What do different isotopes of*onoz rcl-ctocz ,(tx 2(5g8 r3nu9ea a given element have in common? How are they diffeteou* c2r9 85c(a3 lozrnt- n(ogz,xc rent?

What are the elements represented by t, zujowlrjz7x7w * *c0he X in the following: (a) $_{2}^{4}\text{He} + \text{X} \to _{7}^{14}\text{N}$ (b) $_{8}^{18}\text{X}$ (c) $_{92}^{238}\text{U} \to _{90}^{234}\text{Th} + \text{X}$ (d) $_{82}^{206}\text{X}$ (e) $_{82}^{207}\text{X}$

How many protons and how many neutnzj. yy0rot0m0ih c 6-rons do each of the isotopes in Question 2 have?rm 60y0tj0y.n ioh- cz

Identify the element that hamfacgz ;s5 z5:z:s5d as 88 nucleons and 50 neutrons.

Why are the atomic masses of ma)6g.u8d lym 6r (-ab. cf/n hqb q5pws)k,zdmbny elements (see the periodic table) not close to wholg5).8d nwuzk6 s) ( bymdq ca6rh/q,fm b-plb.e numbers?

How do we know there is such a thing as the strong n8s 2b.dljyoo5y; ag(w 98sfr j x6ry:xuclear force?

What are the similarities and the differences between the stronvd6o*kf)k n d,6p 3trdg nuclear force and the electr)d3 d6kd vo6,kpf* rtnic force?

What is the experimental evidence in favor of d*7oe -y-ji://g g)vtmkoba p radioactivity being a nuclear procbyvi:dj/a tm)gkg-o/* e-7o pess?

The isotope $_{92}^{238}\text{U}$ is unusual in that it can decay by $\beta^-$, $\beta^+$, and $\alpha$ emission. What is the resulting nuclide for each case?

A $_{92}^{238}\text{U}$ nucleus decays to a nucleus containing how many neutrons?

Describe, in as many ways ax1bo k3x*-:vlresa7 tqy5 / /xwzj gu-s you can, the difference between $\alpha$, $\beta^-$, $\beta^+$, and $\gamma$ rays.

What element is formed by the radioactive deca:z pch9 *db1ioy of (a) $_{11}^{24}\text{Na}\ (\beta^-)$ (b) $_{11}^{22}\text{Na}\ (\beta^+)$ (c) $_{84}^{210}\text{Po}\ (\alpha)$?

What element is formed by the decay of6 2 pk+zwdqvpl4c/a3x (a) $_{15}^{32}\text{P}\ (\beta^-)$ (b) $_{16}^{35}\text{S}\ (\beta^-)$ (c) $_{83}^{210}\text{Bi}\ (\alpha)$?

Fill in the missing particle or n3rx*r+ 6m5o z6jj lrnnucleus:
(a) $_{20}^{42}\text{Ca} \to _{19}^{42}\text{K} + \text{e}^+ + \nu$
(b) $_{29}^{58}\text{Cu} \to _{28}^{58}\text{Ni} + \text{e}^+ + \nu$
(c) $_{23}^{46}\text{V} \to _{24}^{46}\text{Cr} + \text{e}^- + \bar{\nu}$
(d) $_{94}^{238}\text{Pu} \to _{92}^{234}\text{U} + \alpha$
(e) $_{93}^{239}\text{Np} \to _{94}^{239}\text{Pu} + \text{e}^- + \bar{\nu}$

Immediately after a a- b tnt n4ftbrjgu8x8j-()m4$_{92}^{238}\text{U}$ nucleus decays to $_{90}^{234}\text{Th} + _{2}^{4}\text{He}$, the daughter thorium nucleus still has 92 electrons circling it. Since thorium normally holds only 90 electrons, what do you suppose happens to the two extra ones?

When a nucleus undergo/4m7pg7s8eev c; fmo oes 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?

The alpha particles from a given alpha-emitting : echy,3rmuy /onf3/ jnuclide are generally monoenergetic; that is, they all have the same kinetic energy. But the beta particles from 3//e:fnr3,yuoc h jyma beta-emitting nuclide have a spectrum of energies. Explain the difference between these two cases.

Do isotopes that undeeby 5p)5by,hw euq2 s;oszg /,rgo electron capture generally lie above or below the line of stabi o y/sep);uyw5,z5h qb s2g,eblity in (Fig. Below)?

Can hydrogen or deuteriumjkvm0bw d5ym9+ j1 id) emit an $\alpha$ particle? Explain.

Why are many artificially prod topmu0a5unm fx-tf 9+0k*:lxuced radioactive isotopes rare in nature?

An isotope has a half-life of one month. Afou,j s b d3;a2pv)k:gnter two months, will a given sample of this ison3:2sv odpb)ka g j;u,tope have completely decayed? If not, how much remains?

Why are none of the elements with p 4yaelm*t1y6$Z>92$ stable?

A proton strikes a $_{3}^{6}\text{Li}$ nucleus. As a result, an $\alpha$ particle and another particle are released. What is the other particle?

Can $_{6}^{14}\text{C}$ dating be used to measure the age of stone walls and tablets of ancient civilizations? Explain.

In both internal conversion an6 (id nu4s2oddd $\beta^-$ decay, an electron is emitted. How could you determine which decay process occurred?

  A pi meson has a mass o+l910+djcmrsm fmia 5w+1 m hwf $139\ \text{MeV}/c^2$. What is this in atomic mass units? m =    u

  What is the approximate radius of 9qhtznld vpp 3z4 /+r.an alpha particle $(_{2}^{4}\text{He})$?r =    $ \times 10^{-15}\ \text{m}$

  What is the rest mass of a barehzb q1v2l-n o7c,p5tb $\alpha$ particle in $\text{MeV}/c^2$? $m_{\alpha}$ =    $\ \text{MeV}/c^2$

  (a) What is the approximateuyyswqd8 7b (5zz 64sr radius of a $_{6}^{12}\text{C}$ nucleus? r =    $ \times 10^{-15}\ \text{m}$
(b) Approximately what is the value of A for a nucleus whose radius is $7.0\ \text{fm}$? A =   

  (a) Show that the density of nuclear matter is essentidk n8yy //)learms4qwf y)* zt:0v2zbally the same for all nuclei*qkey n0ad)s mfyr8z/vzl/ w:b4y2)t . $\rho$ =    $ \times 10^{17}\ \text{kg/m}^3$
(b) What would be the radius of the Earth if it had its actual mass but had the density of nuclei? R =    m
(c) What would be the radius of a $_{92}^{238}\text{U}$ nucleus if it had the density of the Earth? $r_{\text{U}} = $    $ \times 10^{-10}\ \text{m}$

  (a) What is the fraction of the hydrogenben b3(gyxi -9 mv/.rj atom's mass that is in the nucleus? $\dfrac{m_{\text{p}}}{(m_{\text{p}} + m_{\text{e}})}$ =   
(b) What is the fraction of the hydrogen atom's volume that is occupied by the nucleus? $\left( \dfrac{r_{\text{nucleus}}}{r_{\text{atom}}} \right)^3$ =    $ \times 10^{-14}$

  Approximately how many nucleons are there in a 1.0-kg object? Doebv6 f 6p4ts-k:u, 4pniizc.dus it matter what the object is ma-4n ,6ci bu:udfpk4zt s6. pvide of? Why or why not? N $\approx $    $\times 10^{26}$ nucleons

  How much energy musthl4z 2368i kbfvbq0pq an $\alpha$ particle have to just "touch" the surface of a $_{92}^{238}\text{U}$ nucleus? $\text{KE}$ =    $MeV$

  Use (Fig. Below) to estimat dhvnnq);zz84 w0lx 5de the total binding energy of
(a) $_{92}^{238}\text{U}$    $ \times 10^{3}\ \text{MeV}$
(b) $_{26}^{56}\text{Fe}$.    MeV

  Use Appendix B to calculate toc2w -519 lpmywffqt0 euac3qg0z5k* he binding energy of $_{1}^{2}\text{H}$ (deuterium). Binding energy =    $MeV$

  Calculate the binding/eyu7c 4 p ks+icwe4f7 energy per nucleon for a $_{26}^{56}\text{Fe}$ nucleus.    $MeV$

  Determine the binding energy of fmec9;4ntyb c,7qswr r6a5(*pqh;jcb 7ir8e the last neutron in a $_{19}^{40}\text{K}$ nucleus. Binding energy =    $MeV$

  Calculate the total binding energy, and thet9 yfbq+a/:hwy.5n os binding energy per nucleon, for
(a) $_{1}^{7}\text{H}$ Binding energy =    $MeV$ the binding energy per nucleon is    $MeV$
(b) $_{26}^{56}\text{Fe}$. Use Appendix B. Binding energy =   $ GeV$ the binding energy per nucleon is    $MeV$

  Compare the average binding energy of a nucleon i . 5rtvymo:7ojn $_{11}^{23}\text{Na}$ to that in $_{11}^{24}\text{Na}$.
the average binding energy per nucleon is    $MeV/nucleon$
the average binding force per nucleon is    $MeV/nucleon$

  How much energy is requiredwjww p *,k)s:e to remove (a) a proton, Energy(p) =    $MeV$
(b) a neutron, from $_{8}^{16}\text{O}$? Energy(n) =    $MeV$
Explain the difference in your answers.

  (a) Show that the nucleus tpnt4io:lk, skdh 48.$_{4}^{8}\text{Be}$ (mass = 8.005305 u) is unstable and will decay into two $\alpha$ particles.
(b) Is $_{6}^{12}\text{C}$ stable against decay into three $\alpha$ particles?  ----待选择----stableunstable 
Show why or why not.

  How much energy is released vst-/x6z,vg t when tritium, $_{1}^{3}\text{H}$, decays by $\beta^-$ emission? Q =    $MeV$

  What is the maximum bblldm:l6s93kinetic energy of an electron emitted in the $\beta^-$ decay of a free neutron? $\text{KE}$ =    $MeV$

Show that the decay ;d/ldh bwln,c 6;+m kuya1) yo$_{6}^{11}\text{C} \to _{5}^{10}\text{B} + \text{p}$ is not possible because energy would not be conserved.

  $_{11}^{22}\text{Na}$ is radioactive. (a) Is it a $\beta^-$ or $\beta^+$ emitter?  ----待选择----$\beta^-$$\beta^+$ 
(b) Write down the decay reaction, and estimate the maximum kinetic energy of the emitted $\beta$ particle. $\text{KE}$ =    MeV

  Give the result of a calculation that shows whether or not w.y4/- xw0l m1uudj pvthe following decays arwp1vd- x0mlyu4. j/ wue possible:
(a) $_{92}^{235}\text{U} \to _{92}^{236}\text{U} + \text{n}$  ----待选择----possiblenot possible 
(b) $_{8}^{16}\text{O} \to _{7}^{15}\text{N} + \text{n}$  ----待选择----possiblenot possible 
(c) $_{11}^{23}\text{Na} \to _{11}^{22}\text{Na} + \text{n}$  ----待选择----possiblenot possible 

  A $_{92}^{238}\text{U}$ 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. $m(^{234}\text{Th}) =$    $\ \text{u}$

  When $_{10}^{23}\text{Ne}$ (mass = 22.9945 u) decays to $_{11}^{23}\text{Na}$ (mass = 22.9898 u) what is the maximum kinetic energy of the emitted electron? $\text{KE}$ =    $MeV$
What is its minimum energy?   
What is the energy of the neutrino in each case?    $\leq E_{\text{v}}\leq $    $\ \text{MeV}$
Ignore recoil of the daughter nucleus.

  A nucleus of mass 238 u, i 6,c9dwvjp 0(1xvpt drnitially at rest, emits an $\alpha$ particle with a KE of 5.0 MeV. What is the KE of the recoiling daughter nucleus? $\text{KE}_{\chi}$=    $MeV$

  What is the maximum buoq*5py( b:-za fww 3KE of the emitted $\beta^-$ particle during the decay of $_{27}^{60}\text{Co}$? $\text{KE}$ =    $MeV$

  The nuclide $_{15}^{32}\text{P}$ decays by emitting an electron whose maximum kinetic energy can be 1.71 MeV.
(a) What is the daughter nucleus?  ----待选择----Sulfur 32Phosphate 31Sulfur 31phosphate 31 
(b) Calculate the daughter's atomic mass (in u). m =    u

  The isotope $_{84}^{218}\text{Po}$ can decay by either $\alpha$ or $\beta^-$ emission. What is the energy release in each case?
The mass of $_{84}^{218}\text{Po}$ is 218.008965 u.
$\alpha$ =    $MeV$
$\beta^-$ =    $MeV$

  How much energy is released in elwe7qrg(; 4kdihl 76 gcectron capture by beryllium: $_{4}^{7}\text{Be} + \text{e}^- \to _{3}^{7}\text{Li} + \nu$? Q =    $MeV$

  A photon with a wavelenujr,2 kf -cea4gth of $1.00 \times 10^{-13}\ \text{m}$ 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. E =    $MeV$

  Determine the maximum kinetic energy o d y,iwblgjk+c :(;2gbf $\beta^+$ particles released when $_{6}^{11}\text{C}$ decays to $_{5}^{11}\text{B}$. What is the maximum energy the neutrino can have? What is its minimum energy? $\text{KE}$ =    $MeV$

  How much recoil energy doez84cvhd.k, zcilc9+ ss a $_{19}^{40}\text{K}$ nucleus get when it emits a 1.46-MeV gamma ray? $\text{KE}_{K}$ =    $eV$

  What is the energy oqcp8*8m m k.o mj7s1g(h yskm(f the $\alpha$ particle emitted in the decay $_{84}^{210}\text{Po} \to _{82}^{206}\text{Pb} + \alpha$? Take into account the recoil of the daughter nucleus. $\text{KE}$ =    $MeV$

  The $\alpha$ particle emitted when $_{92}^{238}\text{U}$ decays has 4.20 MeV of kinetic energy. Calculate the recoil kinetic energy of the daughter nucleus and the Q-value of the decay.
$\text{KE}_{\text{Th}}$=    $MeV$
Q=    $MeV$

Show that when a nucleus decays by kl5sa/2xb n/tm3 1+vyv; gwdvh 8cij/$\beta^+$ decay, the total energy released is equal to
$Q = (M_P - M_D - 2m_e)c^2$
where $M_P$ and $M_D$ are the masses of the parent and daughter atoms (neutral), and $m_e$ is the mass of an electron or positron.

  A radioactivematerial produces 1280x v8c-txq3ly4g5e ,. ulsmxexppw: , * decays per minute at one time, and 4.6 h later produces320 decays per minute. Wx , e x*.vs xegp8:wmpu-lt,ly5x43qchat is its half-life? $T_{\frac{1}{2}}$=    $h$

  (a) What is the decay consta,2puvhs2uv )*dll w a, lzke2 rlt.o5*nt of $_{92}^{238}\text{U}$ whose half-life is $4.5 \times 10^9\ \text{yr}$? $\lambda$ =    $ \times 10^{-10}\ \text{yr}$
(b) The decay constant of a given nucleus is $8.2 \times 10^{-5}\ \text{s}^{-1}$. What is its half-life? $T_{\frac{1}{2}}$ =    $h$

  What is the activity2za.w 5mcn0c ie)nqb ,7.nbb b of a sample of $_{6}^{14}\text{C}$ that contains $3.1 \times 10^{20}$ nuclei? $\dfrac{\Delta N}{\Delta t}$ =    $ \times 10^{9}\ \text{decays/s}$

  What fraction of a sample of pr9 :jbk20unx8n f nq0$_{32}^{68}\text{Ge}$, whose half-life is about 9 months, will remain after 3.0 yr? $\dfrac{N}{N_0}$ =   

  What fraction of a sample is left after exactly 6 halg-kb:a d5:qhbek0 4r uf-lives? $\dfrac{N}{N_0}$=   

  How many nuclei of $_{92}^{238}\text{U}$ remain in a rock if the activity registers 640 decays per second? N =    $ \times 10^{20}\ \text{nuclei}$

  In a series of decays,j5 zrkc7d0;* javrd5uxr6iv: the nuclide $_{92}^{235}\text{U}$ becomes $_{82}^{207}\text{Pb}$. How many $\alpha$ and $\beta^-$ particles are emitted in this series?
$N_{\alpha}$ =    $\alpha$ particles
$N_{\beta}$ =    $\ \beta^-$ particles

  The iodine isotope $_{53}^{131}\text{I}$ is used in hospitals for diagnosis of thyroid function. If $682\ \mu\text{g}$ are ingested by a patient, determine the activity
(a) immediately, $\lambda N$ =    $ \times 10^{12}\ \text{decays/s}$
(b) 1.0 h later when the thyroid is being tested,$\lambda N$ =    $ \times 10^{12}\ \text{decays/s}$
(c) 6 months later. Use Appendix B. $\lambda N$ =    $ \times 10^{5}\ \text{decays/s}$

  $_{55}^{124}\text{Cs}$ has a half-life of 30.8 s.
(a) If we have $8.8\ \mu\text{g}$ initially, how many Cs nuclei are present? $N_0$ =    $ \times 10^{10}\ \text{nuclei}$
(b) How many are present 2.0 min later? N =    $ \times 10^{15}\ \text{nuclei}$
(c) What is the activity at this time? $\lambda N$ =    $ \times 10^{13}\ \text{decays/s}$
(d) After how much time will the activity drop to less than about 1 per second? t =    $min$

  Calculate the mass of a sample of l. f b )ez7f9qn0;jujul)0osw pure $_{19}^{40}\text{K}$ with an initial decay rate of $2.0 \times 10^5\ \text{s}^{-1}$. The half-life of $_{19}^{40}\text{K}$ is $1.28 \times 10^9\ \text{yr}$. m =    $g$

  Calculate the activi5w,1:cd kaakij-y6ma f k9k y7ty of a pure $9.7-\mu\text{g}$ sample of $_{15}^{32}\text{P}\ (T_{1/2}=1.23 \times 10^6\ \text{s})$. $\lambda N$ =    $ \times 10^{11}\ \text{decays/s}$

  The activity of a sample :*, c1xl qdir o*mhvqpw/mq(-of $_{16}^{35}\text{S}\ (T_{1/2}=7.55 \times 10^6\ \text{s})$ is $2.4 \times 10^5$ decays per second. What is the mass of the sample? m =    $ \times 10^{-10}\ \text{g}$

  A sample of $_{6}^{14}\text{C}$ contains $1.2 \times 10^{20}$ nuclei.
(a) What is the decay constant? $\lambda$ =    $\times 10^{-13}\ \text{s}^{-1}$
(b) Approximately how many disintegrations will occur per minute? $\lambda N $ =    $ \times 10^{8}\ \text{decays/min}$

  The activity of a sample drops by a factor of 10 in 8.6 -rmd wiwl8l(1 x.s5 m+rcnf ;aminutes. What is its half- 1r.wn+8l(xmiacwf dm5r ; -lslife? $T_{\frac{1}{2}}$ =    $min$

  A 285-g sample of purevq :-e- hmi2ls carbon contains 1.3 parts in $10^{12}$ (atoms) of $_{6}^{14}\text{C}$. How many disintegrations occur per second? $\lambda N$ =    $decays/s$

  A sample of $_{19}^{40}\text{K}$ is decaying at a rate of $6.70 \times 10^2\ \text{decays/s}$. What is the mass of the sample? m =    $mg$

  The rubidium isotope yxyz **o1/wbi $_{37}^{87}\text{Rb}$, a $\beta^-$ emitter with a half-life of $4.75 \times 10^{10}\ \text{yr}$, is used to determine the age of rocks and fossils. Rocks containing fossils of ancient animals contain a ratio of $_{38}^{87}\text{Sr}$ to $_{37}^{87}\text{Rb}$ of 0.0160. Assuming that there was no $_{38}^{87}\text{Sr}$ present when the rocks were formed, estimate the age of these fossils.
$\Delta t$ =    $\times 10^{9}\ \text{yr}$

  Use (Fig. Below) and calcu/fr h.v bob wf mfxo3+4jp,k28late the relative decay rates for $\alpha$ decay of $_{84}^{218}\text{Po}$ and $_{84}^{214}\text{Po}$.    $ \times 10^{-7}$

  $_{4}^{7}\text{Be}$ 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 $450\ \text{decays/s}$ of $_{4}^{7}\text{Be}$,
(a) how long do we have to wait for the decay rate to drop to 15 per second? $\Delta t$ =    $days$
(b) Estimate the initial mass of $_{4}^{7}\text{Be}$ on the leaf. m =    $\times 10^{-17}\ \text{kg}$

Two of the naturally occurring radioactive decay ssq*4ksxs3 ,:; otp d30dlx 3fmyea/uw equences start with $_{90}^{232}\text{Th}$ and $_{92}^{238}\text{U}$. 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.

  An ancient wooden club is found th:nqs2+b/ y2kqq 2b0lxj+tjay at contains 290 g of carbon and has an activity of 8.0 decays pera xy+/b2kj yjs2 qbt:qn0+2lq second. Determine its age assuming that in living trees the ratio of $_{6}^{14}\text{C}$ to $_{6}^{12}\text{C}$ atoms is about $1.3 \times 10^{-12}$. t =    $\times 10^{4}\ \text{yr}$

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, $N_D$, as a function of time; assume the daughter is stable and that $N_D = 0$ at $t=0$.

Which radioactive isotope of lead is being produced in a reaction wher,ip*rd/b .edf f0a2qo 6m)i bxz3n;wk e the measured activity of a sample drops to 1.050% of its original activity in 4.00 bmpnd k6 eod3b.;i q 20a)r/zw,ff*x ih?

  An old wooden tool is found to contain 6(jj dko*dhm *q z.i3zonly 6.0% of $_{6}^{14}\text{C}$ that a sample of fresh wood would. How old is the tool? t =    $ \times 10^{4}\ \text{yr}$

  A neutron star consists of neutrons at approximately nuclv mx qev +kwb-23rv2w.ear density. Estimate, for a 10-km-d+exk -v 3w mw2r2.bvqviameter neutron star,
(a) its mass number, A =    $ \times 10^{55}$
(b) its mass (kg),m =    $ \times 10^{29}\ \text{kg}$
(c) the acceleration of gravity at its surface. g =    $ \times 10^{11}\ \text{m/s}^2$

  The $_{1}^{3}\text{H}$ 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 $_{1}^{3}\text{H}$ radiation is about $\frac{1}{10}$ that present in new wine. t =    yr

  Some elementary particle theories suggest that the proton may be unstablefp f/ktjuq z* l1gk700, with a halfj/ugt 0k* fzl1f70p qk-life $10^{32}\ \text{yr}$. How long would you expect to wait for one proton in your body to decay (consider that your body is all water)? $\Delta t = $    $ \times 10^{3}\ \text{yr}$

  How long must you wait (in half-lives) das9jk +* tvi+for a radioactive sample to drop to 1.00% of its originasjdv itk9+* +al activity?    $T_{\frac{1}{2}}$

  If the potassium isotopei hfh4yn+ 0 ,nul/e)4gizfii9 6u*b wbjq60ig $_{19}^{40}\text{K}$ gives $60\ \text{decays/s}$ in a liter of milk, estimate how much $_{19}^{40}\text{K}$ and regular $_{19}^{39}\text{K}$ are in a liter of milk. Use Appendix B.
$m_{40}$ =    $mg$
$m_{39}$ =    $mg$

  (a) In $\alpha$ decay of, say, a $_{88}^{226}\text{Ra}$ nucleus, show that the nucleus carries away a fraction $\frac{4}{A_D + 4}$ of the total energy available, where $A_D$ is the mass number of the daughter nucleus. (b) Approximately what percentage of the energy available is thus carried off by the $\alpha$ particle in the case cited?    %

Strontium-90 is produced as 6km wjss1 oq0, 5p,hi;0atbys 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 , ht5;6 qok0yp s ism,a10sjbwmight be similar to chemically, and tell why you think it might be dangerous to ingest. It has too many neutrons, and it decays with a half-life of about 29 yr. How long will we have to wait for the amount of $_{38}^{90}\text{Sr}$ 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.

The nuclide $_{76}^{191}\text{Os}$ 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 $_{76}^{191}\text{Os}$ occur?

  Determine the activitioyd7 ;8isjx h oyq:,)h4wrya1es of (a) 1.0 g of $_{92}^{235}\text{U}\ (T_{1/2}=7.04 \times 10^8\ \text{yr})$ $/lambda N$ =    $\times 10^{15}\ \text{decays/s}$
(b) 1.0 g of $_{92}^{238}\text{U}\ (T_{1/2}=4.47 \times 10^9\ \text{yr})$. $/lambda N$ =    $ \times 10^{4}\ \text{decays/s}$

  Estimate the total binding energy for coppexgs vacj d1 kk*1cw0;4*7pmq vgq8/rfr and then estimate the energy, in joules, needed to break a 3.0-g copper pergf 8v ;m*1qk xwaqj*c1sg 4dv 7/0kcpnny into its constituent nucleons. (Fig. Below)    $ \times 10^{12}\ \text{J}$

  Instead of giving atomic masses for nucl rbx59m-saki :ides as in Appendix B, some Tables give the mass b:-s i9ram5x kexcess, $\Delta$, defined as $\Delta = M - A$, where $A$ is the mass number and $M$ is the mass in u. Determine the mass excess, in u and in $\text{MeV}/c^2$, for:
(a) $_{2}^{4}\text{He}$;    $\ \text{u}$    $\ \text{MeV}/c^2$
(b) $_{6}^{12}\text{C}$;   
(c) $_{47}^{107}\text{Ag}$;    $\ \text{u}$    $\ \text{MeV}/c^2$
(d) $_{92}^{235}\text{U}$;   $\ \text{u}$    $\ \text{MeV}/c^2$
(e) From a glance at Appendix B, can you make a generalization about the sign of $\Delta$ as a function of $Z$ or $A$?

  (a) A 92-gram sample of natural carbon contains the usual fraodko/ 2qf0p5fh ,qgd6ction of $_{6}^{14}\text{C}$. Estimate how long it will take before there is only one $_{6}^{14}\text{C}$ nucleus left. t =    $ \times 10^{5}\ \text{yr}$2.4
(b) How does the answer in (a) change if the sample is 280 grams? What does this tell you about the limits of carbon dating? $10^a$yr a =   

  If the mass of the proton were just a little closer tau(gpn/w qot ot,5+ 6wo the mass of the neutron, the following reaction would be possible even at low collision energies:6ot+ gwouqt5/w,p n(a
$\text{e}^- + \text{p} \to \text{n} + \nu$.
Why would this situation be catastrophic? By what percentage would the proton's mass have to be increased to make this reaction possible? $\frac{KE_{\alpha}}{KE_{\beta}}$ =    $\frac{ \times 10^{-4}}{1}$

  What is the ratio of the kineticefe4-am.x +xk energies for an alpha particle and a beta particle if both make tracks with the same radius of curvature in a magnetic field, oriented perpendicfeexkx a- m4+.ular to the paths of the particles.    $T_{\frac{1}{2}}$

  A 1.00-g sample of naturalk6v s6u5t8z n 2e,gppd samarium emits $\alpha$ particles at a rate of $120\ \text{s}^{-1}$ due to the presence of $_{62}^{147}\text{Sm}$. The natural abundance of $_{62}^{147}\text{Sm}$ is 15%. Calculate the half-life for this decay process.
$T_{\frac{1}{2}}$ =    $ \times 10^{11}\ \text{yr}$

  Almost all of naturally occurring urangxf 7mawu3n2-aita 5cy i; 4/dium is $_{92}^{238}\text{U}$ with a half-life of $4.468 \times 10^9\ \text{yr}$. Most of the rest of natural uranium is $_{92}^{235}\text{U}$ with a half-life of $7.038 \times 10^8\ \text{yr}$. Today a sample contains 0.72% $_{92}^{235}\text{U}$.
(a) What was this percentage 1.0 billion years ago?    %
(b) What percentage of the sample would be $_{92}^{235}\text{U}$ in 100 million years?    %

  A typical banana contains 400 mg of potassium, of which a h3 y;vax yr idig4qqb3b+*e9g5 /up/msmall fraction is the radioactive is/r3 mi/hxbvgu 4ap93d gby;+*qq 5 eyiotope $_{19}^{40}\text{K}$ (see Appendix B). Estimate the activity of an average banana due to $_{19}^{40}\text{K}$. $\lambda N$ =    $\ \text{decays/s}$

  The practical limit for carbon-14 dating is about 60,000lt)c7 gicey/s1,xcs 7 years. If a bone contains 1.0 kg of carbon, and the an s,7clgy7 csx 1ti)/ceimal died 60,000 years ago, what is the activity today?    $\ \text{decays/s}$

Decay series, such as that shown in(Fig. Below), can be classified into four mp.sj1bgtf( 4z 6t3mc families, depending on whether the mass 1c.tb g t3f(pmz js46mnumbers have the form $4n$, $4n+1$, $4n+2$, or $4n+3$, 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.