What do different isotopes of a given element have in common? nnfrp 1.,shgbm 3m+rj t.s f//How are they diffe.1n /r+jhtrbm .sn,f g ms/f3prent?

What are the elements represented by the X4e;xn/uh p:fqmtbc * + 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 neutrons do each of the isod v1p19rir6,jdrags j:( x1ny topes in Question 2 have?paj:y 61gj rvrs1x,9n rdd1(i

Identify the element that has 88 nuc.l refu;0e-g qleons and 50 neutrons.

Why are the atomic masses /myya83l p e:l tsgy(*of many elements (see the periodic table) not close to whole numbert meysapy3y:8*l(l/ gs?

How do we know there 9 cp6wn:gr q3zjabg;( is such a thing as the strong nuclear force?

What are the similarities and the differencessjw3j;fil/( , 7 wq.y pvlexju9i1qn: between the strong nuclear force and the /1u;(jww7 vifjx.en9qjl3:sy i,qp l electric force?

What is the experimental evidence in favor of radioactivity being a nuclear pzxh-6y:5h ay urocess zu6y xhh-ya:5?

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 manyh fbv3xk:l3u :h;8zfj ways as you can, the difference between $\alpha$, $\beta^-$, $\beta^+$, and $\gamma$ rays.

What element is formed by the radioactivesvvam5s) q: i)1ca (oj decay of (a) $_{11}^{24}\text{Na}\ (\beta^-)$ (b) $_{11}^{22}\text{Na}\ (\beta^+)$ (c) $_{84}^{210}\text{Po}\ (\alpha)$?

What element is formedwu 2(krq of28:l4aoeask7 i ylba6q** by the decay of (a) $_{15}^{32}\text{P}\ (\beta^-)$ (b) $_{16}^{35}\text{S}\ (\beta^-)$ (c) $_{83}^{210}\text{Bi}\ (\alpha)$?

Fill in the missing particle or nucleus bv drw-a8l75h:
(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 6j; i i-hvyle *;u,kf ya3ral4$_{92}^{238}\text{U}$ 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 undergoyiu*mo:s ,aa ,es 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 g1x .99r, p :ju :edx;c/sw t9lbynohisiven 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. Ex 99 9:;p1b,jd noly/he s:r.xwsxciutplain the difference between these two cases.

Do isotopes that undergo electron capture )by1w z+six1m generally lie above or below the line of stability in ( )bxmwz1i+1sy Fig. Below)?

Can hydrogen or deuter3lba*dk, f 7uaium emit an $\alpha$ particle? Explain.

Why are many artificially produced radioactive isoto+ 4z)eyv48. n 4emfdub9(pmcjc jtnd 8pes rare in nature?

An isotope has a half-life of one 4q f(.bqhs4 a62bdtn wmonth. After two months, will a given sample of this isotope wbathb4ns4( .f6qd q2have completely decayed? If not, how much remains?

Why are none of the elements twe1ytu 6l/yvixk/ +7with $Z>92$ 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 anddl1/zf izy s0,; (fxks $\beta^-$ decay, an electron is emitted. How could you determine which decay process occurred?

  A pi meson has a mass off3zggs /+,p9/e cnt a(9f0djs cxj )xq $139\ \text{MeV}/c^2$. What is this in atomic mass units? m =    u

  What is the approximate rlks d9w; jppw/l.mj(8 c)uuo(adius of an alpha particle $(_{2}^{4}\text{He})$?r =    $ \times 10^{-15}\ \text{m}$

  What is the rest mass of a.p qk*pmuh ,adik 7up::(v;2f 6zzfvqzu, h0l bare $\alpha$ particle in $\text{MeV}/c^2$? $m_{\alpha}$ =    $\ \text{MeV}/c^2$

  (a) What is the appr+o 7 a 9:o,cftswu)bokoximate 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 densq+ze rd eezmw, krc(r,nkx.*:; brk6njp (k33ity of nuclear matter is essentially the same for all nuclcmjzzn; pr:3w k rr,ne.6q*x+kk(b e,e3d(rkei. $\rho$ =    $ \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 hydrogen atom's masns)s)*mjfux qj(q4 5ns 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? Doe wmd3c:49ax5c t8acle2xe(/2tpqw raga s*z;s it matter what the object is made of? Wh4e:wdtpse3 a x*;(tc9 q5wcx2a2clg za ma8/ ry or why not? N $\approx $    $\times 10^{26}$ nucleons

  How much energy must fvdx43iyf+0 b an $\alpha$ particle have to just "touch" the surface of a $_{92}^{238}\text{U}$ nucleus? $\text{KE}$ =    $MeV$

  Use (Fig. Below) to estimate the total bindinjcmss y-i :,yuoagspa, .j1 ;9/dt 2.uwjggd 7g energy of
(a) $_{92}^{238}\text{U}$    $ \times 10^{3}\ \text{MeV}$
(b) $_{26}^{56}\text{Fe}$.    MeV

  Use Appendix B to calculate the bindinghfv ..h;kzat9o+5wdl energy of $_{1}^{2}\text{H}$ (deuterium). Binding energy =    $MeV$

  Calculate the binding energy pens59cqz zfd hpym -/6.r nucleon for a $_{26}^{56}\text{Fe}$ nucleus.    $MeV$

  Determine the binding energy of the last new2w-(h s-pmr6 -cszln x3w0wc utron in a $_{19}^{40}\text{K}$ nucleus. Binding energy =    $MeV$

  Calculate the total binding energy, and the binding en-1qezwhfs-7m mz5 9dhergy 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 fj-4qf17atk pof a nucleon in $_{11}^{23}\text{Na}$ 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 required to remove (a) a protogm73m zmu 0nvk :m3q)ln, Energy(p) =    $MeV$
(b) a neutron, from $_{8}^{16}\text{O}$? Energy(n) =    $MeV$
Explain the difference in your answers.

  (a) Show that the nucleu1go0mos,(qib s $_{4}^{8}\text{Be}$ (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 when tritiume nluglq+rtpj y o7 .g(+3*fb:, $_{1}^{3}\text{H}$, decays by $\beta^-$ emission? Q =    $MeV$

  What is the maximum kinetic energy of an eleck vob.yus,faj-5u:+f tron emitted in the $\beta^-$ decay of a free neutron? $\text{KE}$ =    $MeV$

Show that the decay tosq8ju/-) h2ee x9mi $_{6}^{11}\text{C} \to _{5}^{10}\text{B} + \text{p}$ 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 thakmn.3 5:xcg) g : ,xyt;yjmfb*h0 ijeqt shows whether or not the following decays ar*),0iyte xbgjm: :3mj5gqxhky. n ;cfe 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, initially at rest, emits avd(i5g . gho9jn $\alpha$ 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 KE of d+ile ocu1i9ue2 jv5fz5b2a 9the 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 releasedsgdv)kp:mq f c4*w1)pe xq5 .f in electron capture by beryllium: $_{4}^{7}\text{Be} + \text{e}^- \to _{3}^{7}\text{Li} + \nu$? Q =    $MeV$

  A photon with a wavelez.i3newika;p d 7w ih4d)32vrngth 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 kineticp7 kj,;q ri /vtna:7tt energy of $\beta^+$ 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 doesqeie)+4v)uvsfkl 1i + a $_{19}^{40}\text{K}$ nucleus get when it emits a 1.46-MeV gamma ray? $\text{KE}_{K}$ =    $eV$

  What is the energy of the2rd6j*c yxo mf 2irz,9md0.be $\alpha$ 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 nucleushxn7xvp z:9 x( decays by $\beta^+$ 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 1280 decays per minut7msmf+jtggu6-7lxl q -+un5ke at one time, and 4.6 h later produces320 decays per minute. What is its half-lifqg7 6mjum -xu g+-5tfllksn7+ e? $T_{\frac{1}{2}}$=    $h$

  (a) What is the deca7w3v4;lq ohy ty constant 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 activity of a j 6q,yowz b d chq*,.-cyziv43sample 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*mi t4nsmhg*+ $_{32}^{68}\text{Ge}$, whose half-life is about 9 months, will remain after 3.0 yr? $\dfrac{N}{N_0}$ =   

  What fraction of a sample is lyl, cyqu61k0ieft after exactly 6 half-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, the nuc)c4cm tsi7i;x:em d;l lide $_{92}^{235}\text{U}$ 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 po c 4 ;+cc-qnda lw5tohc()vk3ure $_{19}^{40}\text{K}$ 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 activity of a purv-23sa4r;agpd/nv nh .zs( pce $9.7-\mu\text{g}$ 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 samplk:hl u :po1kb5,l5 mdpe 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 minutes. What is its hadl;cx e. 4h58 yff8-jnmgt, kulf-lifedyuem-,84h c;knx8fl tj f5.g ? $T_{\frac{1}{2}}$ =    $min$

  A 285-g sample of pure c*zceo5r*; 3u omwj*d oarbon 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 isotope1pe*wp mj 0re /c,6 l0kgwet7g $_{37}^{87}\text{Rb}$, 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 calculate the relative decay rates for xovvnbn 1o:49$\alpha$ 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 radioac;: g b a:.daxw4iw5)krh1 akuntive decay sequences 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 that contains 290 g of carbon andgyw8 z+ontw+ g8., bdq has an activity of 8.0 decays per second. Determine its age assuming that in living trees thezo8qdg.w g+bw, nt y8+ 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 qnniz7vz 5- +mdit+1b3qz s +uin a reaction where the measured activity of a sample drops to 1.050% of its original - viqbqn+d 5z m3sz1z+7 t+inuactivity in 4.00 h?

  An old wooden tool is found toowipxha g9 3 mfn 7n(x)b-6u10ka ttz: contain only 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 ap3/ 3xo4i4qyc frsz:3 z-ufjo cproximately nuclear density. Estimate, for a 10-km-di4cf:iz o/xsf 3-yq ju3cozr34ameter 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 part8vt9d 4tgjzp9 *kod 7iicle theories suggest that the proton may be unstable, with a half-lifedv4ogjk9ti8*d9 zt7p $10^{32}\ \text{yr}$. 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-livec*g:w: b, fe)o zp9aans) for a radioactive sample to drop to 1.00% of its orinp9, gf ac ze*w:a)ob:ginal activity?    $T_{\frac{1}{2}}$

  If the potassium isotopewjznpk9) j7 el(a*) nr $_{19}^{40}\text{K}$ 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 a nuclear fir l0c: xt7 npydcs8gv2 q-nc9j6i)ie,ssion 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 t6jdn9c)2 rygvc:7 c epqs0, i8n -lixthink 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 activities o +0 (nb2h li6vr/gcamwf (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 fond r8) c35ydzpr copper and then estimate the energy, in joules, needed to break a 3.0-g p5yd)drc 8 z3ncopper penny into its constituent nucleons. (Fig. Below)    $ \times 10^{12}\ \text{J}$

  Instead of giving atomic masses for nuclides qr4*zjkyq .5n m2 klx0as in Appendix B, some Tables give thenlx k ky05m4zr. *qqj2 mass excess, $\Delta$, 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 naturai)z(j x ougdw.gkerd))3w .6t,s7o nt l carbon contains the usual fraction 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 prot m ay9yje0tqkc1/ a83don were just a little closer to the mass of the neutron, the following reaction would be possible even at low collision energies: tq aym 90y1dk83j ea/c
$\text{e}^- + \text{p} \to \text{n} + \nu$.
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 kineti.0ff u bt; gv04e,otcyc energies for an alpha particle and a beta particle if both make tracks with the same radius of curvature in a magnetic fig,ut.fo bf e v400ct;yeld, oriented perpendicular to the paths of the particles.    $T_{\frac{1}{2}}$

  A 1.00-g sample of natural samarium emity2jx.x3* fwi/f xy+ mvs $\alpha$ 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 naturall:u /b-y f7kqndy occurring uranium 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 whichf; fl7uli 2ln bbe;xd4h-.mp.tc , o9z/ousy 3 a small fraction is the radioactive isotoculihptl xlfb 9n, f.e;.7o bzus 3 4y2do;m-/pe $_{19}^{40}\text{K}$ (see Appendix B). Estimate the activity of an average banana due to $_{19}^{40}\text{K}$. $\lambda N$ =    $\ \text{decays/s}$

  The practical limit forq8;x(1xfs qlt carbon-14 dating is about 60,000 years. If a bone contains 1.0 kg of carbon, and the animal diet lq;s81fxq( xd 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 fj(cy9ae xdg 8r0ie9e+if4qe 4 amilies, depending on whether the mass numbers hafa i8e49cy0qieer+ xdjeg94( ve 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.