What do different isotopes of a given element have in common? How arce e:gu5cdc9h)oj- x0e they differg9eu5 ehc xc-c j0)od:ent?

What are the elements represented by the X in the followinwmgj -9ef o/y+i.f p7wg: (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 maa eon*-bup ;g(ny neutrons do each of the isotopes in Question 2 havp;augo-(*be n e?

Identify the element that has4;1ijsh 7y)c glx5 d.q ll6ihn 88 nucleons and 50 neutrons.

Why are the atomic masses of marbo3m: f1mj(k ny elements (see the periodic table) not close to wholek 3j1mfb (r:om numbers?

How do we know there is such a thing am.fznn b3 nne+oir 9+dvb* 0r +0fv7sxs the strong nuclear force?

What are the similarities and the differences between the stroh-ibnqfll73 l/dtkzm )q; )f.ng nuclear force andhb lqk.dl n /iffq;3- l)ztm7) the electric force?

What is the experimental e m jbck 1a7lk.( ap-ph505cuyxd;eqh-vidence in favor of radioactivity being a nuclear procebeadkq1j5x-l (h ay0pp 75k;m.uc - hcss?

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 as you can, the differe 6,xaav05wzhs nce between $\alpha$, $\beta^-$, $\beta^+$, and $\gamma$ rays.

What element is formed by the radioactiveznot9w 7aw* t*p)hvd- m5w k6i decay of (a) $_{11}^{24}\text{Na}\ (\beta^-)$ (b) $_{11}^{22}\text{Na}\ (\beta^+)$ (c) $_{84}^{210}\text{Po}\ (\alpha)$?

What element is formed by i8n slddc,3mp+ m2b4ythe decay of (a) $_{15}^{32}\text{P}\ (\beta^-)$ (b) $_{16}^{35}\text{S}\ (\beta^-)$ (c) $_{83}^{210}\text{Bi}\ (\alpha)$?

Fill in the missing ki,f t+n0f gfd z.6ox;particle or nucleus:
(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 vlfb 9wb5, y3k$_{92}^{238}\text{U}$ 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 undergoes eitith;v //tmqsq, mn7s5her $\beta^-$ 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-emig5w72 )f+dn uhsquc t/tting nuclide are generally monoenergetic; that is, they all have the same kinetic energy. But the betasdhc ug)/7uq n25t+wf particles from a beta-emitting nuclide have a spectrum of energies. Explain the difference between these two cases.

Do isotopes that undergo electron caw)qiyyij;e 4xmni3, )qf7. xlpture generally lie above or below the line of i;q7x w4n3. jmii yeyf,q))lx stability in (Fig. Below)?

Can hydrogen or deuterium em*ptp82aavzg00h ibb- it an $\alpha$ particle? Explain.

Why are many artificially produced radioactive isotfng-g1zm30.5 nxn b.zo 5 zfalopes rare in nature?

An isotope has a half-life of one month. Afp l ao yxz7pd8t9uqb(p 64h+2kn37h nfter two months, will a given sample of this iso8q 6tn9l43 p7poknhy bzx(f2hu7+da ptope have completely decayed? If not, how much remains?

Why are none of the eleme bo 57l4sp+y-wabygv) nts with $Z>92$ 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 ywo2:ocqgre 5yeuy59k3qp :;and $\beta^-$ decay, an electron is emitted. How could you determine which decay process occurred?

  A pi meson has a mas cc. ,emi)b.g6go 3ixmb+or t.s of $139\ \text{MeV}/c^2$. What is this in atomic mass units? m =    u

  What is the approximate radius of an alpha pj3.kw j-ji6,dk xkc;m)g3 qrzarticle $(_{2}^{4}\text{He})$?r =    $ \times 10^{-15}\ \text{m}$

  What is the rest mass of a bare q7 pd888axtb-5yjc tb wi9xiddztp:f5s 5: 3f$\alpha$ particle in $\text{MeV}/c^2$? $m_{\alpha}$ =    $\ \text{MeV}/c^2$

  (a) What is the approximate radius ogpi gpw0-pml23kohqqo 4a 5 -)f 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 essentially the same for all z c1,d/tqjcr8g9wdv9j9 ejwe g ..haz5 *mw*gnuclei..wg. a d5g/1 e9*9c98gzzw,*qter jjc hjwdmv $\rho$ =    $ \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 mass that is in the nucleus? gk m4jcq3dv6qz/sw8t jc.x */ $\dfrac{m_{\text{p}}}{(m_{\text{p}} + m_{\text{e}})}$ =   
(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 th pgma3++b av0*g9c;3c nfltm sere in a 1.0-kg object? Does it matter what thbg+afvm*sp 3 ccl+t0 n m3a9g;e object is made of? Why or why not? N $\approx $    $\times 10^{26}$ nucleons

  How much energy must an ib9bh *7 u, brh0oo(ow vl fx/5eq1m1z$\alpha$ particle have to just "touch" the surface of a $_{92}^{238}\text{U}$ nucleus? $\text{KE}$ =    $MeV$

  Use (Fig. Below) to estimate the totazjy) :amf 1xy/ i*o8y*d2z snal binding energy of
(a) $_{92}^{238}\text{U}$    $ \times 10^{3}\ \text{MeV}$
(b) $_{26}^{56}\text{Fe}$.    MeV

  Use Appendix B to calculatsvc8yo*mun 5t9n(obakj );l7e the binding energy of $_{1}^{2}\text{H}$ (deuterium). Binding energy =    $MeV$

  Calculate the binding energy per vvf5j/ke7-b g nucleon for a $_{26}^{56}\text{Fe}$ nucleus.    $MeV$

  Determine the binding energy of the laj+ s(ncnvp 4o) :o dt5;ackn;wst neutron in a $_{19}^{40}\text{K}$ nucleus. Binding energy =    $MeV$

  Calculate the total binding energy, an a3i/z5 iwudt n8h:gstkx2 y10d the 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 bijrsz538ckm. 8n*jdc, sn2 dm lnding energy of 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 t.f0ot; d6a2 k;j(f s*yiqtr aoo 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 nucl35tn t y645ezkkyzolx iw56 w6eus $_{4}^{8}\text{Be}$ (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 t;1-kjz f1(v vaoqre z*ritium, $_{1}^{3}\text{H}$, decays by $\beta^-$ emission? Q =    $MeV$

  What is the maximum kinetic energy of an feu/ds)iloa (gh1(/nelectron emitted in the $\beta^-$ decay of a free neutron? $\text{KE}$ =    $MeV$

Show that the decay x3xh9 8n6hy,/,jfffs w wah x6$_{6}^{11}\text{C} \to _{5}^{10}\text{B} + \text{p}$ 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 whethz3)wx tvzef; o +o zzit(3n4p:er or not the following decays are possiblezw 4:znz +ofo)p3 ;(it3evzxt :
(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 fvtof (s;/ vy0n 3nm8dat 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 KE of the emitted vl0-l: tuk/tjd0 o1jj$\beta^-$ 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 eleookv9of34q 3e znctt. .je)o/ctron capture by beryllium: $_{4}^{7}\text{Be} + \text{e}^- \to _{3}^{7}\text{Li} + \nu$? Q =    $MeV$

  A photon with a wavelength ofx+i,f wj ;pa+fevm i6: $1.00 \times 10^{-13}\ \text{m}$ 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 kineticnfnz0 d8uox .l3mi9lm agomx9+ /z*)v 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 qbe,q( p.-jgnyb;n)ndoes 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 th jh7u;n+nphf dlm-ce:hv2w g2ou :b(w 1bk.d2e $\alpha$ 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 decayc1 6hg7ebh6bls 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 decaysc5 46zsf5skysnd 46td sje5m; per minute at one time, and 4.6 h later produces320 decays per minute. What is its h k5fs;td y 65 zss6mje5ncsd44alf-life? $T_{\frac{1}{2}}$=    $h$

  (a) What is the decay constant of v8ft+-s* 2aa4vykums $_{92}^{238}\text{U}$ 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 cm*v6 dm.y j.dsample 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 sampleij3ni 8hf7kf 7 of $_{32}^{68}\text{Ge}$, whose half-life is about 9 months, will remain after 3.0 yr? $\dfrac{N}{N_0}$ =   

  What fraction of a sample is left afo cw.hx.h fsir29j*u ;ter 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 decayd2: l1ef mxwq6 j78jy7aph i,ms, 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 samplstrj,y2 (07j;p4 runy*zya pue of 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 activity of a pur ,9 lkyguwh5.ie $9.7-\mu\text{g}$ 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 sampl,jo0*2:qm.tnca-x tf+wp w91l hvqy ie 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 uqu:htud 17ld.u*/ wkof 10 in 8.6 minutes. What is its half-life? u1 :.d*d 7wu/hk tquul $T_{\frac{1}{2}}$ =    $min$

  A 285-g sample of pure carbon contains 1.3 parts in b: ibx9 (s.xwr$10^{12}$ (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 h s e1 7hap-5kl0 4scfacxnk8:$_{37}^{87}\text{Rb}$, 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 calcug3da6l x4 qnhw7yp/ 8ulate 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 sequences start s1pco6uz6 *vgwith $_{90}^{232}\text{Th}$ 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 and has (zuyl: uiymyf0c 4t(-an activity of 8.0 decays :0 -fu (c4zlymyiy tu(per 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 being11*ba ag*c jlia/w9leh4mg (t produced in a reaction where the measured activity of a sample drops to 1.050% of its original acl m a gc/ge1h(ba19a*liw4j*ttivity in 4.00 h?

  An old wooden tool is found to l/ aco.j 8z0oncontain 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 approximately n9;wve vo e5qjkrkdv .j4z2 02luclear density. Estimate, for a 10-km-diameter neutr2evw 9dlj0rk ;zve 54v.2joqkon 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 ma 4yu eredz se(+45+ lbw2hhov2y be unstable, with a lhr oe(z4wve2 e +uyd+h5sb24half-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 half3(nz6a nz:i zb-lives) for a radioactive sample to drop to 1.00% of its ori6b (zz3zn:ainginal activity?    $T_{\frac{1}{2}}$

  If the potassium iso7q3/o 9 ,fruhjbvi+tp tope $_{19}^{40}\text{K}$ 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 produje436p pf*tmb(qet e8 ced 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 t4eb3ej m t8 fptep6q(*oo 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 of (a)6 eelhtsc(6 i5 d1jer0 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 copper and then estimate t2vim0cn0 qpj9he energy, in joules, needed to break a 3.0-g copper penny into its constituent nupji90 q c20mvncleons. (Fig. Below)    $ \times 10^{12}\ \text{J}$

  Instead of giving atomic masses for nuclides as in Appendix B, some Tables givez q1v7. 82hc xm:twfif the mass excess.zqm c8f:htxw1 i 72vf, $\Delta$, 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 contai 7ll;p knbd/: cvj.4tsns 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 proton were just ay :g)g ,srysq*m+wdp 2 little closer to the mass of the neutron, the following reaction would be possible even at l qgg swrd2*pm+ )yys,:ow collision energies:
$\text{e}^- + \text{p} \to \text{n} + \nu$.
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 kinetic energies for an alpha particle and a be*d- 5h nyibzzzco.5 ,pta particle if both make tracks widz izb-z *.ncpyho55,th the same radius of curvature in a magnetic field, oriented perpendicular to the paths of the particles.    $T_{\frac{1}{2}}$

  A 1.00-g sample of natural s o *azq nr)z 6glu(ey./6zo.fsamarium 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 ocm crm2 rs7yvvml-+2z ,curring 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 which a smal ;a :;o2 fmgwl(ny 1t1*ngakerl fraction is the radioactive isotopak ( go1nn2aw ;; mlgyt*r1ef:e $_{19}^{40}\text{K}$ (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 60,000 years. If a bonqw6ha 3* +x.gdy4di x 3cvk9sie contain4. icih vqds*yw693gxkx +3ad s 1.0 kg of carbon, and the animal died 60,000 years ago, what is the activity today?    $\ \text{decays/s}$

Decay series, such as that su 3 dqzu4ry5+ kpsyv*:hown in(Fig. Below), can be classified into four families, depending on whether the mass numbers have the form5: 3v+ us*pdkyyruq4z $4n$, $4n+1$, $4n+2$, 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.