Two of the naturally occurring radioactive decay sequences

(I) A pi meson has a mass of \(139 MeV/c^{2}\). What is this in atomic mass units? Equation Transcription: Text Transcription: 139 MeV/c^2

(I) What is the approximate radius of an \(\alpha\) particle \(\left({ }_{2}^{4} \mathrm{He}\right)\) ? Equation Transcription: Text Transcription: alpha {}_({2}^{4}He

(I) By what \% is the radius of \({ }_{92}^{238} \mathrm{U}\) greater than the radius of \({ }_{92}^{232} \mathrm{U}\)? Equation Transcription: Text Transcription: { }_{92}^{238}U { }_{92}^{238}U

(II) (a) What is the approximate radius of a \({ }_{48}^{112} \mathrm{Cd}\) nucleus? (b) Approximately what is the value of \(A\) for a nucleus whose radius is \(3.7 \times 10^{-15} \mathrm{~m}\)? Equation Transcription: Text Transcription: { }_{48}^{112} Cd A 3.7 x 10^-15m

(II) What is the mass of a bare \(\alpha\) particle (without electrons) in \(\mathrm{MeV} / c^{2}\)? Equation Transcription: Text Transcription: alpha MeV/c^2

Suppose two alpha particles were held together so they were just touching(use Eq.301). Estimate the electrostatic repulsive force each would exert on the other. What would be the acceleration of an alpha particle subjected to this force?

(II) (a) What would be the radius of the Earth if it had its actual mass but had the density of nuclei? (b) By what factor would the radius of a \({ }_{92}^{238} \mathrm{U}\) nucleus increase if it had the Earth's density? Equation Transcription: Text Transcription: { }_{92}^{238}U

(II) What stable nucleus has approximately half the radius of a uranium nucleus? [Hint: Find \(A\) and use Appendix B to get \(Z\).] Equation Transcription: Text Transcription: A Z

(II) If an alpha particle were released from rest near the surface of a \({ }_{100}^{257} \mathrm{Fm}\) nucleus, what would its kinetic energy be when far away? Equation Transcription: Text Transcription: { }_{100}^{257}Fm

(II) (a) What is the fraction of the hydrogen atom's mass \(\left({ }_{1}^{1} \mathrm{H}\right)\) that is in the nucleus? (b) What is the fraction of the hydrogen atom's volume that is occupied by the nucleus? Equation Transcription: Text Transcription: ({ }_{1}^{1}H)

Approximately how many nucleons are there in a 1.0-kg object? Does it matter what the object is made of? Why or why not?

How much kinetic energy, in MeV, must an particle have to just touch the surface of a nucleus?

(I) Estimate the total binding energy for \(^{63} _{29} Cu\), using Fig. 30-1.

(I) Use Fig. 30-1 to estimate the total binding energy of (a) \({ }_{92}^{238} \mathrm{U}\), and (b) \({ }_{36}^{84} \mathrm{Kr}\). Equation Transcription: Text Transcription: { }_{92}^{238} U { }_{36}^{84} Kr

(II) Calculate the binding energy per nucleon for a \({ }_{7}^{15} \mathrm{~N}\) nucleus, using Appendix B. Equation Transcription: Text Transcription: { }_{7}^{15}N

(II) Use Appendix B to calculate the binding energy of \({ }_{1}^{2} \mathrm{H}\) (deuterium). Equation Transcription: Text Transcription: { }_{1}^{2}H

(II) Determine the binding energy of the last neutron in a \({ }_{11}^{23} \mathrm{Na}\) nucleus. Equation Transcription: Text Transcription: { }_{11}^{23} Na

(II) Calculate the total binding energy, and the binding energy per nucleon, for (a) \({ }_{3}^{7} \mathrm{Li}\), (b) \({ }_{78}^{195} \mathrm{Pt}\). Use Appendix B. Equation Transcription: Text Transcription: { }_{3}^{7} Li { }_{78}^{195} Pt

(II) Compare the average binding energy of a nucleon in \(^{23} _{11} Na\) to that in \(^{24} _{11} Na\), using Appendix B.

(III) How much energy is required to remove (a) a proton, (b) a neutron, from \({ }_{7}^{15} \mathrm{~N}\)? Explain the difference in your answers. Equation Transcription: Text Transcription: { }_{7}^{15} N

(III) (a) Show that the nucleus \(^8 _4 Be\) (mass = 8.005305 u) is unable and will decay into two \(\alpha\) particles. (b) Is \(^{12} _6 C\) stable against decay into three \(\alpha\) particles? Show why or why not.

(I) The \({ }_{3}^{7} \mathrm{Li}\) nucleus has an excited state 0.48 MeV above the ground state. What wavelength gamma photon is emitted when the nucleus decays from the excited state to the ground state? Equation Transcription: Text Transcription: { }_{3}^{7} Li

(II) Show that the decay \(^{11} _6 C\ \rightarrow\ ^{10} _5 B + p\) is not possible because energy would not be conserved.

(II) Calculate the energy released when tritium, \(^3 _1H\), decays by \(\beta^-\) emission.

(II) What is the maximum kinetic energy of an electron emitted in the \(\beta\) decay of a free neutron? Equation Transcription: Text Transcription: beta

(II) Give the result of a calculation that shows whether or not the following decays are possible: (a) \({ }_{92}^{233} \mathrm{U} \rightarrow{ }_{92}^{232} \mathrm{U}+\mathrm{n}\); (b) \({ }^{14}{ }_{7} \mathrm{~N} \rightarrow{ }_{7}^{13} \mathrm{~N}+\mathrm{n}\); (c) \({ }_{19}^{40} \mathrm{~K} \rightarrow{ }_{19}^{39} \mathrm{~K}+\mathrm{n}\). Equation Transcription: Text Transcription: { }_{92}^{233} U rightarrow{ }_{92}^{232} U + n { }^{14}{ }_{7} N rightarrow{ }_{7}^{13} N} + n { }_{19}^{40} K rightarrow{ }_{19}^{39} K + n

(II) \({ }_{11}^{24} \mathrm{Na}\) is radioactive. (a) Is it a \(\beta^{-}\)or \(\beta^{+}\) emitter? (b) Write down the decay reaction, and estimate the maximum kinetic energy of the emitted \(\beta\). Equation Transcription: Text Transcription: { }_{11}^{24} Na beta^- beta^+ beta

(II) A \({ }_{92}^{238} \mathrm{U}\) nucleus emits an \(\alpha\) particle with kinetic energy = 4.20 MeV. (a) What is the daughter nucleus, and (b) what is the approximate atomic mass (in u) of the daughter atom? Ignore recoil of the daughter nucleus. Equation Transcription: Text Transcription: { }_{92}^{238} U alpha

(II) Calculate the maximum kinetic energy of the \(\beta\) particle emitted during the decay of \(^{60} _{27} Co\).

(II) How much energy is released in electron capture by beryllium: \({ }_{4}^{7} \mathrm{Be}+\mathrm{e}^{-} \rightarrow{ }_{3}^{7} \mathrm{Li}+\nu\)? Equation Transcription: Text Transcription: { }_{4}^{7} Be + {e}^{-} \rightarrow{ }_{3}^{7} Li + nu

(II) The isotope \({ }_{84}^{218}Po\) can decay by either \(\alpha\) or \(\beta^{-}\) emission. What is the energy release in each case? The mass of \({ }_{84}^{218} \mathrm{Po}\) is 218.008973 u. Equation Transcription: Text Transcription: { }_{84}^{218}Po alpha beta { }_{84}^{218}Po

(II) The nuclide \({ }_{15}^{32} \mathrm{P}\) decays by emitting an electron whose maximum kinetic energy can be 1.71 MeV. (a) What is the daughter nucleus? (b) Calculate the daughter's atomic mass (in u). Equation Transcription: Text Transcription: { }_{15}^{32} \mathrm{P}

(II) A photon with a wavelength of \(1.15 \times 10^{-13}\ m\) is ejected from an atom. Calculate its energy and explain why it is a \(\gamma\) ray from the nucleus or a photon from the atom.

(II) How much recoil energy does a \({ }_{19}^{40} \mathrm{~K}\) nucleus get when it emits a 1.46-MeV gamma ray? Equation Transcription: Text Transcription: { }_{19}^{40} K

(II) Determine the maximum kinetic energy of \(\beta^{+}\) particles released when \({ }_{6}^{11} \mathrm{C}\) decays to \({ }_{5}^{11} \mathrm{~B}\). What is the maximum energy the neutrino can have? What is the minimum energy of each? Equation Transcription: Text Transcription: beta^+ { }_{6}^{11} C { }_{5}^{11} B

(III) Show that when a nucleus decays by \(\beta^{+}\)decay, the total energy released is equal to \(\left(M_{\mathrm{P}}-M_{\mathrm{D}}-2 m_{\mathrm{e}}\right) c^{2}\), where \(M_{\mathrm{P}}\) and \(M_{\mathrm{D}}\) are the masses of the parent and daughter atoms (neutral), and \(m_{\mathrm{e}}\) is the mass of an electron or positron. Equation Transcription: Text Transcription: beta^+ (M_P - M_D - 2m_e)c^2 M_P M_D m_e

(III) When \({ }_{92}^{238} \mathrm{U}\) decays, the \(\alpha\) particle emitted has 4.20 MeV of kinetic energy. Calculate the recoil kinetic energy of the daughter nucleus and the \(Q\)-value of the decay. Equation Transcription: Text Transcription: { }_{92}^{238} U alpha Q

(I) (a) What is the decay constant of \(^{238} _{92} U\) whose half-life is \(4.5 \times 10^9\ yr\)? (b) The decay constant of a given nucleus is \(3.2 \times 10^{-5}\ s^{-1}\). What is its half-life?

A radioactive material produces 1120 decays per minute at one time, and 3.6 h later produces 140 decays per minute. What is its half-life?

(I) What fraction of a sample of \({ }_{32}^{68} \mathrm{Ge}\), whose half-life is about 9 months, will remain after 2.5 yr? Equation Transcription: Text Transcription: { }_{32}^{68} Ge

(I) What is the activity of a sample of \({ }_{6}^{14} \mathrm{C}\) that contains \(6.5 \times 10^{20}\) nuclei? Equation Transcription: Text Transcription: { }_{6}^{14} C 6.5 x 10^20

What fraction of a radioactive sample is left after exactly 5 half-lives?

(II) The iodine isotope \({ }_{53}^{131} \mathrm{I}\) is used in hospitals for diagnosis of thyroid function. If \(782 \mu \mathrm{g}\) are ingested by a patient, determine the activity (a) immediately, (b) 1.50 h later when the thyroid is being tested, and (c) 3.0 months later. Use Appendix B. Equation Transcription: Text Transcription: { }_{53}^{131}I 782 mu g

(II) How many nuclei of \({ }_{92}^{238} \mathrm{U}\) remain in a rock if the activity registers 420 decays per second? Equation Transcription: Text Transcription: { }_{92}^{238} U

(II) In a series of decays, the nuclide \({ }_{92}^{235} \mathrm{U}\) becomes \({ }_{82}^{207} \mathrm{~Pb}\). How many \(\alpha\) and \(\beta^{-}\) particles are emitted in this series? Equation Transcription: Text Transcription: { }_{92}^{235} U { }_{82}^{207} Pb alpha beta^-

(II) \({ }_{55}^{124} \mathrm{Cs}\) has a half-life of 30.8 s. (a) If we have \(8.7 \mu \mathrm{g}\) initially, how many Cs nuclei are present? (b) How many are present 2.6 min later? (c) What is the activity at this time? (d) After how much time will the activity drop to less than about 1 per second? Equation Transcription: { }_{55}^{124}Cs Text Transcription: { }_{55}^{124}Cs 8.7 mu g

(II) Calculate the mass of a sample of pure \(^{40} _{19} K\) with an initial decay rate of \(2.4 \times 10^5\ s^{-1}\). The half-life of \(^{40} _{19} K\) is \(1.248 \times 10^9\ yr\).

(II) Calculate the activity of a pure \(6.7- \mu \mathrm{g}\) sample of \({ }_{15}^{32} \mathrm{P}\) \(\left(T_{\frac{1}{2}}=1.23 \times 10^{6} \mathrm{~s}\right)\). Equation Transcription: Text Transcription: 6.7 mu g { }_{15}^{32} P (T_ {frac{1}{2}} = 1.23 \times 10^{6}s)

(II) A sample of \({ }_{92}^{233} \mathrm{U} \quad\left(T_{\frac{1}{2}}=1.59 \times 10^{5} \mathrm{yr}\right)\) contains \(4.50 \times 10^{18}\) nuclei. (a) What is the decay constant? (b) Approximately how many disintegrations will occur per minute? Equation Transcription: Text Transcription: { }_{92}^{233} U \quad (T_{\frac{1}{2}}=1.59 x 10^{5} yr 4.50 x 10^18

The activity of a sample drops by a factor of 6.0 in 9.4 minutes. What is its half-life?

(II) A 345-g sample of pure carbon contains 1.3 parts in \(10^{12}\) (atoms) of \({ }_{6}^{14} \mathrm{C}\). How many disintegrations occur per second? Equation Transcription: Text Transcription: 10^12 { }_{6}^{14}C

(II) A sample of \({ }_{92}^{238} \mathrm{U}\) is decaying at a rate of \(4.20 \times 10^{2}\) decays/s. What is the mass of the sample? Equation Transcription: Text Transcription: { }_{92}^{238}U 4.20 x 10^2

(II) Rubidium-strontium dating. The rubidium isotope \({ }_{37}^{87} \mathrm{Rb}\), a \(\beta\) emitter with a half-life of \(4.75 \times 10^{10} \mathrm{yr}\), is used to determine the age of rocks and fossils. Rocks containing fossils of ancient animals contain a ratio of \({ }_{38}^{87} \mathrm{Sr}\) to \({ }_{37}^{87} \mathrm{Rb}\) of 0.0260. Assuming that there was no { }_{38}^{87} \mathrm{Sr}\) present when the rocks were formed, estimate the age of these fossils. Equation Transcription: Text Transcription: { }_{37}^{87} Rb beta 4.75 x 10^10 yr { }_{38}^{87} Sr { }_{37}^{87} Rb { }_{38}^{87} Sr

(II) Two of the naturally occurring radioactive decay sequences start with \({ }_{90}^{232}Th\) and with \({ }_{92}^{235} \mathrm{U}\). The first five decays of these two sequences are: \(\alpha, \beta, \alpha, \beta, \alpha\) and \(\alpha, \beta, \alpha, \beta, \alpha.\) Determine the resulting intermediate daughter nuclei in each case. Equation Transcription: Text Transcription: { }_{90}^{232}Th { }_{92}^{235}U \alpha, \beta, \alpha, \beta, \alpha \alpha, \beta, \alpha, \beta, \alpha.

(II) An ancient wooden club is found that contains 73 g of carbon and has an activity of 7.0 decays per second. Determine its age assuming that in living trees the ratio of \({ }^{14} \mathrm{C} /{ }^{12} \mathrm{C}\) atoms is about \(1.3 \times 10^{-12}\). Equation Transcription: Text Transcription: { }^{14} C /{ }^{12} C 1.3 x 10^-12

(II) Use Fig. 30-11 and calculate the relative decay rates for \(\alpha\) decay of \({ }_{84}^{218} \mathrm{Po}\) and \({ }_{84}^{214} \mathrm{Po}\). Equation Transcription: Text Transcription: alpha { }_{84}^{218} Po { }_{84}^{214} Po

The activity of a radioactive source decreases by 5.5% in 31.0 hours. What is the half-life of this source?

(III) \({ }_{4}^{7}Be\) decays with a half-life of about 53 d. It is produced in the upper atmosphere and filters down onto the Earth's surface. If a plant leaf is detected to have 350 decays/s of \({ }_{4}^{7} \mathrm{Be}\),(a) how long do we have to wait for the decay rate to drop to 25 per second? (b) Estimate the initial mass of \({ }_{4}^{7} \mathrm{Be}\) on the leaf. Equation Transcription: Text Transcription: { }_{4}^{7}Be { }_{4}^{7}Be { }_{4}^{7}Be

(III) At \(t=0\), a pure sample of radioactive nuclei contains \(N_{0}\) nuclei whose decay constant is \(\lambda\). Determine a formula for the number of daughter nuclei, \(N_{\mathrm{D}}\), as a function of time; assume the daughter is stable and that \(N_{\mathrm{D}}=0\) at \(t=0\). Equation Transcription: Text Transcription: t = 0 N_0 lambda N_D N_D = 0 t = 0

Which radioactive isotope of lead is being produced if the measured activity of a sample drops to 1.050% of its original activity in 4.00 h?

An old wooden tool is found to contain only 4.5 % of the \({ }_{6}^{14} \mathrm{C}\) that an equal mass of fresh wood would. How old is the tool? Equation Transcription: Text Transcription: { }_{6}^{14}C

A neutron star consists of neutrons at approximately nuclear density. Estimate, for a 10-km-diameter neutron star, (a) its mass number, (b) its mass (kg), and (c) the acceleration of gravity at its surface

Tritium dating. The \({ }_{1}^{3} \mathrm{H}\) isotope of hydrogen, which is called tritium (because it contains three nucleons), has a half-life of 12.3 yr. It can be used to measure the age of objects up to about 100 yr. It is produced in the upper atmosphere by cosmic rays and brought to Earth by rain. As an application, determine approximately the age of a bottle of wine whose \({ }_{1}^{3} \mathrm{H}\) radiation is about \(\frac{1}{10}\) that present in new wine. Equation Transcription: Text Transcription: { }_{1}^{3} H { }_{1}^{3} H frac{1}{10}

Some elementary particle theories (Section 32-11) suggest that the proton may be unstable, with a half-life \(\geq 10^{33} \mathrm{yr}\). (a) How long would you expect to wait for one proton in your body to decay (approximate your body as all water)? (b) Of the roughly 7 billion people on Earth, about how many would have a proton in their body decay in a 70 yr lifetime? Equation Transcription: Text Transcription: geq 10^{33} yr

The original experiments which established that an atom has a heavy, positive nucleus were done by shooting alpha particles through gold foil. The alpha particles had a kinetic energy of 7.7 MeV. What is the closest they could get to the center of a gold nucleus? How does this compare with the size of the nucleus?

How long must you wait (in half-lives) for a radioactive sample to drop to 2.00% of its original activity?

If the potassium isotope \({ }_{19}^{40} \mathrm{~K}\) gives 42 decays/s in a liter of milk, estimate how much \({ }_{19}^{40} \mathrm{~K}\) and regular \({ }_{19}^{39} \mathrm{~K}\) are in a liter of milk. Use Appendix B. Equation Transcription: Text Transcription: ({ }_{19}^{40} K ({ }_{19}^{40} K ({ }_{19}^{39} K

Strontium-90 is produced as a nuclear fission product of uranium in both reactors and atomic bombs. Look at its location in the Periodic Table to see what other elements it might be similar to chemically, and tell why you think it might be dangerous to ingest. It has too many neutrons to be stable, and it decays with a half-life of about 29 yr. How long will we have to wait for the amount of \({ }_{38}^{90} \mathrm{Sr}\) on the Earth's surface to reach 1 % of its current level, assuming no new material is scattered about? Write down the decay reaction, including the daughter nucleus. The daughter is radioactive: write down its decay. Equation Transcription: Text Transcription: { }_{38}^{90} Sr

The activity of a sample of \({ }_{16}^{35} \mathrm{~S} \quad\left(T_{\frac{1}{2}}=87.37\right \) days) is \(4.28 \times 10^{4}\) decays per second. What is the mass of the sample? Equation Transcription: Text Transcription: { }_{16}^{35} S \quad (T_{\frac{1}{2}}=87.37days) 4.28 x 10^4

The nuclide \({ }_{76}^{191} \ \mathrm {Os}\) decays with \(\beta^{-}\) energy of 0.14 MeV accompanied by \(\gamma\) rays of energy 0.042 MeV and 0.129 MeV. (a) What is the daughter nucleus? (b) Draw an energy-level diagram showing the ground states of the parent and daughter and excited states of the daughter (c) To which of the daughter states does \(\beta^{-}\) decay of \({ }_{76}^{191} \mathrm{Os}\) occur?

Determine the activities of (a) \(1.0 \mathrm{~g}\) of \({ }_{53}^{131}I \mathrm{I}\left(T_{\frac{1}{2}}=8.02\right\) days) and (b) \(1.0 \mathrm{~g}\) of \({ }_{92}^{238} \mathrm{U}\left(T_{\frac{1}{2}}=4.47 \times 10^{9} \mathrm{yr}\right)\). Equation Transcription: Text Transcription: 1.0 g { }_{53}^{131}I (T_{\frac{1}{2}}=8.02 days) 1.0 g { }_{92}^{238} U (T_{\frac{1}{2}}=4.47 x 10^{9} yr)

Use Fig. 30–1 to estimate the total binding energy for copper and then estimate the energy, in joules, needed to break a 3.0-g copper penny into its constituent nucleons.

Instead of giving atomic masses for nuclides as in Appendix B, some Tables give the mass excess, \(\Delta\), defined as \(\Delta=M-A\), where \(A\) is the atomic mass number and \(M\) is the mass in u. Determine the mass excess, in u and in \(\mathrm{MeV} / c^{2}\), for: (a) \({ }_{2}^{4} \mathrm{He}\); (b) \({ }_{6}^{12} \mathrm{C}\); (c) \({ }_{38}^{86} \mathrm{Sr}\); \((d){ }_{92}^{235} \mathrm{U}\). ( e ) From a glance at Appendix B, can you make a generalization about the sign of \(\Delta\) as a function of \(Z\) or \(A\) ? Equation Transcription: Text Transcription: Delta Delta = M - A { }_{2}^{4} He { }_{6}^{12} C { }_{38}^{86} Sr { }_{92}^{235} U Delta Z A

When water is placed near an intense neutron source, the neutrons can be slowed down to almost zero speed by collisions with the water molecules, and are eventually captured by a hydrogen nucleus to form the stable isotope called deuterium, \({ }_{1}^{2} \mathrm{H}\), giving off a gamma ray. What is the energy of the gamma ray? Equation Transcription: Text Transcription: { }_{1}^{2} H

The practical limit for carbon-14 dating is about 60,000 years. If a bone contains 1.0 kg of carbon, and the animal died 60,000 years ago, what is the activity today?

Using Section 30-2 and Appendix B, determine the energy required to remove one neutron from \({ }_{2}^{4} \mathrm{He}\). How many times greater is this energy than the binding energy of the last neutron in \({ }_{6}^{13} \mathrm{C}\)? Equation Transcription: Text Transcription: { }_{2}^{4} He { }_{6}^{13} C

(a) If all of the atoms of the Earth were to collapse and simply become nuclei, what would be the Earths new radius? (b) If all of the atoms of the Sun were to collapse and simply become nuclei, what would be the Suns new radius?

(a) A 72-gram sample of natural carbon contains the usual fraction of \({ }_{6}^{14} \mathrm{C}\). Estimate roughly how long it will take before there is only one \({ }_{6}^{14} \mathrm{C}\) nucleus left. (b) How does the answer in (a) change if the sample is 340 grams? What does this tell you about the limits of carbon dating? Equation Transcription: Text Transcription: { }_{6}^{14} C { }_{6}^{14} C

If the mass of the proton were just a little closer to the mass of the neutron, the following reaction would be possible even at low collision energies: \(\mathrm{e}^{-}+\mathrm{p} \rightarrow \mathrm{n}+\nu\) (a) Why would this situation be catastrophic? (See last paragraph of Chapter 33.) (b) By what percentage would the proton's mass have to be increased to make this reaction possible? Equation Transcription: Text Transcription: e^{-} + p \rightarrow n + nu

What is the ratio of the kinetic energies for an alpha particle and a beta particle if both make tracks with the same radius of curvature in a magnetic field, oriented perpendicular to the paths of the particles?

A 1.00-g sample of natural samarium emits \(\alpha\) particles at a rate of \(120 \mathrm{~s}^{-1}\) due to the presence of \({ }_{62}^{147} \mathrm{Sm}\). The natural abundance of \({ }_{62}^{147} \mathrm{Sm}\) is 15 %. Calculate the half-life for this decay process. Equation Transcription: Text Transcription: alpha 120 s^-1 { }_{62}^{147} Sm { }_{62}^{147} Sm

Almost all of naturally occurring uranium is \({ }_{92}^{238} \mathrm{U}\) with a half-life of \(4.468 \times 10^{9} \mathrm{yr}\). Most of the rest of natural uranium is \({ }_{92}^{235} \mathrm{U}\) with a half-life of \(7.04 \times 10^{8} \mathrm{yr}\). Today a sample contains 0.720 % \({ }_{92}^{235} \mathrm{U}\). (a) What was this percentage 1.0 billion years ago? (b) What percentage of uranium will be \({ }_{92}^{235} \mathrm{U}\) 100 million years from now? Equation Transcription: Text Transcription: { }_{92}^{238} U 4.468 x 10^9 yr { }_{92}^{235} U 7.04 x 10^8 yr { }_{92}^{235} U { }_{92}^{235} U

A banana contains about 420 mg of potassium, of which a small fraction is the radioactive isotope \({ }_{19}^{40} \mathrm{~K}\) (Appendix B). Estimate the activity of an average banana due to \({ }_{19}^{40} \mathrm{~K}\). Equation Transcription: Text Transcription: { }_{19}^{40} K { }_{19}^{40} K

When \({ }_{10}^{23} \mathrm{Ne}\) (mass =22.9947 u ) decays to \({ }_{11}^{23} \mathrm{Na}\) (mass = 22.9898 u), what is the maximum kinetic energy of the emitted electron? What is its minimum energy? What is the energy of the neutrino in each case? Ignore recoil of the daughter nucleus. Equation Transcription: Text Transcription: { }_{10}^{23} Ne { }_{11}^{23} Na

(a) In \(\alpha\) decay of, say, a \({ }_{88}^{226}Ra\) nucleus, show that the nucleus carries away a fraction \(1 /\left(1+\frac{1}{4} A_{\mathrm{D}}\right)\) of the total energy available, where \(A_{\mathrm{D}}\) is the mass number of the daughter nucleus. [Hint: Use conservation of momentum as well as conservation of energy.] (b) Approximately what percentage of the energy available is thus carried off by the \(\alpha\) particle when \({ }_{88}^{226}Ra\) decays? Equation Transcription: Text Transcription: alpha { }_{88}^{226}Ra 1/(1 + frac{1}{4} A_D) A_D alpha { }_{88}^{226}Ra

Decay series, such as that shown in Fig. 30-11, can be classified into four families, depending on whether the mass numbers have the form \(4 n, 4 n+1,4 n+2\), or \(4 n+3\), where \(n\) is an integer. Justify this statement and show that for a nuclide in any family, all its daughters will be in the same family. Equation Transcription: Text Transcription: 4n, 4n + 1, 4n + 2 4n + 3 n

Guess now! If half of an \(80-\mu g\) sample of \({ }_{27}^{66} \mathrm{Co}\) decays in years, how much \({ }_{27}^{60} \mathrm{Co}\) is left in years? (a) \(10 \mu g\). (b) \(20 \mu g\) (c) \(30 \mu g\) (d) \(40 \mu g\) (e) \(0 \mu g\) Equation Transcription: Text Transcription: 80- \mug 27 over 66 Co 27 over 60 Co 10 \mu g 20 \mu g 30 \mu g 40 \mu g 0 \mu g

Problem 1MCQ Elements of the Periodic Table are distinguished by (a) the number of protons in the nucleus. (b) the number of neutrons in the nucleus. (c) the number of electrons in the atom. (d) Both (a) and (b). (e) (a), (b), and (c).

Problem 1P (I) A pi meson has a mass of 139Me V/c2. What is this in atomic mass units?

Problem 1Q What do different isotopes of a given element have in common? How are they different?

Problem 1SL Describe in detail why we think there is a strong nuclear force.

Problem 2MCQ A nucleus has (a) more energy than its component neutrons and protons have. (b) less energy than its component neutrons and protons have. (c) the same energy as its component neutrons and protons have. (d) more energy than its component neutrons and protons have when the nucleus is at rest but less energy than when it is moving.

\(\text { (I) }\) What is the approximate radius of an particle \(\left(\frac{4}{2} \mathrm{He}\right)\) ? Equation Transcription: Text Transcription: (I) (\frac 4 2 He)

What are the elements represented by the \(X\) in the following: (a) \({ }_{92}^{232} X\) (b) \({ }_{7}^{18} X\) (c) \({ }_{1}^{1} X\) (d) \({ }_{38}^{86} X\) (e) \({ }_{100}^{252} X\) Equation Transcription: Text Transcription: X 92^232X 7^18X 1^1X 38^86X 100^252X

Problem 2SL (a) Under what circumstances could a fermium nucleus decay into an einsteinium nucleus? (b) What about the reverse, an Es nucleus decaying into Fm?

Problem 3MCQ Which of the following will generally create a more stable nucleus? (a) Having more nucleons. (b) Having more protons than neutrons. (c) Having a larger binding energy per nucleon. (d) Having the same number of electrons as protons. (e) Having a larger total binding energy.

\(\text { (I) }\) By what \(\%\) is the radius of \({ }_{92}^{238} U\) greater than the radius of \({ }_{92}^{232} \mathrm{U}\)? Equation Transcription: Text Transcription: (I) % 92^238U 92^232U

How many protons and how many neutrons do each of the isotopes in Question 2 have?

Problem 3SL Using the uncertainty principle and the radius of a nucleus, estimate the minimum possible kinetic energy of a nucleon in, say, iron. Ignore relativistic corrections. [Hint:A particle can have a momentum at least as large as its momentum uncertainty.]

Problem 4MCQ There are 82 protons in a lead nucleus. Why doesn’t the lead nucleus burst apart? (a) Coulomb repulsive force doesn’t act inside the nucleus. (b) Gravity overpowers the Coulomb repulsive force inside the nucleus. (c) The negatively charged neutrons balance the positively charged protons. (d) Protons lose their positive charge inside the nucleus. (e) The strong nuclear force holds the nucleus together.

\(\text { (II) }\) What is the approximate radius of \(a_{48}^{112} \mathrm{Cd}\) nucleus? (b) Approximately what is the value of \(A\) for a nucleus whose radius is \(3.7 \times 10^{-15} \mathrm{~m}\) ? Equation Transcription: Text Transcription (II) A 48^112Cd A 3.7 x 10^-15m

Problem 4Q Identify the element that has 87 nucleons and 50 neutrons.

In Fig. 30-17, a nucleus decays and emits a particle that enters a region with a uniform magnetic field of \(0.012 T\) directed into the page. The path of the detected particle is shown. (a) What type of radioactive decay is this? (b) If the radius of the circular arc is \(4.7 \mathrm{~mm}\), what is the velocity of the particle? Equation Transcription: Text Transcription: 0.012T 4.7 mm

Problem 5MCQ The half-life of a radioactive nucleus is (a) half the time it takes for the entire substance to decay. (b) the time it takes for half of the substance to decay. (c) the same as the decay constant. (d) Both (a) and (b) (they are the same). (e) All of the above.

Problem 5P (II) What is the mass of a bare ? particle (without electrons) Me V/c2 in

Problem 5Q Why are the atomic masses of many elements (see the Periodic Table) not close to whole numbers?

Problem 5SL In both internal conversion and ? decay, an electron is emitted. How could you determine which decay process occurred?

Problem 6MCQ As a radioactive sample decays, (a) the half-life increases. (b) the half-life decreases. (c) the activity remains the same. (d) the number of radioactive nuclei increases. (e) None of the above.

(II) Suppose two alpha particles were held together so they were just “touching”(use Eq.30–1). Estimate the electrostatic repulsive force each would exert on the other. What would be the acceleration of an alpha particle subjected to this force?

Problem 6Q Why are atoms much more likely to emit an alpha particle than to emit separate neutrons and protons?

Problem 6SL Suppose we discovered that several thousand years ago cosmic rays had bombarded the Earth’s atmosphere a lot more than we had thought. Compared to previous calculations of the carbon-dated age of organic matter, we would now calculate it to be older, younger, or the same age as previously calculated? Explain.

Problem 7MCQ If the half-life of a radioactive sample is 10 years, then it should take _____ years for the sample to decay completely. (a) 10. (b) 20. (c) 40. (d) Cannot be determined.

\(\text { (II) }\) (a) What would be the radius of the Earth if it had its actual mass but had the density of nuclei? (b) By what factor would the radius of \(a_{92}^{238} \mathrm{U}\) nucleus increase if it had the Earth's density? Equation Transcription: Text Transcription: (II) A 92 ^ 238U

What are the similarities and the differences between the strong nuclear force and the electric force?

In 1991 , the frozen remains of a Neolithic-age man, nicknamed Otzi, were found in the Italian Alps by hikers. The body was well preserved, as were his bow, arrows, knife, axe, other tools, and clothing. The date of his death can be determined using carbon-14 dating. (a) What is the decay constant for \({ }_{6}^{14} C\)? (b) How many \({ }_{6}^{14} C\) atoms per gram of \({ }_{6}^{12} C\)are there in a living organism? What is the activity per gram in naturally occurring carbon for a living organism? For Otzi, the activity per gram of carbon was measured to be \(0.121\). How long ago did he live? Equation Transcription: Text Transcription: 6^14C 6^14C 6^12C 0.121

A sample's half-life is 1 day. What fraction of the original sample will have decayed after 3 days? (a) \(\frac{1}{8} \text {. }\) (b) \(\frac{1}{4} \text {. }\) (c) \(\frac{1}{2} \text {. }\) (d) \(\frac{3}{4} \text {. }\) (e) \(\frac{7}{8} \text {. }\) () All of it. Equation Transcription: Text Transcription: 1 over 8 dot 1 over 4 dot 1 over 2 dot 3 over 4 dot 7 over 8 dot

Problem 8P (II) What stable nucleus has approximately half the radius of a uranium nucleus? [Hint: Find Aand use Appendix B to get Z.]

Problem 8Q What is the experimental evidence in favor of radioactivity being a nuclear process?

After three half-lives, what fraction of the original radioactive material is left? None \(\frac{1}{16}\) (c) \(\frac{1}{8}\) (d) \(\frac{1}{4}\) (e) \(\frac{3}{4}\) (f) \(\frac{7}{8}\) Equation Transcription: Text Transcription 1 over 16 1 over 8 1 over 4 3 over 4 7 over 8

Some radioactive isotopes have half-lives that are greater than the age of the universe (like gadolinium or samarium). The only way to determine these half-lives is to monitor the decay rate of a sample that contains these isotopes. For example, suppose we find an asteroid that currently contains about 15,000 \mathrm{~kg}\) of \({ }_{64}^{152} G d\) (gadolinium) and we detect an activity of 1 decay . Estimate the half-life of gadolinium (in years). Equation Transcription: Text Transcription: 15,000 kg 64^152Gd

(II) If an alpha particle were released from rest near the surface of a \(^{257} _{100} Fm\) nucleus, what would its kinetic energy be when far away?

The isotope \({ }_{29}^{64} \mathrm{Cu}\) is unusual in that it can decay by \(\gamma, \beta^{-} \text {, and } \beta^{+}\) emission. What is the resulting nuclide for each case? Equation Transcription: Text Transcription: 29 ^ 64Cu \gamma, \beta^-, and \beta^+

\(\text { (II) }\) (a) What is the fraction of the hydrogen atom's mass \(\left({ }_{1}^{1} H\right)\) that is in the nucleus? What is the fraction of the hydrogen atom's volume that is occupied by the nucleus? Equation Transcription: Text Transcription: (II) (1^1H)

A \({ }_{92}^{238} \mathrm{U}\) nucleus decays via decay to a nucleus containing how many neutrons? Equation Transcription: Text Transcription: 92 ^ 238 U

Problem 11MCQ A material having which decay constant would have the shortest half-life? (a) 100 second. (b) 5 year. (c) 8 century. (d) 109 /day.

Problem 11P (II) Approximately how many nucleons are there in a 1.0-kg object? Does it matter what the object is made of? Why or why not?

Describe, in as many ways as you can, the difference between \(\alpha, \beta, \text { and } \gamma\) rays. Equation Transcription: Text Transcription: \alpha, \beta, \text { and } \gamma

Problem 12MCQ Uranium-238 decays to lead-206 through a series of (a) alpha decays. (b) beta decays. (c) gamma decays. (d) some combination of alpha, beta, and gamma decays.

\((I I I)\) How much kinetic energy, in \(\mathrm{MeV}\), must an particle have to just "touch" the surface of \(a^{232} O\) nucleus? Equation Transcription: Text Transcription: (III) MeV a^232O

Fill in the missing particle or nucleus: (a) \(^{45} _{20} Ca\ \rightarrow\ ? + e^- + \overline{v}\) (b) \(^{58} _{29} Cu^*\ \rightarrow\ ? + \gamma\) (c) \(^{46} _{24} Cr\ \rightarrow\ ^{46} _{23} V + ?\) (d) \(^{234} _{94} Pu\ \rightarrow\ ? + \alpha\) (e) \(^{239} _{93} Np\ \rightarrow\ ^{239} _{94} Pu + ?\)

Problem 13MCQ Carbon dating is useful only for determining the age ofobjects less than about _____ years old. (a) 4.5 million. (b) 1.2 million. (c) 600,000. (d) 60,000. (e) 6000.

\(\text { (I) }\) Estimate the total binding energy for \({ }_{29}^{63} \mathrm{Cu}\) using Fig. Equation Transcription: Text Transcription: (I) 29^63Cu

Problem 14MCQ Radon has a half-life of about 1600 years. The Earth is several billion years old, so why do we still find radon on this planet? (a) Ice-age temperatures preserved some of it. (b) Heavier unstable isotopes decay into it. (c) It is created in lightning strikes. (d) It is replenished by cosmic rays. (e) Its half-life has increased over time. (f ) Its half-life has decreased over time.

\(\text { (I) }\) Use Fig. 30-1 to estimate the total binding energy of (a) \({ }_{92}^{238} U\), and (b) \({ }_{36}^{84} K r\) Equation Transcription: Text Transcription: (I) 92 ^ 238U 36 ^ 84Kr

When a nucleus undergoes either \(\beta^{-} \text {or } \beta^{+}\) decay, what happens to the energy levels of the atomic electrons? What is likely to happen to these electrons following the decay? Equation Transcription: Text Transcription: \beta^- or \beta^+

Problem 15MCQ How does an atom’s nucleus stay together and remain stable? (a) The attractive gravitational force between the protons and neutrons overcomes the repulsive electrostatic force between the protons. (b) Having just the right number of neutrons overcomes the electrostatic force between the protons. (c) A strong covalent bond develops between the neutrons and protons, because they are so close to each other. (d) None of the above.

Problem 15Q The alpha particles from a given alpha-emitting nuclide are generally monoenergetic; that is, they all have the same kinetic energy. But the beta particles from a beta-emitting nuclide have a spectrum of energies. Explain the difference between these two cases.

\(\text { (II) }\) Calculate the binding energy per nucleon for a \({ }_{7}^{15} N\) nucleus, using Appendix . Equation Transcription: Text Transcription: (II) 7 ^ 15N

Problem 16MCQ What has greater mass? (a) A neutron and a proton that are far from each other (unbound). (b) A neutron and a proton that are bound together in a hydrogen (deuterium) nucleus. (c) Both the same.

\(\text { (II) }\) Use Appendix \(B\) to calculate the binding energy of \({ }_{1}^{2} H\) (deuterium). Equation Transcription: Text Transcription: (II) B 1 2H

\(\text { (II) }\) Determine the binding energy of the last neutron in a \({ }_{11}^{23} \mathrm{Na}\) nucleus. Equation Transcription: Text Transcription: (II) 11^ 23Na

Problem 17Q Can hydrogen or deuterium emit an particle? Explain.

Do isotopes that undergo electron capture generally lie above or below the stable nuclides in Fig. 30–2?

\(\text { (II) }\) Calculate the total binding energy, and the binding energy per nucleon, for \({ }_{3}^{7} L i\) \({ }_{78}^{195} \mathrm{Pt}\) Use Appendix . Equation Transcription: Text Transcription: (II) 3 ^ 7Li, 78 ^ 195Pt

\(\text { (II) }\) Compare the average binding energy of a nucleon in \({ }_{11}^{23} \mathrm{Na}\) to that in \({ }_{11}^{23} \mathrm{Na}\) , using Appendix \(B\) Equation Transcription: Text Transcription: (II) 11 ^ 23Na 11 ^ 23Na B

Problem 19Q An isotope has a half-life of one month. After two months, will a given sample of this isotope have completely decayed? If not, how much remains?

(III) How much energy is required to remove a proton, (b) a neutron, from \({ }_{7}^{15} N\) ? Explain the difference in your answers. Equation Transcription: Text Transcription: 7 ^ 15N

Why are none of the elements with Z > 92 stable?

\(\text { (III) }\) Show that the nucleus \({ }_{4}^{8} B e(\text { mass }=8.005305 u)\) is unstable and will decay into two \(\alpha\) particles. (b) Is \({ }_{6}^{12} C\) stable against decay into three \(\alpha\) particles? Show why or why not. Equation Transcription: Text Transcription: (III) 48Be (mass=8.005305) \alpha 6 ^ 12C \alpha

A proton strikes a \({ }_{3}^{6} \mathrm{Li}\) nucleus. As a result, an \(\alpha\) particle and another particle are released. What is the other particle? Equation Transcription: Text Transcription: 3 ^ 6 Li \alpha

\(\text { (I) }\) The \({ }_{3}^{7} L i\) nucleus has an excited state \(0.48 \mathrm{MeV}\) above the ground state. What wavelength gamma photon is emitted when the nucleus decays from the excited state to the ground state? Equation Transcription: Text Transcription: (I) 3 7 Li 0.48MeV

Can \({ }_{6}^{14} \mathrm{C}\) dating be used to measure the age of stone walls and tablets of ancient civilizations? Explain. Equation Transcription: Text Transcription: 6 14C

(II) Show that the decay \(^{11} _6 C \rightarrow ^{10} _5 B + p\) is not possible because energy would not be conserved.

Explain the absence of \(\beta^{+}\) emitters in the radioactive decay series of Fig. . Equation Transcription: Text Transcription: \beta^+

\(\text { (II) }\) Calculate the energy released when tritium, \({ }_{1}^{3} H\), decays by \(\beta^{-}\) emission. Equation Transcription: Text Transcription: (II) _1^3 H \beta^-

As \({ }_{86}^{222} \mathrm{Rn}\) decays into \({ }_{82}^{206} \mathrm{~Pb}\), how many alpha and beta particles are emitted? Does it matter which path in the decay series is chosen? Why or why not? Equation Transcription: Text Transcription: 86^222Rn 82^206Pb

Problem 25P (II) What is the maximum kinetic energy of an electron emitted in the ? decay of a free neutron?

A \({ }^{238} U\) nucleus (initially at rest) decays into \(a^{234} T h\) nucleus and an alpha particle. Which has the greater (i) momentum, (ii) velocity, (iii) kinetic energy? Explain. (a) The \({ }^{234} \mathrm{Th}\) nucleus. (b) The alpha particle. (c) Both the same. Equation Transcription: Text Transcription: ^238U a^234Th ^234Th

(II) \({ }_{11}^{24} \mathrm{Na}\) is radioactive. Is it a \(\beta^{-} \text {or } \beta^{+}\) emitter? (b) Write down the decay reaction, and estimate the maximum kinetic energy of the emitted \(\beta\) Equation Transcription: Text Transcription: 11 ^ 24Na \beta^- or \beta^+ \beta

(II) Give the result of a calculation that shows whether or not the following decays are possible: (a) \({ }_{92}^{233} U \rightarrow{ }_{92}^{232} U+n\) (b) \({ }_{7}^{14} N \rightarrow{ }_{7}^{13} N+n\) (c) \({ }_{19}^{40} K \rightarrow{ }_{19}^{39} K+n\) Equation Transcription: Text Transcription: 92 ^ 233 U \rightarrow 92 ^ 232 U + n 7 ^ 14 N \rightarrow 7 ^ 13 N + n 19 ^ 40 K \rightarrow 19 ^ 39 K + n

(II) A \({ }_{92}^{238} U\) nucleus emits an \(\alpha\) particle with kinetic energy \(=4.20 \mathrm{MeV}\) (a) What is the daughter nucleus, and (b) what is the approximate atomic mass (in u) of the daughter atom? Ignore recoil of the daughter nucleus. Equation Transcription: Text Transcription: 92 ^ 238U \alpha =4.20MeV

\(\text { (II) }\) Calculate the maximum kinetic energy of the particle emitted during the decay of \({ }_{27}^{60} \mathrm{Co}\) Equation Transcription: Text Transcription: (II) 27 ^ 60Co

Determine how much less the mass of the \({ }_{3}^{7} \mathrm{Li}\) nucleus is compared to that of its constituents. See Appendix \(B\). Equation Transcription: Text Transcription: 3 ^ 7Li B

\(\begin{array}{ll}154 & 15 \\& 66\end{array} D y\) decays by \(\alpha\) emission to what element? \((a) P b,(b) G d,(c) S m,(d) E r,(e) Y b\) Equation Transcription: Text Transcription: 154 66 15 Dy \alpha (a)Pb, (b)Gd, (c)Sm, (d)Er, (e)Yb

Determine the binding energy per nucleon for \(^{16} _8 O\).

The half-life of \({ }_{11}^{22} \mathrm{Na}\) is years. How much \({ }_{11}^{22} \mathrm{Na}\) will be left of a pure \(1.0-\mu g\) sample after yr? (a) None. (b) \(\frac{1}{8} \mu g\) (c) \(\frac{1}{4} \mu g\) (d) \(\frac{1}{2} \mu g\) (e) \(0.693 \mu g\) Equation Transcription: Text Transcription: 11 ^ 22 Na 11 ^ 22 Na 1.0-\mu g \frac{1}{8} \mu g \frac{1}{4} \mu g \frac{1}{2} \mu g 0.693 \mu g

Return to the Chapter-Opening Question, page 857, and answer it again now. Try to explain why you may have answered differently the first time.

\((I I)\) How much energy is released in electron capture by beryllium: \({ }_{4}^{7} B e+e^{-} \rightarrow{ }_{3}^{7} L i+v\)? Equation Transcription: Text Transcription: (II) 4 ^ 7Be+e^-3 ^ 7Li+v

\(\text { (II) }\) The isotope \({ }_{84}^{218} \mathrm{Po}\) can decay by either \(\alpha \text { or } \beta^{-}\) emission. What is the energy release in each case? The mass of \({ }_{84}^{218} \mathrm{Po} \text { is } 218.008973 \mathrm{u}\). Equation Transcription: Text Transcription: (II) 84 ^ 218Po \alpha \text { or } \beta^{-} 84 ^ 218 Po is 218.008973 u

\(\text { (II) }\) The nuclide \({ }_{15}^{32} P\) decays by emitting an electron whose maximum kinetic energy can be \(\text { 1.71MeV }\). ( ) What is the daughter nucleus? (b) Calculate the daughter's atomic mass (in u). Equation Transcription: Text Transcription: (II) 15 ^ 32P 1.71MeV

Problem 33P (II) A photon with a wavelength of 1.15 X 10-13 m is ejected from an atom. Calculate its energy and explain why it is a ? ray from the nucleus or a photon from the atom.

(II) How much recoil energy does \(a_{19}^{40} K\) nucleus get when it emits a \(\text { 1.46-MeV }\) gamma ray? Equation Transcription: Text Transcription: a 19 ^ 40K 1.46-MeV

\(\text { (II) }\) Determine the maximum kinetic energy of \(\beta^{+}\) particles released when \({ }_{6}^{11} \mathrm{C}\) decays to \({ }_{5}^{11} B\). What is the maximum energy the neutrino can have? What is the minimum energy of each? Equation Transcription: Text Transcription: (II) \beta^{+} 6 ^ 11C 5 ^ 11B

Problem 36P (III) Show that when a nucleus decays by ?+ decay, the total energy released is equal to (MP - MD - 2me)C2 Where Mp and MD are the masses of the parent and daughter atoms (neutral), and is the mass of an electron or positron.

(III) When \(^{238} _{92} U\) decays, the \(\alpha\) particle emitted has 4.20 MeV of kinetic energy. Calculate the recoil kinetic energy of the daughter nucleus and the Q-value of the decay.

(I) (a) What is the decay constant of \(^{238} _{92} U\) whose half-life is \(4.5 \times 10^9\ yr\)? (b) The decay constant of a given nucleus is \(3.2 \times 10^{-5}\ s^{-1}\). What is its half-life?

Problem 39P (I) A radioactive material produces 1120 decays per minute at one time, and 3.6 h later produces 140 decays per minute. What is its half-life?

(I) What fraction of a sample of \(^{68} _{32} Ge\), whose half-life is about 9 months, will remain after 2.5 yr?

\(\text { (I) }\) What is the activity of a sample of \({ }_{6}^{14} \mathrm{C}\) that contains \(6.5 \times 10^{20}\) nuclei? Equation Transcription: Text Transcription: (I) 6 ^ 14C 6.5 x 10 ^ 20

Problem 42P (I) What fraction of a radioactive sample is left after exactly 5 half-lives?

(II) The iodine isotope \({ }_{53}^{131} I\) is used in hospitals for diagnosis of thyroid function. If \(782 \mu g\) are ingested by a patient, determine the activity (a) immediately, (b) 1.50 h later when the thyroid is being tested, and (c) 3.0 months later. Use Appendix B.

\(\text { (II) }\) How many nuclei of \({ }_{92}^{238} U\) remain in a rock if the activity registers 420 decays per second? Equation Transcription: Text Transcription: (II) 92 ^ 238U

\(\text { (II) }\) In a series of decays, the nuclide \({ }_{92}^{235} \mathrm{U}\) becomes \(\frac{207}{82} \mathrm{~Pb}\) How many \(\alpha \text { and } \beta\) - particles are emitted in this series? Equation Transcription: Text Transcription: (II) 92 ^ 235 U 207 ^ 82 Pb \alpha and \beta

(II) \({ }_{55}^{124} \mathrm{Cs}\) has a half-life of 30.8 s. (a) If we have \(8.7 \mu g\) initially, how many Cs nuclei are present? (b) How many are present \(2.6 \mathrm{~min}\) later? What is the activity at this time? (d) After how much time will the activity drop to less than about 1 per second? Equation Transcription: Text Transcription: 55 ^ 124 Cs 30.8 s 8.7 \mu g 2.6 min

\(\text { (II) }\) Calculate the mass of a sample of pure \({ }_{19}^{40} K\) with an initial decay rate of \(2.4 \times 10^{5} s^{-1}\). The half-life of \({ }_{19}^{40} K \text { is } 1.248 \times 10^{8} y r\). Equation Transcription: Text Transcription: (II) 19 ^ 40K 2.4 x 10^5s^-1 19^40 K is 1.248 x 10^8yr

\((I I)\) Calculate the activity of a pure \(6.7-\mu g\) sample of \({ }_{15}^{32} P\left(T_{j}=1.23 \times 10^{6} \mathrm{~s}\right)\) Equation Transcription: Text Transcription: (II) 6.7-\mu g 15 ^ 32 P (Tj=1.23 x 10^6s)

\(\text { (II) }\) A sample of \({ }_{92}^{233} U\left(T \frac{1}{2}=1.59 \times 10^{5} y r\right)\) contains\(4.50 \times 10^{18}\) nuclei. (a) What is the decay constant? (b) Approximately how many disintegrations will occur per minute? Equation Transcription: Text Transcription: (II) 92^233 U(T \frac1 2=1.59 \times 10^5 y r) 4.50 \times 10^18

Problem 50P (II) The activity of a sample drops by a factor of 6.0 in 9.4 minutes. What is its half-life?

\(\text { (II) }\) A \(345-g\) sample of pure carbon contains 1.3 parts in \(10^{12}\) (atoms) of \(\frac{1}{6} C\) How many disintegrations occur per second? Equation Transcription: Text Transcription: (II) 345-g 10 ^ 12 1 over 6 C

(II) A sample of \({ }_{92}^{235} \mathrm{U}\) is decaying at a rate of \(4.20 \times 10^{2}\) Equation Transcription: Text Transcription: 92 ^ 235U 4.20 x 10^2

(II) Rubidium-strontium dating. The rubidium isotope \({ }_{37}^{87} R b, a \beta\) emitter with a half-life of \(4.75 \times 10^{10} y r\), is used to determine the age of rocks and fossils. Rocks containing fossils of ancient animals contain a ratio of \({ }_{38}^{87} S r \text { to }{ }_{37}^{87} R b \text { of } 0.0260\). Assuming that there was no \({ }_{38}^{87} \mathrm{Sr}\) present when the rocks were formed, estimate the age of these fossils. Equation Transcription: Text Transcription: _37^87 R b, a \beta 4.75 \times 10^10 y r _38^87 S r to_37^87 R bof 0.0260

(II) Two of the naturally occurring radioactive decay sequences start with \({ }_{90}^{232} \mathrm{Th}\) and with \({ }_{92}^{235} U\). The first five decays of these two sequences are: \(\alpha, \beta, \beta, \alpha, \alpha\) and \(\alpha, \beta, \alpha, \beta, \alpha\) Determine the resulting intermediate daughter nuclei in each case. Equation Transcription: Text Transcription: 90 ^ 232Th 92 ^ 235U \alpha, \beta, \beta, \alpha, \alpha \alpha, \beta, \alpha, \beta, \alpha

Problem 55P (II) An ancient wooden club is found that contains 73 g of carbon and has an activity of 7.0 decays per second. Determine its age assuming that in living trees the ratio of 14C/12C atoms is about 1.3 X 10-12

(II) Use Fig. 30-11 and calculate the relative decay rates for \(\alpha\) decay of \({ }_{84}^{218} \mathrm{Poand}{ }_{84}^{214} \mathrm{Po}\) Equation Transcription: Text Transcription: \alpha 84 ^ 218 Po and 84 ^ 214 Po

Problem 57P (III) The activity of a radioactive source decreases by 5.5% in 31.0 hours. What is the half-life of this source?

(III) \({ }_{4}^{7} \mathrm{Be}\) decays with a half-life of about 53 d. It is produced in the upper atmosphere, and filters down onto the Earth's surface. If a plant leaf is detected to have \(350 \text { decays } / \mathrm{s}\) of \({ }_{4}^{7} \mathrm{Be}\), (a) how long do we have to wait for the decay rate to drop to 25 per second? (b) Estimate the initial mass of \({ }_{4}^{7} \mathrm{Be}\) on the leaf. Equation Transcription: Text Transcription: 4 ^ 7Be 350 decays/s 4 ^ 7Be 4 ^ 7Be

Problem 59P (III) At t =0, a pure sample of radioactive nuclei contains N0 nuclei whose decay constant is ? Determine a formula for the number of daughter nuclei, ND, as a function of time; assume the daughter is stable and that ND =0 at t = 0.

Problem 60GP Which radioactive isotope of lead is being produced if themeasured activity of a sample drops to 1.050% of its original activity in 4.00 h?

Problem 62GP A neutron star consists of neutrons at approximatelynuclear density. Estimate, for a 10-km-diameter neutronstar, (a) its mass number, (b) its mass (kg), and (c) theacceleration of gravity at its surface.

An old wooden tool is found to contain only 4.5% of the \(^{14} _6 C\) that an equal mass of fresh wood would. How old is the tool?

Tritium dating. The \({ }_{1}^{3} \mathrm H\) isotope of hydrogen, which is called tritium (because it contains three nucleons), has a half-life of 12.3 yr. It can be used to measure the age of objects up to about 100 yr. It is produced in the upper atmosphere by cosmic rays and brought to Earth by rain. As an application, determine approximately the age of a bottle of wine whose \({ }_{1}^{3} \mathrm H\) radiation is about \(\frac{1}{10}\) that present in new wine.

Problem 64GP Some elementary particle theories (Section 32–11) suggestthat the proton may be unstable, with a half-life ? 1033 yr. (a) How long would you expect to wait for one proton inyour body to decay (approximate your body as all water)? (b) Of the roughly 7 billion people on Earth, about howmany would have a proton in their body decay in a 70 yrlifetime?

The original experiments which established that an atom has a heavy, positive nucleus were done by shooting alpha particles through gold foil. The alpha particles had a kinetic energy of 7.7 MeV. What is the closest they could get to the center of a gold nucleus? How does this compare with the size of the nucleus?

Problem 66GP How long must you wait (in half-lives) for a radioactivesample to drop to 2.00% of its original activity?

If the potassium isotope \({ }_{19}^{40} K\) gives 42 decays/s in a liter of milk, estimate how much \({ }_{19}^{40} K\) and regular \({ }_{19}^{39} K\) are in a liter of milk. Use Appendix B. Equation Transcription: Text Transcription: 19^40K 19^40K 19^39K

Strontium-90 is produced as a nuclear fission product of uranium in both reactors and atomic bombs. Look at its location in the Periodic Table to see what other elements it might be similar to chemically, and tell why you think it might be dangerous to ingest. It has too many neutrons to be stable, and it decays with a half-life of about 29 yr. How long will we have to wait for the amount of \({ }_{38}^{90} S r\) on the Earth's surface to reach \(1 \%\) of its current level, assuming no new material is scattered about? Write down the decay reaction, including the daughter nucleus. The daughter is radioactive: write down its decay. Equation Transcription: Text Transcription: 38^90Sr 1%

The activity of a sample of \({ }_{16}^{35} S\left(T_{\frac{1}{2}}=87.37 \text { days }\right)\) is \(4.28 \times 10^{4}\) decays per second. What is the mass of the sample? Equation Transcription: Text Transcription: 16^35S (T_12=87.37 days) 4.28 x 10^4

The nuclide \({ }_{76}^{191} O s\) decays with \(\beta^{-}\) energy of \(0.14 \mathrm{MeV}\) accompanied by \(\gamma\) rays of energy \(0.042 \mathrm{MeV} \text { and } 0.129 \mathrm{MeV}\). (a) What is the daughter nucleus? (b) Draw an energy-level diagram showing the ground states of the parent and daughter and excited states of the daughter (c) To which of the daughter states does \(\beta^{-}\) decay of \({ }_{76}^{191} \mathrm{Os}\) occur? Equation Transcription: Text Transcription: 76^191 Os \beta^{-} 0.14 MeV \gamma 0.042 MeV and 0.129 MeV \beta^{-} 76^191 Os

Determine the activities of (a) \(1.0 \mathrm{~g} \text { of }{ }_{53}^{131} \mid\left(\mathrm{T}_{\frac{1}{2}}=8.02 \text { days}\right)\) and (b) \(\text { 1.0g of }{ }_{92}^{238} U\left(T_{1}=4.47 \times 10^{9} \mathrm{yr}\right)\) Equation Transcription: Text Transcription: 1.0g of 53^131 I (T_1 over 2=8.02 days) 1.0g of 92^238 U (T_1 over 2=4.47 x 10^9yr)

Use Fig. 30-1 to estimate the total binding energy for copper and then estimate the energy, in joules, needed to break a \(3.0 \mathrm{~g}\) copper penny into its constituent nucleons. Equation Transcription: Text Transcription: 3.0g

When water is placed near an intense neutron source, the neutrons can be slowed down to almost zero speed by collisions with the water molecules, and are eventually captured by a hydrogen nucleus to form the stable isotope called deuterium, \(^2 _1 H\), giving off a gamma ray. What is the energy of the gamma ray?

Instead of giving atomic masses for nuclides as in Appendix B, some Tables give the mass excess, \(\Delta\), defined as \(\Delta = M - A\), where A is the atomic mass number and M is the mass in u. Determine the mass excess, in u and in \(MeV/C^2\), for: (a) \(^4 _2 He\); (b) \(^{12} _6 C\); (c) \(^{86} _{38} Sr\); (d) \(^{235} _{92} U\). (e) From a glance at Appendix B, can you make a generalization about the sign of \(\Delta\) as a function of Z or A?

Problem 75GP The practical limit for carbon-14 dating is about 60,000 years.If a bone contains 1.0 kg of carbon, and the animal died60,000 years ago, what is the activity today?

Using Section 30-2 and Appendix B, determine the energy required to remove one neutron from \({ }_{2}^{4} \mathrm{He}\) . How many times greater is this energy than the binding energy of the last neutron in \({ }_{6}^{13} \mathrm{C}\)? Equation Transcription: Text Transcription: 2 ^ 4He 6 ^ 13C

Problem 77GP (a) If all of the atoms of the Earth were to collapse andsimply become nuclei, what would be the Earth’s newradius? (b) If all of the atoms of the Sun were to collapseand simply become nuclei, what would be the Sun’s newradius?

(a) A \(72 \text { - gram }\) sample of natural carbon contains the usual fraction of \({ }_{6}^{14} C\). Estimate roughly how long it will take before there is only one \({ }_{6}^{14} C\) nucleus left. (b) How does the answer in change if the sample is \(340 \text { grams }\)? What does this tell you about the limits of carbon dating? Equation Transcription: Text Transcription: 72-gram 6^14C 6^14C 340 grams

Problem 79GP If the mass of the proton were just a little closer to themass of the neutron, the following reaction would be possible even at low collision energies: e– + p ? n + v. (a) Why would this situation be catastrophic? (See lastparagraph of Chapter 33.) (b) By what percentage wouldthe proton’s mass have to be increased to make this reactionpossible?

Problem 80GP What is the ratio of the kinetic energies for an alpha particleand a beta particle if both make tracks with the sameradius of curvature in a magnetic field, oriented perpendicular to the paths of the particles?

A \(1.00-g\) sample of natural samarium emits \(\alpha\) particles at rate of \(120 s^{-1}\) due to the presence of \({ }_{62}^{147} \mathrm{Sm}\). The natural abundance of is \({ }_{62}^{147} \mathrm{Sm}\) is \(15 \%\) Calculate the half-life for this decay process. Equation Transcription: Text Transcription: 1.00-g \alpha 120s^-1 62^147Sm 62^147Sm 15%

Almost all of naturally occurring uranium is \({ }_{92}^{238} \mathrm{U}\) with half-life of \(4.468 \times 10^{9} y r\). Most of the rest of natural uranium is \({ }_{92}^{235} \mathrm{U}\) with a half-life of \(7.04 x 10^{5} y r\) Today sample contains \(0.720 \%_{92}^{235} U\) (a) What was this percentage 1.0 billion years ago? (b) What percentage of uranium will be \({ }_{92}^{235} U\) 100 million years from now? Equation Transcription: Text Transcription: 92^238 U 4.468 x 109yr 92^235U 7.04 x 105yr 0.720% 92^235U 92^235U

A banana contains about \(420 \mathrm{mg}\) of potassium, of which a small fraction is the radioactive isotope \({ }_{19}^{40} K\) (Appendix ). Estimate the activity of an average banana due to \({ }_{19}^{40} K\) Equation Transcription: Text Transcription: 420 mg 19^40K 19^40K

When \({ }_{10}^{23} \mathrm{Ne}(\text { mass }=22.9947 u)\) decays to \({ }_{11}^{23} N a(\text { mass }=22.9898 u)\), what is the maximum kinetic energy of the emitted electron? What is its minimum energy? What is the energy of the neutrino in each case? Ignore recoil of the daughter nucleus. Equation Transcription: Text Transcription: 10^23Ne( mass=22.9947u) 11^23Na( mass=22.9898u)

(a) In decay of, say, a \({ }_{88}^{226} \mathrm{Ra}\) nucleus, show that the nucleus carries away a fraction \(1 /\left(1+\frac{1}{4} A_{D}\right)\) of the total energy available, where \(A_{D}\) is the mass number of the daughter nucleus. [Hint: Use conservation of momentum as well as conservation of energy.] (b) Approximately what percentage of the energy available is thus carried off by the particle when \({ }_{88}^{226} R a\) decays? Equation Transcription: Text Transcription: 88^226Ra 1/(1+1 over 4A_D) A_D 88^226Ra

Decay series, such as that shown in Fig. 30–11, can be classified into four families, depending on whether the mass numbers have the form \(4 n, 4 n,+1,4 n+3\), where n is an integer. Justify this statement and show that for a nuclide in any family, all its daughters will be in the same family. Equation Transcription: Text Transcription: 4n, 4n,+1, 4n+3

A pi meson has a mass of What is this in atomic mass units?

What is the approximate radius of an particle A2 a 4 HeB?

(I) By what % is the radius of \(^{238} _{92} U\) greater than the radius of \(^{232} _{92} U\)?

(II) (a) What is the approximate radius of a \(^{112} _{48} Cd\) nucleus? (b) Approximately what is the value of A for a nucleus whose radius is \(3.7 \times 10^{-15}\ m\)?

What is the mass of a bare particle (without electrons) in MeVc2?

Suppose two alpha particles were held together so they were just touching(use Eq.301). Estimate the electrostatic repulsive force each would exert on the other. What would be the acceleration of an alpha particle subjected to this force?

(a) What would be the radius of the Earth if it had its actual mass but had the density of nuclei? (b) By what factor would the radius of a nucleus increase if it had the Earths density?

What stable nucleus has approximately half the radius of a uranium nucleus? [Hint: Find A and use Appendix B to get Z.]

If an alpha particle were released from rest near the surface of a nucleus, what would its kinetic energy be when far away?

(a) What is the fraction of the hydrogen atoms mass that is in the nucleus? (b) What is the fraction of the hydrogen atoms volume that is occupied by the nucleus?

Approximately how many nucleons are there in a 1.0-kg object? Does it matter what the object is made of? Why or why not?

How much kinetic energy, in MeV, must an particle have to just touch the surface of a nucleus?

Estimate the total binding energy for using Fig. 301

Use Fig. 301 to estimate the total binding energy of (a) and (b) 84 36Kr

(II) Calculate the binding energy per nucleon for a \({ }_{7}^{15}\mathrm N\) nucleus, using Appendix B.

Use Appendix B to calculate the binding energy of (deuterium)

Determine the binding energy of the last neutron in a nucleus.

(II) Calculate the total binding energy, and the binding energy per nucleon, for (a) \(^7 _3 Li\), (b) \(^{195} _{78} Pt\). Use Appendix B.

Compare the average binding energy of a nucleon in to that in , using Appendix B.

How much energy is required to remove (a) a proton, (b) a neutron, from Explain the difference in your answers.

(III) (a) Show that the nucleus \(^8 _4 Be\) (mass = 8.005305 u) is unstable and will decay into two \(\alpha\) particles (b) Is \(^{12} _6 C\) stable against decay into three \(\alpha\) particles? Show why or why not.

The nucleus has an excited state 0.48 MeV above the ground state. What wavelength gamma photon is emitted when the nucleus decays from the excited state to the ground state?

Show that the decay is not possible because energy would not be conserved.

(II) Calculate the energy released when tritium, \(^3 _1 H\), decays by \(\beta^-\) emission.

What is the maximum kinetic energy of an electron emitted in the decay of a free neutron?

Give the result of a calculation that shows whether or not the following decays are possible:

is radioactive. (a) Is it a or emitter? (b) Write down the decay reaction, and estimate the maximum kinetic energy of the emitted b

A nucleus emits an particle with kinetic (a) What is the daughter nucleus, and (b) what is the approximate atomic mass (in u) of the daughter atom? Ignore recoil of the daughter nucleus

Calculate the maximum kinetic energy of the particle emitted during the decay of

(II) How much energy is released in electron capture by beryllium: \(^7 _4 Be+e^- \rightarrow ^7 _3 Li+v\)?

The isotope can decay by either or emission. What is the energy release in each case? The mass of is 218.008973 u

The nuclide decays by emitting an electron whose maximum kinetic energy can be 1.71 MeV. (a) What is the daughter nucleus? (b) Calculate the daughters atomic mass (in u)

(II) A photon with a wavelength of \(1.15 \times 10^{-13} \ \mathrm m\) is ejected from an atom. Calculate its energy and explain why it is a \(\gamma\) ray from the nucleus or a photon from the atom.

How much recoil energy does a nucleus get when it emits a 1.46-MeV gamma ray

Determine the maximum kinetic energy of particles released when decays to What is the maximum energy the neutrino can have? What is the minimum energy of each?

Show that when a nucleus decays by decay, the total energy released is equal to where and are the masses of the parent and daughter atoms (neutral), and is the mass of an electron or positron

When decays, the particle emitted has 4.20 MeV of kinetic energy. Calculate the recoil kinetic energy of the daughter nucleus and the Q-value of the decay

(a) What is the decay constant of whose half-life is (b) The decay constant of a given nucleus is What is its half-life?

A radioactive material produces 1120 decays per minute at one time, and 3.6 h later produces 140 decays per minute. What is its half-life?

What fraction of a sample of whose half-life is about 9 months, will remain after 2.5 yr?

What is the activity of a sample of that contains 6.5 * 1020 nuclei?

What fraction of a radioactive sample is left after exactly 5 half-lives?

The iodine isotope is used in hospitals for diagnosis of thyroid function. If are ingested by a patient, determine the activity (a) immediately, (b) 1.50 h later when the thyroid is being tested, and (c) 3.0 months later. Use Appendix B

How many nuclei of remain in a rock if the activity registers 420 decays per second?

(II) In a series of decays, the nucleus \(^{235} _{92} U\) becomes \(^{207} _{82} Pb\). How many \(\alpha\) and \(\beta^-\) particles are emitted in this series?

has a half-life of 30.8 s. (a) If we have initially, how many Cs nuclei are present? (b) How many are present 2.6 min later? (c) What is the activity at this time? (d) After how much time will the activity drop to less than about 1 per second?

Calculate the mass of a sample of pure with an initial decay rate of The half-life of is

(II) Calculate the activity of a pure \(6.7-\mu g\) sample of \({ }_{15}^{32} \mathrm{P}\) \(\left(T_{\frac{1}{2}}=1.23 \times 10^6 \mathrm{~s}\right)\).

A sample of contains (a) What is the decay constant? (b) Approximately how many disintegrations will occur per minute

The activity of a sample drops by a factor of 6.0 in 9.4 minutes. What is its half-life?

A 345-g sample of pure carbon contains 1.3 parts in (atoms) of How many disintegrations occur per second?

A sample of is decaying at a rate of What is the mass of the sample?

(II) Rubidium;strontium dating. The rubidium isotope \(^{87} _{37} Rb\), a \(\beta\) emitter with a half-life of \(4.75 \times 10^{10}\ yr\), is used to determine the age of rocks and fossils. Rocks containing fossils of ancient animals contain a ratio of \(^{87} _{38} Sr\) to \(^{87} _{37} Rb\) of 0.0260. Assuming that there was no \(^{87} _{38} Sr\) present when the rocks were formed, estimate the age of these fossils.

Two of the naturally occurring radioactive decay sequences start with and with The first five decays of these two sequences are: and Determine the resulting intermediate daughter nuclei in each cas

An ancient wooden club is found that contains 73 g of carbon and has an activity of 7.0 decays per second. Determine its age assuming that in living trees the ratio of atoms is about

Use Fig. 3011 and calculate the relative decay rates for decay of

The activity of a radioactive source decreases by 5.5% in 31.0 hours. What is the half-life of this source?

decays with a half-life of about 53 d. It is produced in the upper atmosphere, and filters down onto the Earths surface. If a plant leaf is detected to have of (a) how long do we have to wait for the decay rate to drop to 25 per second? (b) Estimate the initial mass of on the leaf

At a pure sample of radioactive nuclei contains nuclei whose decay constant is Determine a formula for the number of daughter nuclei, as a function of time; assume the daughter is stable and that at t = 0.

Which radioactive isotope of lead is being produced if the measured activity of a sample drops to 1.050% of its original activity in 4.00 h?

An old wooden tool is found to contain only 4.5% of the that an equal mass of fresh wood would. How old is the tool?

A neutron star consists of neutrons at approximately nuclear density. Estimate, for a 10-km-diameter neutron star, (a) its mass number, (b) its mass (kg), and (c) the acceleration of gravity at its surface.

Tritium dating. The isotope of hydrogen, which is called tritium (because it contains three nucleons), has a half-life of 12.3 yr. It can be used to measure the age of objects up to about 100 yr. It is produced in the upper atmosphere by cosmic rays and brought to Earth by rain. As an application, determine approximately the age of a bottle of wine whose radiation is about that present in new wine

Some elementary particle theories (Section 32–11) suggest that the proton may be unstable, with a half-life \(\geq\ 10^{33}\ yr\). (a) How long would you expect to wait for one proton in your body to decay (approximate your body as all water)? (b) Of the roughly 7 billion people on Earth, about how many would have a proton in their body decay in a 70 yr lifetime?

The original experiments which established that an atom has a heavy, positive nucleus were done by shooting alpha particles through gold foil. The alpha particles had a kinetic energy of 7.7 MeV. What is the closest they could get to the center of a gold nucleus? How does this compare with the size of the nucleus?

How long must you wait (in half-lives) for a radioactive sample to drop to 2.00% of its original activity?

If the potassium isotope gives in a liter of milk, estimate how much and regular are in a liter of milk. Use Appendix B.

Strontium-90 is produced as a nuclear fission product of uranium in both reactors and atomic bombs. Look at its location in the Periodic Table to see what other elements it might be similar to chemically, and tell why you think it might be dangerous to ingest. It has too many neutrons to be stable, and it decays with a half-life of about 29 yr. How long will we have to wait for the amount of on the Earths surface to reach 1% of its current level, assuming no new material is scattered about? Write down the decay reaction, including the daughter nucleus. The daughter is radioactive: write down its decay.

The activity of a sample of is decays per second. What is the mass of the sample?

The nuclide \({ }_{76}^{191} \mathrm{Os}\) decays with \(\beta^{-}\)energy of 0.14 MeV accompanied by \(\gamma\) rays of energy 0.042 MeV and 0.129 MeV. (a) What is the daughter nucleus? (b) Draw an energy-level diagram showing the ground states of the parent and daughter and excited states of the daughter. (c) To which of the daughter states does \(\beta^{-}\)decay of \({ }_{76}^{191}\) Os occur?

Determine the activities of (a) 1.0 g of and (b)

Use Fig. 301 to estimate the total binding energy for copper and then estimate the energy, in joules, needed to break a 3.0-g copper penny into its constituent nucleons

Instead of giving atomic masses for nuclides as in Appendix B, some Tables give the mass excess, defined as where A is the atomic mass number and M is the mass in u. Determine the mass excess, in u and in for: (a) (b) (c) (d) (e) From a glance at Appendix B, can you make a generalization about the sign of as a function of Z or A?

When water is placed near an intense neutron source, the neutrons can be slowed down to almost zero speed by collisions with the water molecules, and are eventually captured by a hydrogen nucleus to form the stable isotope called deuterium, giving off a gamma ray. What is the energy of the gamma ray?

The practical limit for carbon-14 dating is about 60,000 years. If a bone contains 1.0 kg of carbon, and the animal died 60,000 years ago, what is the activity today?

Using Section 302 and Appendix B, determine the energy required to remove one neutron from How many times greater is this energy than the binding energy of the last neutron in

(a) If all of the atoms of the Earth were to collapse and simply become nuclei, what would be the Earths new radius? (b) If all of the atoms of the Sun were to collapse and simply become nuclei, what would be the Suns new radius?

(a) A 72-gram sample of natural carbon contains the usual fraction of Estimate roughly how long it will take before there is only one nucleus left. (b) How does the answer in (a) change if the sample is 340 grams? What does this tell you about the limits of carbon dating?

If the mass of the proton were just a little closer to the mass of the neutron, the following reaction would be possible even at low collision energies: (a) Why would this situation be catastrophic? (See last paragraph of Chapter 33.) (b) By what percentage would the protons mass have to be increased to make this reaction possible?

What is the ratio of the kinetic energies for an alpha particle and a beta particle if both make tracks with the same radius of curvature in a magnetic field, oriented perpendicular to the paths of the particles?

A 1.00-g sample of natural samarium emits particles at a rate of due to the presence of The natural abundance of is 15%. Calculate the half-life for this decay process

Almost all of naturally occurring uranium is with a half-life of Most of the rest of natural uranium is with a half-life of Today a sample contains 0.720% (a) What was this percentage 1.0 billion years ago? (b) What percentage of uranium will be 100 million years from now?

A banana contains about 420 mg of potassium, of which a small fraction is the radioactive isotope (Appendix B). Estimate the activity of an average banana due to

When decays to what is the maximum kinetic energy of the emitted electron? What is its minimum energy? What is the energy of the neutrino in each case? Ignore recoil of the daughter nucleus

(a) In decay of, say, a nucleus, show that the nucleus carries away a fraction of the total energy available, where is the mass number of the daughter nucleus. [Hint: Use conservation of momentum as well as conservation of energy.] (b) Approximately what percentage of the energy available is thus carried off by the particle when decays?

Decay series, such as that shown in Fig. 3011, can be classified into four families, depending on whether the mass numbers have the form 4n, or where n is an integer. Justify this statement and show that for a nuclide in any family, all its daughters will be in the same family