive.)