What element is formed by the decay of (a) ; (b) (c) ?

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

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

What is the approximate radius of an alpha particle \(\left({ }_2^4 \mathrm{He}\right)\) ?

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

Problem 6P (II(a) What is the fraction of the hydrogen atom’s mass (|H) that is in the nucleus? (b) What is the fraction of the hydrogen atom’s volume that is occupied by the nucleus?

Problem 7P (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?

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

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

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

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

A \({ }_{92}^{238} \mathrm{U}\) nucleus decays to a nucleus containing how many neutrons?

Problem 11P (II) Use Appendix B to calculate the binding energy of Jh (deuterium).

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

(II) Determine the binding energy of the last neutron in a \({ }_{19}^{41} \mathrm{~K}\) nucleus.

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

Problem 15P (II) Compare the average binding energy of a nucleon in 23^a to that in ffNa, , using Appendix B.

Immediately after a \({ }_{92}^{238} \mathrm{U}\) nucleus decays to \({ }_{90}^{234} \mathrm{Th}+{ }_{2}^{4} \mathrm{He}\), the daughter thorium nucleus may still have 92 electrons circling it. Since thorium normally holds only 90 electrons, what do you suppose happens to the two extra ones? ________________ Equation Transcription: Text Transcription: _{92}^{238}U _{90}^{234}Th+_{2}^{4}He

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

(a) Show that the nucleus \({ }_{4}^{8} \mathrm{Be}\ (\mathrm{mass}=8.005305\ \mathrm {u})\) is unstable and will decay into two \(\alpha\) particles. (b) Is \({ }_{6}^{12} \mathrm{C}\) stable against decay into three a particles? Show why or why not. ________________ Equation Transcription: Text Transcription: _4^8Be (mass=8.005305 u) alpha _6^12C

Problem 17Q 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.

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

Problem 19P (II) What is the maximum kinetic energy of an electron emitted in the p decay of a free neutron?

Problem 19Q Can hydrogen or deuterium emit an a particle? Explain.

Show that the decay \({ }_{6}^{11} \mathrm{C} \rightarrow{ }^{10} \mathrm{~B}+\mathrm{p}\) is not possible because energy would not be conserved. ________________ Equation Transcription: Text Transcription: _6^11C{rightarrow}_5^10 B+p

Problem 20Q Why are many artificially produced radioactive isotopes rare in nature?

\(_{11}^{22} \mathrm{N a}\) 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: _11^22Na beta^- beta^+ beta

Problem 21Q n 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?

Problem 22Q Why are none of the elements with Z > 92 stable?

(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.

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: _3^6Li alpha

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

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: _15^32P

The isotope \({ }_{84}^{218} \mathrm{Po}\) can decay by either \(\alpha\) or \(\beta^-\) emission. What is the energy release in each case? The mass of \({ }_{84}^{218} \mathrm{Po}\) is 218.008965 u. ________________ Equation Transcription: Text Transcription: _84^218Po alpha beta^- _84^218Po

How much energy is released in electron capture by beryllium: \({ }_{4}^{7} \mathrm{Be}+{ }_{-1}^{0} \mathrm{e} \rightarrow{ }_{3}^{7} \mathrm{Li}+\nu\)?

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

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

Problem 35P (Ill) Show that when a nucleus decays by (3+ 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 me is the mass of an electron or positron.

Two of the naturally occurring radioactive decay sequences start with \({ }_{90}^{232} \mathrm{Th}\), and \({ }_{92}^{235} \mathrm{U}\). 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.

(II) An ancient wooden club is found that contains 290 g of carbon and has an activity of 8.0 decays per second. Determine its age assuming that in living trees the ratio of \(^{14}{C}/^{12}{C}\) atoms is about \(1.3 \times \ 10^?{12}\).

(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.

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?

Problem 60GP 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.

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: _38^90Sr

Problem 72GP 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?

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 _62^147Sm _62^147Sm

What are the elements represented by the X in the following: \({ }_{92}^{232}\mathrm {X}\); \({ }_{7}^{18}\mathrm {X}\); \({ }_{1}^{1}\mathrm {X}\); \({ }_{38}^{82}\mathrm {X}\); \({ }_{97}^{247}\mathrm {X}\)? ________________ Equation Transcription: Text Transcription: (a)_92^232X (b)_71^8X (c)_1^1X (d)_38^82X (e)_97^247X

Problem 3P What is the rest mass of a bare ? particle in MeV/c2?

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

(a) What is the approximate radius of a \({ }_{29}^{64}\mathrm {Cu}\) nucleus? (b) Approximately what is the value of A for a nucleus whose radius is \(3.9 \times 10^{-15}\ \mathrm m\)? ________________ Equation Transcription: Text Transcription: _29^64Cu 3.9x10^-15 m

Problem 4Q Identify the element that has 88 nucleons and 50 neutrons.

(II) (a) Show that the density of nuclear matter is essentially the same for all nuclei. (b) What would be the radius of the Earth if it had its actual mass but had the density of nuclei? (c) What would be the radius of a \({ }_{92}^{238} \mathrm{U}\) nucleus if it had the density of the Earth?

Problem 6Q How do we know there is such a thing as the strong nuclear force?

How much energy must an \(\alpha\) particle have to just "touch" the surface of a \({ }_{92}^{238} \mathrm{U}\) nucleus?

(I) Estimate the total binding energy for \({ }_{20}^{40} \mathrm{Ca}\), using Fig. 30-1.

(II) Calculate the binding energy per nucleon for a \({ }_{7}^{14}\mathrm {N}\) nucleus. ________________ Equation Transcription: Text Transcription: { }_{7}^{14}\mathrm {N}

What element is formed by the radioactive decay of (a) \({ }_{11}^{24} \mathrm{Na}\left(\beta^{-}\right)\) ;(b) \({ }_{11}^{22} \mathrm{Na}\left(\beta^{+}\right)\); (c) \({ }_{84}^{210} \mathrm{Po}(\alpha)\) ? [Hint: see Appendix B.]

What element is formed by the decay of \((a)\ { }_{15}^{32} \mathrm{P}\ \left(\beta^{-}\right)\); \((b)\ { }_{16}^{35} \mathrm{S}\ \left(\beta^{-}\right)\); \((c)\ { }_{83}^{211} \mathrm{Bi}\ (\alpha)\)? [Hint: see Appendix B.] ________________ Equation Transcription: Text Transcription: (a)_15^32P (beta^-) (b)_16^35S (beta^-) (c)_83^211Bi (alpha)

(II) Calculate the total binding energy, and the binding energy per nucleon, for \((a)\ \ { }_{3}^{6} \mathrm{Li}\), \((b)\ \ { }_{82}^{208} \mathrm{Pb} \). Use Appendix B.

(III) How much energy is required to remove (a) a proton, (b) a neutron, from \({ }_8^{16} \mathrm{O}\) ? Explain the difference in your answers.

(I) How much energy is released when tritium, \({ }_{1}^{3} \mathrm{H}\), decays by \(\beta^-\) emission? ________________ Equation Transcription: Text Transcription: _1^3H beta^-

(II) Give the result of a calculation that shows whether or not the following decays are possible: \((a)\ { }_{92}^{236} \mathrm{U} \rightarrow{ }_{92}^{235} \mathrm{U}+\mathrm{n};\) \((b)\ { }_{8}^{16} \mathrm{O} \rightarrow{ }_{8}^{15} \mathrm{O}+\mathrm{n};\) \((c)\ { }_{11}^{23} \mathrm{Na} \rightarrow{ }_{11}^{22} \mathrm{Na}+\mathrm{n}.\) ________________ Equation Transcription: Text Transcription: (a) _{92}^{236}U_92}^{235}U+n; (b) _{8}^{16}O_{8}^{15}O+n; (c)_{11}^{23}Na_{11}^{22}Na+n.

(II) When \({ }_{10}^{23} \mathrm{Ne}\) (mass = 22.9945 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: _10^23Ne _11^23Na

(II) A nucleus of mass 238 u, initially at rest, emits an ? particle with KE of 5.0 MeV. What is them KE of the recoiling daughter nucleus?

Problem 25Q In both internal conversion and ? decay, an electron is emitted. How could you determine which decay process occurred?

(II) What is the maximum KE of the emitted \(\beta\) particle during the decay of \({ }_{27}^{60} \mathrm{Co}\)? ________________ Equation Transcription: Text Transcription: beta _27^60Co

A photon with a wavelength of \(1.00 \times 10^{?13} \mathrm {m}\) 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.

(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 its minimum energy?

(III) What is the energy of the \(\alpha\) particle emitted in the decay \({ }_{84}^{210} \mathrm{Po} \rightarrow{ }_{82}^{206} \mathrm{Pb}+\alpha\)? Take into account the recoil of the daughter nucleus. ________________ Equation Transcription: Text Transcription: alpha _84^210Po{rightarrow}_82^206Pb+alpha

Problem 36P A radioactive material produces 1280 decays per minute at one time, and 4.6 h later produces 320 decays per minute. What is its half-life?

(I) () What is the decay constant of \({ }_{92}^{238} \mathrm{U}\) whose half-life is \(4.5\times 10^9\ \mathrm{yr}\)? () The decay constant of a given nucleus is \(8.2\times 10^{-5}\ \mathrm{s}^{-1}\). What is its half-life? ________________ Equation Transcription: Text Transcription: _92^238U 4.5x109 yr 8.2x10^-5 s^-1

(I) What is the activity of a sample of \({ }_{6}^{14} \mathrm{C}\) that contains \(3.1\times 10^{20}\) nuclei?

(I) What fraction of a sample of \({ }_{32}^{68} \mathrm{Ge}\), whose half-life is about 9 months, will remain after 3.0 yr? ________________ Equation Transcription: Text Transcription: _32^68Ge

Problem 40P What fraction of a sample is left after exactly 6 half-lives?

(II) How many nuclei of \({ }_{92}^{238} \mathrm{U}\) remain in a rock if the activity registers 640 decays per second? ________________ Equation Transcription: Text Transcription: _92^238U

(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: _92^235U _82^207Pb alpha beta^-

(II) The iodine isotope \({ }_{53}^{131} \mathrm{I}\) is used in hospitals for diagnosis of thyroid function. If \(682\ \mu \mathrm{g}\) are ingested by a patient, determine the activity (a) immediately, (b) 1.0 h later when the thyroid is being tested, and (c) 6 months later. Use Appendix B.

(II) \({ }_{55}^{124} \mathrm{Cs}\) has a half-life of If we have \(8.8\ \mu \mathrm{g}\) initially, how many Cs nuclei are present? (b) How many are present min later? What is the activity at this time? After how much time will the activity drop to less than about 1 per second? ________________ Equation Transcription: Text Transcription: _55^124Cs 8.8 {mu}g

(II) Calculate the mass of a sample of pure \({ }_{19}^{40} \mathrm{K}\) with an initial decay rate of \(2.0\times 10^{-5}\ \mathrm{s}^{-1}\). The half-life of \({ }_{19}^{40} \mathrm{K}\) is \(1.28\times 10^9\ \mathrm{yr}\). ________________ Equation Transcription: Text Transcription: _19^40K 2.0x10^5s^-1 _19^40K 1.28x10^9 yr

(II) Calculate the activity of a pure \(9.7\text - \mu \mathrm{g}\) sample of \({ }_{15}^{32} \mathrm{P}\) \(\left(T_{\frac{1}{2}}=1.23 \times 10^{6} \mathrm{~s}\right)\). ________________ Equation Transcription: Text Transcription: 9.7-{mu}g _15^32P (T_frac{1}{2}=1.23x10^6 s)

The activity of a sample of \({ }_{10}^{35} \mathrm{~S}\left(T_{\frac{1}{2}}=7.55 \times 10^6 \mathrm{~s}\right)\) is \(2.65 \times 10^5\) decays per second. What is the mass of the sample?

(II) A sample of \({ }_{92}^{233} \mathrm{U}\left(T_{\frac{1}{2}}=1.59 \times 10^5 \mathrm{yr}\right)\) contains \(7.50 \times 10^{19}\) nuclei. (a) What is the decay constant? (b) Approximately how many disintegrations will occur per minute?

Problem 49P The activity of a sample drops by a factor of 10 m 8.6 minutes. What is its half-life?

(II) A sample of pure carbon contains parts in \(10^{12}\) (atoms) of \({ }_{6}^{14} \mathrm{C}\). How many disintegrations occur per second? ________________ Equation Transcription: Text Transcription: 10^12 _6^14C

(II) A sample of \({ }_{19}^{40} \mathrm{K}\) is decaying at a rate of \(6.70\times 10^2\ \mathrm{decays/s}\). What is the mass of the sample? ________________ Equation Transcription: Text Transcription: _19^40K 6.70x10^2 decays/s

The rubidium isotope \({ }_{37}^{87} \mathrm{Rb}\), a \(\beta\) emitter with a halflife 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 0.0160. Assuming that there was no \({ }_{38}^{87} \mathrm{Sr}\) present when the rocks were formed, estimate the age of these fossils. [Hint: use Eq. 30-3.]

(II) Use Fig. and calculate the relative decay rates for \(\alpha\) decay of \({ }_{84}^{218} \mathrm{Po}\) and \({ }_{84}^{214} \mathrm{Po}\). ________________ Equation Transcription: Text Transcription: alpha _84^218Po _84^214Po

(II) \({ }_{4}^{7} \mathrm{Be}\) 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 450 decays/s of \({ }_{4}^{7} \mathrm{Be}\), how long do we have to wait for the decay rate to drop to 15 per second? (b) Estimate the initial mass of \({ }_{4}^{7} \mathrm{Be}\) on the leaf. ________________ Equation Transcription: Text Transcription: _4^7Be _4^7Be _4^7Be

An old wooden tool is found to contain only 6.0% of \({ }_{6}^{14} \mathrm{C}\) that a sample of fresh wood would. How old is the tool?

The \(_{1}^{3}\mathrm H\) isotope of hydrogen, which is called tritium (because it contains three nucleons), has a half-life of 12.33 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 62GP Some elementary particle theories (Section 32–11) suggest that the proton may be unstable, with a half-life ? 1032 yr. How long would you expect to wait for one proton in your body to decay (consider that your body is all water)?

How long must you wait (in half-lives) for a radioactive sample to drop to 1.00% of its original activity?

If the potassium isotope \({ }_{19}^{40} \mathrm{~K}\) gives 60 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.

In decay of, say, a \({ }_{88}^{226} \mathrm{Ra}\) nucleus, show that the nucleus carries away a fraction \(1/1(1+\frac{1}{4}A_\mathrm {D})\) 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 in the case cited? ________________ Equation Transcription: Text Transcription: _88^226Ra 1/(1+frac{1}{4}A_D) A_D

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. To which of the daughter states does \(\beta^-\) decay of \({ }_{76}^{191} \mathrm{Os}\) occur?

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

Estimate the total binding energy for copper and then estimate the energy, in joules, needed to break a copper penny into its constituent nucleons. [Hint: use Fig.

Instead of giving atomic masses for nuclides as in Appendix , some Tables give the mass excess, \(\Delta\), defined as \(\Delta=M-A\), where is the atomic number and is the mass in u. Determine the mass excess, in and in \(\mathrm {MeV}/c^2\), for: \((a)\ \ { }_{2}^{4} \mathrm{He}\); \((b)\ \ { }_{6}^{12} \mathrm{C}\); \((c)\ \ { }_{47}^{107} \mathrm{Ag}\); \((d)\ \ { }_{92}^{235} \mathrm{U}\). (e) From a glance at Appendix , can you make a generalization about the sign of as a function of or ________________ Equation Transcription: Text Transcription: Delta =M-A MeV/c^2 (a) _24^He (b) _61^2C (c) _47^107Ag (d) _92^235U Delta

(a) A 92-gram sample of natural carbon contains the usual fraction of \({ }_{6}^{14} \mathrm{C}\). Estimate how long it will take before there is only one \({ }_{6}^{14} \mathrm{C}\) nucleus left. ( ) How does the answer in (a) change if the sample is 280 grams? What does this tell you about the limits of carbon dating? ________________ Equation Transcription: Text Transcription: _6^14C _6^14C

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 \(7.038\times 10^8\ \mathrm{yr}\). Today a sample contains 0.72% \({ }_{92}^{235} \mathrm{U}\). (a) What was this percentage billion years ago? (b) What percentage of the sample would be \({ }_{92}^{235} \mathrm{U}\) in 100 million years? Equation Transcription: Text Transcription: _92^238U 4.468x10^9 yr 7.038x10^8 yr _92^235U _92^235U _92^235U

A typical banana contains \(400 \mathrm{mg}\) of potassium, of which a small fraction is the radioactive isotope \({ }_{19}^{40} \mathrm{~K}\) (see Appendix B). Estimate the activity of an average banana due to \({ }_{19}^{40} \mathrm{~K}\).

Problem 77GP 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?

Decay series, such as that shown in Fig. , can be classified into four families, depending on whether the mass numbers have the form \(4n\), \(4n+1\), \(4n+2\) or \(4n+3\), where 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