Solved: The following nuclei are observed to decay by

Problem 92PP If the half-life of iodine-131 were only half of its actual value, would the activity of the sample in Problem. be increased or decreased? Problem 91. · If a sample of iodine-131 contains 4.5 × 1016 nuclei, what is the activity of the sample? Express your answer in curies. A. 0.27 Ci B. 1.2 Ci. C. 1.7 Ci D. 4.5 Ci

Problem 1CQ (Answers to odd-numbered Conceptual Questions can be found in the back of the book,) Nucleus A and nucleus B have different numbers of protons and different numbers of neutrons. Explain how it is still possible for these nuclei to have equal radii.

Identify , and for the following isotopes: (a) \({ }_{92}^{238} U\), (b) \({ }_{94}^{239} P u\) (c) \({ }_{60}^{144} N d\) Equation Transcription: Text Transcription: 92^238U 94^239Pu 60^144Nd

Identify , and for the following isotopes: (a) \({ }^{202} \mathrm{Hg}\) (b) \({ }_{220} \mathrm{Rn}\), (c) \(\frac{93}{41} \mathrm{Nb}\). Equation Transcription: Text Transcription: 80 ^202 Hg 220 Rn 93 over 41 Nb

Problem 3CQ (Answers to odd-numbered Conceptual Questions can be found in the back of the book,) Is it possible for a form of heavy hydrogen to decay by emitting an ? particle? Explain.

Problem 2CQ (Answers to odd-numbered Conceptual Questions can be found in the back of the book,) Win en ? particles are emitted in a nuclear decay, they have well-defined energies. In contrast, ß particles are found to be emitted with a range of energies. Explain this difference.

What are the nuclear radii of (a) \({ }_{79}^{197} \mathrm{Au}\) and (b) \({ }_{27}^{60} \mathrm{Co}\) ? Equation Transcription: Text Transcription: 79^197 Au 27^60 Co

Problem 4CQ (Answers to odd-numbered Conceptual Questions can be found in the back of the book,) Which is more likely to expose film kept in a cardboard box, ? particles or ß particles? Explain.

Problem 4P A certain chlorine nucleus has a radius of approximately 4.0 × 10?15 m. How many neutrons are in this nucleus?

Problem 5CQ (Answers to odd-numbered Conceptual Questions can be found in the back of the book,) It is not possible for a stable nucleus to contain more than one proton without also having at least one neutron. Explain why neutrons are necessary in a stable, multi particle nucleus.

(a) What is the nuclear density of \(\frac{228}{90} T h\) ? (b) Do you expect the nuclear density of an alpha particle to be greater than, less than, or the same as that of \(\frac{228}{90} T h\)? Explain. (c) Calculate the nuclear density of an alpha particle. Equation Transcription: Text Transcription: \frac{228}{90} T h \frac{228}{90} T h

Problem 6CQ (Answers to odd-numbered Conceptual Questions can be found in the back of the book,) Different isotopes of a given element have different masses, but they have the same chemical properties. Explain why chemical properties are unaffected by a change of isotope.

Problem 6P IP (a) What initial kinetic energy must an alpha particle bave if it is to approach a stationary gold nucleus to within a distance of 22.5 fm? (b) If the initial speed of the alpha particle is reduced by a factor of 2,by what factor is the distance of closest approach changed? Explain.

Problem 7CQ (Answers to odd-numbered Conceptual Questions can be found in the back of the book,) (a) Give three examples of objects for winch carbon-14 dating would give useful results. (b) Give three examples of objects for which carbon-14 dating would not be useful.

IP An \(\alpha\) particle with a kinetic energy of approaches a stationary gold nucleus. (a) What is the speed of the \(\alpha\) particle? (b) What is the distance of closest approach between the \(\alpha\) particle and the gold nucleus? (c) If this same \(\alpha\) particle were fired at a copper nucleus instead, would its distance of closest approach be greater than, less than, or the same as that found in part (b)? Explain. (To obtain the mass of an alpha particle, refer to Appendix and subtract the mass of two electrons from the mass of \({ }_{2}^{4} \mathrm{He}\).) Equation Transcription: Text Transcription: \alpha \alpha \alpha \alpha 24He

Problem 8CQ (Answers to odd-numbered Conceptual Questions can be found in the back of the book,) Explain why the large, stable nuclei in Figure 32-1 are found to lie above the N = Z line, rather than below the une.

Problem 8P Suppose a marble with a radius of 1.5 cm has the density of a nucLeus, as given in Example 32–2. (a) What is the mass of this marble? (b) How many of these marbles would be required to have a mass equal to the mass of Earth?

Problem 9CQ (Answers to odd-numbered Conceptual Questions can be found in the back of the book,) Suppose each of the following items is about 10,000 years old: a feather, a tooth, an obsidian arrowhead, a deer hide moccasin. Which of these items cannot be dated with carbon-14? Explain.

IP (a) Find the nuclear radius of \(\frac{30}{15} P\), (b) What mass number would be required for a nucleus to have twice the radius found in part (a)? (c) Verify your answer to part (b) with an explicit calculation. Equation Transcription: Text Transcription: \frac{30}{15} P

Problem 10CQ (Answers to odd-numbered Conceptual Questions can be found in the back of the book,) Can carbon-14 dating give the age of fossil dinosaur skeletons? Explain.

An alpha particle is the nucleus of \(a_{2}^{4} H e\) atom. (a) How many nucleons are in a nucleus with twice the radius of an alpha particle? Explain. (b) Write the symbol for a phosphorus nucleus that has twice the radius of an alpha particle. Equation Transcription: Text Transcription: a_{2}^{4} H e

Problem 11CQ (Answers to odd-numbered Conceptual Questions can be found in the back of the book,) Two different samples contain the same radioactive isotope. Is it possible for these samples to have different activities? Explain.

Problem 11P IP Suppose a uranium-236 nucleus undergoes fission by splitting into two smaller nuclei of equal size. (a) Is the radius of each of the smaller nuclei one-half, more than one-half, or less than one-half the radius of the uranium-236 nucleus? Explain. (b) Calculate the radius of the uranium-236 nucleus. (c) Calculate the radii of the two smaller nuclei.

Problem 12CQ (Answers to odd-numbered Conceptual Questions can be found in the back of the book,) Two samples contain different radioactive isotopes. Is it possible for these samples to have the same activity? Explain.

Problem 12P A hypothetical nucleus weighs 11b. (a) How many nucleons are in this nucleus? (b) What is the radius of this nucleus?

Problem 13CQ (Answers to odd-numbered Conceptual Questions can be found in the back of the book,) Two different types of radiation deliver the same amount of energy to a sample of tissue. Does it follow that each of these types of radiation has the same RBE? Explain.

Problem 13P CE Predict/Explain Consider a nucleus that undergoes ? decay. (a) Is the radius of the resulting daughter nucleus greater than, less than, or equal to the radius of the original nucleus? (b) Choose the test explanation from among the following: I. The decay adds an alpha particle to the nucleus, causing its radius to increase. II. When the nucleus undergoes decay it ejects two neutrons and two protons. This decreases the number of nucleons in the nucleus, and therefore its radius will decrease. III. An ? decay leaves the number of nucleons unchanged. As a result, the radius of the nucleus stays the same.

Problem 14P CE Predict/Explain Consider a nucleus that undergoes ß decay. (a) Is the radius of the resulting daughter nucleus greater than, less than, or the same as that of the original nucleus? (b) Choose the best explanation from among the following: I. Capturing a ß particle will cause the radius of a nucleus to increase. Therefore, the daughter nucleus has the greater radius. II. The original nucleus emits a ß particle, and anytime a particle is emitted from a nucleus the result is a smaller radius. Therefore, the radius of the daughter nucleus is less than the radius of the original nucleus, III When a nucleus emits a ? particle a neutron is convened proton, but the number of nucleons is unchanged. As a result, the radius of the daughter nucleus is the same as that of the original nucleus.

Complete the following nuclear reaction: \({ }_{3}^{7} \mathrm{Li}+{ }_{1} \mathrm{H} \rightarrow{ }_{2}^{4} \mathrm{He}+\) ? Equation Transcription: Text Transcription: _3^7 Li +_1 H \rightarrow _2 ^ 4 He+

Complete the following nuclear reaction: \({ }_{90}^{234} \mathrm{Th} \rightarrow{ }_{88}^{230} \mathrm{Ra}+\)? Equation Transcription: Text Transcription: _90^234 Th \rightarrow_88^230 Ra+

Complete the following nuclear reaction:? \(\rightarrow{ }_{7}^{14} N+e^{-}+v^{-}\) Equation Transcription: Text Transcription: \rightarrow_7^14 N+e^-+v^-

One possible decay series for \({ }_{92}^{238} \mathrm{U} i S_{9}^{23} \mathrm{Th},{ }_{91}^{234} \mathrm{~Pa},{ }^{234} U,{ }^{230} \mathrm{Th},{ }_{88}^{226} \mathrm{Ra},{ }^{222} 86 \mathrm{R},{ }^{218} \mathrm{P}_{8},{ }^{218} \mathrm{At},{ }^{218} \mathrm{Rn},{ }^{214} \mathrm{P}_{84},{ }^{210} \mathrm{~Pb},{ }^{210} \mathrm{Bi},{ }^{206} \mathrm{Tl}\) and \({ }_{82}^{206} \mathrm{~Pb}\) Identify, in the order given, each of the 14 decays that occur in this series. Equation Transcription: Text Transcription: 92^238U is 9^23Th, 91^234 Pa, 234 U, 90^230Th, 88^226Ra, 222^86R, 84^218Po, 85^218At, 82^18Rn, 84^214Po, 82^210Pb, 83^210Bi, 81^206Tl 82^206Pb

Complete the following nuclear reaction and determine the amount of energy it releases: \({ }_{1}^{3} H \rightarrow{ }_{2}^{3} H e+?+?\) Be sure to take into account the mass of the electrons associated with the neutral atoms. Equation Transcription: Text Transcription: { }_{1}^{3} H \rightarrow{ }_{2}^{3} H e+?+?

The following nuclei are observed to decay by emitting an particle: (a) \({ }_{84}^{212} P_{0}\) and (b) \({ }_{94}^{239} P u\) Write out the decay process for each of these nuclei, and determine the energy released in each reaction. Be sure to take into account the mass of the electrons associated with the neutral atoms. Equation Transcription: Text Transcription: 84^212Po 94^239Pu

The following nuclei are observed to decay by emitting a \(\beta^{-}\) particle: 1. \({ }_{16}^{35} S\) and 2. \({ }_{82}^{212} P b\) Write out the decay process for each of these nuclei, and determine the energy released in each reaction. Be sure to take into account the mass of the electrons associated with the neutral atoms. Equation Transcription: Text Transcription: \beta^- 16^35S 82^212Pb

The following nuclei are observed to decay by emitting a \(\beta^{+}\) particle: (a) \({ }^{18} \mathrm{~F}\) and (b) \({ }_{11}^{22} \mathrm{Na}\). Write out the decay process for each of these nuclei, and determine the energy released in each reaction. Be sure to take into account the mass of the electrons associated with the neutral atoms. Equation Transcription: Text Transcription: \beta^{+} 18F 11^22Na

Find the energy released when \({ }_{82}^{211} \mathrm{~Pb}\) undergoes \(\beta^{-}\) decay to become \({ }_{83}^{211} \mathrm{Bi}\). Be sure to take into account the mass of the electrons associated with the neutral atoms. Equation Transcription: Text Transcription: 82^211Pb \beta^{-} 83^211Bi

It is observed that \({ }_{28}^{66} \mathrm{Ni}\), with an atomic mass of , decays by \(\beta^{-}\) emission. (a) Identify the nucleus that results from this decay. (b) If the nucleus found in part (a) has an atomic mass of , what is the maximum kinetic energy of the emitted electron? Equation Transcription: Text Transcription: 28^66Ni \beta^{-}

Problem 26P · CE The half-life of carbon-14 is 5730 y. (a) Is it possible for a particular nucleus in a sample of carbon-14 to decay after only 1 s has passed? Explain. (b) Is it possible for a particular nucleus to decay after 10,000 y? Explain.

Problem 27P · CE Suppose we were to discover that the ratio of carbon-14 to carbon-12 in the atmosphere was significantly smaller 10,000 years ago than it is today. How would this affect the ages we have assigned to objects on the basis of carbon-14 dating? In particular, would the true age of an object be greater than or less than the age we had previously assigned to it? Explain.

Problem 28P · CE A radioactive sample is placed in a closed container. Two days later only one-quarter of the sample is still radioactive. What is the half-life of this sample?

Problem 29P · Radon gas has a half-life of 3.82 d. What is the decay constant for radon?

Problem 30P · A radioactive substance has a decay constant equal to 8.9 × 10?3 s?1. What is the half-life of this substance?

Problem 31P The number of radioactive nuclei in a particular sample decreases over a period of 18 d to one-sixteenth the original number. What is the half-life of these nuclei?

The half-life of \({ }_{8}^{15} O\) is . How long does it take for the number of \({ }_{8}^{15} O\) nuclei in a given sample to decrease by a factor of \(10^{-4}\) ? Equation Transcription: Text Transcription: 8^15O 8^15O 10-^4

A Radioactive Tag A drug prepared for a patient is tagged with \({ }_{43}^{99} T c\), which has a half-life of . (a) What is the decay constant of this isotope? (b) How many \({ }_{43}^{99} T c\) nuclei are required to give an activity of \(1.50 \mu C i\)? Equation Transcription: Text Transcription: 43^99Tc 43^99Tc 1.50 \mu C i

Referring to Problem 33, suppose the drug containing \({ }_{43}^{99} T c\) with an activity of \(1.50 \mu C i) is injected into the patient after it is prepared. What is its activity at the time it is injected? Equation Transcription: Text Transcription: 43^99Tc 1.50 \mu C i

Problem 35P An archeologist on a dig finds a fragment of an ancient basket woven from grass. Later, it is determined that the carbon-14 content of the grass in the basket is 9.25% that of an equal carbon sample from present-day grass. What is the age of the basket?

Problem 36P The bones of a saber-toothed tiger are found to have an activity per gram of carbon that is 15.0% of what would be found in a similar live animal. How old are these bones?

Problem 37P Charcoal from an ancient fire pit is found to have a carbon-14 content that is only 17.5% that of an equivalent sample of carbon from a living tree. What is the age of the fire pit?

Smoke Detectors The radioactive isotope \({ }_{95}^{241} \mathrm{Am}\), with a half-life of , is the active element in many smoke detectors. Suppose such a detector will no longer function if the activity of the \({ }^{241} \mathrm{Am}\) it contains drops below \(\frac{1}{525}\) of its initial activity. How long will this smoke detector work? Equation Transcription: Text Transcription: 95^241 Am 24^1Am 15 over 25

BIO Radioactivity in the Bones Because of its chemical similarity to calcium, \({ }_{38} S r\) can collect in the bones and present a health risk. What percentage of \({ }_{38}^{90} \mathrm{Sr}\) present initially still exists after a period of (a) \(50.0 y \) (b) \(60.0 y \), and (c) \(70.0 y \)? Equation Transcription: Text Transcription: _38 Sr 38^90 Sr 50.0y 60.0y 70.0y

One of the many isotopes used in cancer treatment is \({ }_{79}^{198} \mathrm{Au}\) with a half-life of 2.70 d. Determine the mass of this isotope that is required to give an activity of 225 Ci. Equation Transcription: Text Transcription: 79^198Au

Problem 41P The atomic mass of gold-197 is 196.96654 u. How much energy is required to completely separate the nucleons in a gold-197 nucleus?

Problem 42P The atomic mass of lithium-7 is 7.016003 u. How much energy is required to completely separate the nucleons in a lithium-7 nucleus?

Calculate the average binding energy per nucleon of (a) \({ }_{26}^{56} \mathrm{Fe}\) and (b) \({ }_{92}^{238} \mathrm{U}\) Equation Transcription: Text Transcription: 26^56 Fe 92^238 U

Calculate the average binding energy per nucleon of (a) \({ }_{2}^{4} \mathrm{He}\) and (b) \({ }_{3}^{64} \mathrm{Zn}\). Equation Transcription: Text Transcription: 2^4 He 3^64 Zn

Find the energy required to remove one neutron from \({ }_{8}^{16} \mathrm{O}\) Equation Transcription: Text Transcription: 8^16O

(a) Consider the following nuclear process, in which a proton is removed from an oxygen nucleus: \({ }_{8}^{16} \mathrm{O}+\text { energy } \rightarrow{ }_{7}^{15} \mathrm{~N}+{ }_{1} \mathrm{H}\) Find the energy required for this process to occur. (b) Now consider a process in which a neutron is removed from an oxygen nucleus: \({ }_{8}^{16} \mathrm{O}+\text { energy } \rightarrow{ }_{8}^{15} \mathrm{~N}+{ }_{0}^{1} \mathrm{H}\) Find the energy required for this process to occur. (c) Which particle, the proton or the neutron, do you expect to be more tightly bound in the oxygen nucleus? Verify your answer. Equation Transcription: Text Transcription: _8^16 O+ energy \rightarrow_7^15 N+_1 H _8^16 O+energy \rightarrow _8^15 N+_0^1H

Find the number of neutrons released by the following fission reaction: \({ }_{0}^{1} \mathrm{n}+{ }_{92}^{235} \mathrm{U} \rightarrow \frac{132}{50} \mathrm{Sn}+{ }_{42}^{101} \mathrm{Mo}+(?) \text { neutrons }\) Equation Transcription: Text Transcription: _0^1 n+ _92^235 U \rightarrow \frac{132 50 Sn+ _42^101 Mo+(?) neutrons

Complete the following fission reaction and determine the amount of energy it releases: \({ }_{0}^{1} \mathrm{n}+{ }_{92}^{235} \mathrm{U} \rightarrow{ }_{51}^{133} \mathrm{Sb}+?+5_{0}^{1} \mathrm{n}\) Equation Transcription: Text Transcription: _0^1 n+_92^235 U \rightarrow{_51^133 Sb+?+5_0^1 n

Complete the following fission reaction and determine the amount of energy it releases: \({ }_{0}^{1} n+{ }_{92}^{235} U \rightarrow{ }_{38}^{88} S r+{ }_{54}^{136} X e+(?) \text { neutrons }\) Equation Transcription: Text Transcription: _0^1 n+_92^235 U \rightarrow_38^88 S r+_54^136 X e+(?) neutrons

A gallon of gasoline releases about \(2.0 \times 10^{8} J\) of energy when it is burned. How many gallons of gas must be burned to release the same amount of energy as is released when \(1.0 \mathrm{lb}\) of \({ }_{92}^{235} \mathrm{U}\) undergoes fission. (Assume that each fission reaction in \({ }_{92}^{235} \mathrm{U}\) releases \(173 \mathrm{MeV}\).) Equation Transcription: Text Transcription: * 2.0 \times 10^8 J 1.0 lb _92^235 U _92^235 U 173 MeV

Assuming a release of \(173 \mathrm{MeV}\) per fission reaction, determine the minimum mass of \({ }_{92}^{235} \mathrm{U}\) that must undergo fission to supply the annual energy needs of the United States. (The amount of energy consumed in the United States each year is \(8.4 \times 10^{19} \mathrm{~J}\).) Equation Transcription: Text Transcription: 173 MeV 92^235 U 8.4 x 10^19 J

Problem 52P Assuming a release of 173 MeV per fission reaction, calculate how many reactions must occur per second to produce a power output of 150 MW.

Problem 53P Consider a fusion reaction in which two deuterium nuclei fuse to form a tritium nucleus and a proton.How much energy is released in this reaction?

Problem 54P Consider a fusion reaction in which a proton fuses with a neutron to form a deuterium nucleus. How much energy is released in this reaction?

Find the energy released in the following fusion reaction: \({ }_{1}^{1} H+{ }_{1}^{2} H \rightarrow{ }_{2}^{3} H e+\gamma\) Equation Transcription: Text Transcription: _1^1 H+_1^2 H \rightarrow _2^3 H e+\gamma

Problem 58P BIO Radiation Damage A sample of tissue absorbs a 55-rad dose of ? particles (RBE = 20). How many rad of protons (RBB = 10) cause the same amount of damage to the tissue?

Problem 59P BIO X-ray Damage How many rad of 200-keV X-rays cause the same amount of biological damage as 50 rad of heavy ions?

Problem 60P IP BIO (a) Find the energy absorbed by a 78-kg person who is exposed to 52 mrem of ? particles with an “RBE of 15. (b) If the RBE of the ? particles is increased, does the energy absorbed increase, decrease, or stay the same? Explain.

Problem 61P BIO A patient undergoing radiation therapy for cancer receives a 225-rad dose of radiation. (a) Assuming the cancerous growth has a mass of 0.17 kg, calculate how much energy it absorbs. (b) Assuming the growth to have the specific heat of water, determine its increase in temperature.

Problem 62P BIO Alpha particles with an RBE of 13 deliver a 32-mrad whole-body radiation dose to a 72-kg patient. (a) What dosage, in rem, does the patient receive? (b) How much energy is absorbed by the patient?

A Radioactive Pharmaceutical As part of a treatment program, a patient ingests a radioactive pharmaceutical containing \({ }_{15}^{32} P\), which emits \(\beta\) rays with an of The halflife of \({ }_{15}^{32} P\) is , and the initial activity of the medication is MBq. (a) How many electrons are emitted over the period of If the \(\beta\) rays have an energy of , what is the total amount of energy absorbed by the patient's body in ? (c) Find the absorbed dosage in rem, assuming the radiation is absorbed by \(125 \mathrm{~g}\) of tissue. Equation Transcription: Text Transcription: _{15}^{32} P \beta _{15}^{32} P \beta 125 g

Problem 64GP CE An ? particle (charge + 2e)and a ß particle (charge ? e) deflect in opposite directions when they pass through a magnetic field. Which particle defLects by a greater amount, give that both particles have the same speed? Explain.

Problem 65GP CE Radioactive samples A and B have equal half-lives. The initial activity of sample A is twice that of sample B. What is the ratio of the activity of sample A to that of sample B after two half-lives have elapsed?

Problem 66GP CE The initial activity of sample A is twice that of sample B After two half-lives of sample A have elapsed, the two samples have the same activity. What is the ratio of the half-life of B to the half-life of A?

To produce a given amount of electrical energy, is the amount of coal burned in a coal-burning power plant greater than, less than, or the same as the amount of \({ }_{92}^{235} U\) consumed in a nuclear power plant? Explain. Equation Transcription: Text Transcription: _{92}^{235} U

Determine the number of neutrons and protons in (a) \({ }_{90}^{232} \mathrm{Th}\), (b) \({ }_{82}^{211} \mathrm{~Pb}\), and (c) \({ }_{27}^{60} \mathrm{Co}\) Equation Transcription: Text Transcription: _{90}^{232} Th _{82}^{211} Pb _{27}^{60} Co

Identify the daughter nucleus that results when (a) \({ }_{82}^{210} \mathrm{~Pb}\) undergoes \(\alpha\) decay, (b) \({ }_{92}^{239} U\) undergoes \(\beta^{-}\) decay, and (c) \({ }_{6}^{11} C\) undergoes \(\beta^{+}\) decay. Equation Transcription: Text Transcription: { }_{82}^{210} Pb \alpha _{92}^{239} U \beta^{-} { }_{6}^{11} C \beta^{+}

Problem 70GP Suppose it is desired to give a cancerous tumor a dose of 3800 rem. How many rads are needed if the tumor is exposed to alpha radiation?

Problem 71GP A patient is exposed to 260 rad of gamma rays. What is the dose the patient receives in rem?

The two radioactive decay series that begin with \({ }_{90}^{232} \mathrm{Th}\) and end with \({ }_{82}^{208} \mathrm{~Pb}\) are shown in Figure 32–14. Identify the ten intermediary nuclei that appear in these series. Equation Transcription: Text Transcription: _{90}^{232} Th _{82}^{208} Pb

Problem 73GP Moon Rocks In one of the rocks brought back from the Moon, it is found that 80.5% of the initial potassium-40 in the rock has decayed to argon-40. (a) If the half-life for this decay is 1.20 × 109 years, how old is the rock? (b) How much longer will it take before only 10.0% of the original potassium-40 is still present in the rock?

Mantles in Gas Lanterns Gas lanterns used on camping trips have mantles (small lacy bags that give off light) made from a rayon mesh impregnated with thorium and other materials. Thorium is used, even though it is radioactive, because it forms an oxide that can withstand being incandescent for long periods of time. Almost all natural thorium is \({ }_{90}^{232} T h\) which has a half-life of \(1.405 \times 10^{10} y\). (a) A typical mantle contains 325 mg of thorium. What is the activity of the mantle? (b) If the half-life of thorium had been double its actual value, by what factor would the activity of a mantle be changed? Explain. Equation Transcription: Text Transcription: _{90}^{232} T h 1.405 \times 10^{10} y

Identify the nucleus whose \(\beta^{-}\) decay produces the same nucleus as that produced by the decay of \({ }_{84}^{214} \mathrm{PO}\). Equation Transcription: Text Transcription: \beta^- _84^214 PO

Problem 76GP An ? particle fired head-on at a stationary nickel nucleus approaches to a radius of 15 fm before being turned around. (a) What is the maximum Coulomb force exerted on the ? particle? (b) What is the electric potential energy of the ? particle at its point of closest approach? (c) Find the initial kinetic energy of the ? particle.

Calculate the number of disintegrations per second that one would expect from a 1.7-g sample of \({ }_{88}^{226} R a\) What is the activity of this sample in curies? Equation Transcription: Text Transcription: _88^226 R a

Problem 78GP IP Initially, a sample of radioactive nuclei of type A contains four times as many nuclei as a sample of radioactive nuclei of type B. Two days later (2.00 d) the two samples contain the same number of nuclei. (a) Which type of nucleus has the longer half-life? Explain. (b) Determine the half-life of type B nuclei if the half-life of type A nuclei is known to be 0.500 d.

Problem 79GP Stable nuclei have mass numbers that range from a minimum of 1 to a maximum of 209. (a) Find the corresponding range in nuclear radii. (b) Assuming all nuclei to be spherical, determine the ratio of the surface area of the largest stable nucleus to the surface area of the smallest nucleus. (c) Repeat part (b), only this time find the ratio of the volumes.

Problem 80GP Radius of a Neutron Star Neutron stars are so named because they are composed of neutrons and have a density the same as that of a nucleus. Referring to Example 32–2 for the nuclear density, find the radius of a neutron star whose mass is 0.50 that of the Sun.

Problem 81GP A specimen taken from the wrappings of a mummy contains 7.82 g of carbon and has an activity of 1.38 Bq. How old is the mummy? (Refer to pages 1132 and 1133 for relevant information regarding the isotopes of carbon.)

(a) How many fission reactions are required to light a 120-W light bulb for 2.5 d? Assume an energy release of 212 MeV per fission reaction and a 32% conversion efficiency. (b) What mass of \({ }_{92}^{235} U\) corresponds to the number of fission reactions found in part (a)? Equation Transcription: Text Transcription: _92^235 U

Problem 83GP IP Energy is released when three ? particles fuse to form carbon-12. (a) Is the mass of carbon-12 greater than, less than, or the same as the mass of three ? particles? Explain. (b) Calculate the energy given off in this fusion reaction.

Problem 84GP Find the dose of y rays that must be absorbed by a block of ice at 0 °C to convert it to water at 0 °C.-Givc the dosage inrad.

Problem 85GP IP (a) What dosage (in rad) must a 1.0-kg sample of water absorb to increase its temperature by 1.0 C°? (b) Tf the mass of the water sample is increased, does the dosage found in part (a) increase, decrease, or stay the same? Explain.

Problem 86GP BIO Chest X-rays A typical chest X-ray uses X-rays with an RBE of 0.85. If the radiation dosage is 35 mrem, find the energy absorbed by a 72-kg patient, assuming one-quarter of the patient’s body is exposed to the X-rays.

A \(\gamma\) ray photon emitted by \({ }_{88}^{226} R a\) has an energy of 0.186 MeV. Use conservation of linear momentum to calculate the recoil speed of a \({ }_{88}^{226} R a\) nucleus after such a ray is emitted. Assume that the nucleus is at rest initially, and that relativistic effects can be ignored. Equation Transcription: Text Transcription: \gamma _88^226 R a _88^226 R a

The energy released by \(\alpha\) decay in a 50.0-g sample of \({ }_{94}^{239} P u\) is to be used to heat 4.75 kg of water. Assuming all the energy released by the radioactive decay goes into heating the water, find how much the temperature of the water increases in 1.00 h. Equation Transcription: Text Transcription: \alpha _94^239 P u

Consider a solid sphere of \({ }_{92}^{235} U\) with a radius of 2.25 cm in a room with a temperature of 293 K. Assume that all the energy released by decay goes into heating the sphere, and that the sphere radiates heat to its surroundings as a blackbody. What is the change in temperature of the sphere as a result of the \(\alpha\) decay? (Note: The density of uranium is \(118.95 \mathrm{~g} / \mathrm{cm}^{3}\).) Equation Transcription: Text Transcription: _92^235 U \alpha 18.95 g/cm^3

Problem 90PP What is the decay constant, A, for iodine-131? A. 9.98 ×10?7 s?1 B. 1.44 × ×10?6 s?1 C. 2.39 ×10?5 s?1 D. 5.99 ×10?5 s?1

Problem 91PP If a sample of iodine-131 contains 4.5 × 1016 nuclei, what is the activity of the sample? Express your answer in curies. A. 0.27 Ci B. 1.2 Ci. C. 1.7 Ci D. 4.5 Ci

Problem 15P CE Which of the three decay processes (?, ß or ?)results in a new element? Explain.

(a) Complete the following fusion reaction and determine the energy it releases: \({ }_{1}^{2} \mathrm{H}+{ }_{1}^{3} \mathrm{H} \rightarrow ?+{ }_{0}^{1} \mathrm{n}\) (b) How many of these reactions must occur per second to produce a power output of 25 MW? Equation Transcription: Text Transcription: _1^2 H+ _1^3 H \rightarrow ?+_0^1 n

Problem 57P The Evaporating Sun The Sun radiates energy at the prodigious rate of 3.90 × 1026 W. (a) At what rate, in kilograms per second, does the Sun convert mass into energy? (b) Assuming that the Sun has radiated at this same rate for its entire lifetime of 4.50 × 109 y, and that the current mass of the Sun is 2.00 × 1030 kg, what percentage of its original mass has been converted to energy?.