What do different isotopes of a given element*clgim8gp 0o 5 have in common? How are they differentmgg* i0lp 8co5?

What are the elements represented by the X in the followh5wyp9t7xp;.s:x5fniao pj5 .* okjfing: (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 neutr m*wv0x l*rbwl)7 jsy1jqq74 aons do each of the isotopes in Question 2 have?*xwaljq )y40l 1 m7wv*rs7q bj

Identify the element that has 88 nucleonx+ ,j(ld;st/utl-tc+ guxjt y w( r.w0s and 50 neutrons.

Why are the atomic masses j *.p 0yzin10vu-z xgiof many elements (see the periodic table) not close to whole numbiz0p0-.1xvu z*gjn iy ers?

How do we know there is such a thing hw 7eg9 u6hos6 y j;/uvh7jdv35ml 5ukas the strong nuclear force?

What are the similaritiehz/mau (y 2 53co qn1vh9mig-vs and the differences between the strong nuclear force and the electric force?5/on3vy v 2cz1g9 ahqhmm(ui-

What is the experimental evidence in favor of radioactivity being aw(qlzru9 w ns2rg nr kk28441+ y)daky nuclear process?r21da2gryw(rl8k z4 n)wusqkk 9 4+n y

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 wayqthp;meu- b:a7r6f6t s as you can, the difference between $\alpha$, $\beta^-$, $\beta^+$, and $\gamma$ rays.

What element is formed by the radioactive decay f3kpu g11i nqo5uv h6)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 of (a) /bf/a3bs zca3$_{15}^{32}\text{P}\ (\beta^-)$ (b) $_{16}^{35}\text{S}\ (\beta^-)$ (c) $_{83}^{210}\text{Bi}\ (\alpha)$?

Fill in the missing particle or nucl,-lz y4klhoo *eus:
(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 5du/ 3f; fl 0xuf*ssrsyfkwx1 am( .3x$_{92}^{238}\text{U}$ 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 undergoelqiz0etvcf wissg )79--5n,y s 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 nuclide are genzl*4 e.slw:20 ;hswst mxm 7xrerally monoenergetic; that is, t x7lrs:m4stz*e2; shwl x.0 wmhey 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 underg3fofn py0r;5uk:x f4:g qsi,u o electron capture generally lie above or below the line of stability in (Fig. Below)? rup 3:fx5,nfg4q:f0 oskyu i;

Can hydrogen or deuterium emit ++,ni) aw0aaz 4im cpian $\alpha$ particle? Explain.

Why are many artificially produced radioactive isotopes r/)2vd yo lhow5are in nature?

An isotope has a half-life of one month.m unmd)(lopu iix561. After two months, will a given sample of this isotope have completely d uiuo.()ml6dmi n51xpecayed? If not, how much remains?

Why are none of the elemi50pw n) tu4btmpm2 5 bcrb1y8ents 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 convers:af-rx;own )e s/sz/0y4kn5fi4b t zt ion and $\beta^-$ decay, an electron is emitted. How could you determine which decay process occurred?

  A pi meson has a mass ofz3xd,e.)x dp z $139\ \text{MeV}/c^2$. What is this in atomic mass units? m =    u

  What is the approximate radius of an al.,v) jo,e wype apz1vmss 8j,5pha particle $(_{2}^{4}\text{He})$?r =    $ \times 10^{-15}\ \text{m}$

  What is the rest mass of a bare*es1ks 3bnehv- k8t -t $\alpha$ particle in $\text{MeV}/c^2$? $m_{\alpha}$ =    $\ \text{MeV}/c^2$

  (a) What is the approximate radiusxfx)h-hx8rq 1 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 essentially the same fo:tcr 34io) 9+z0dntijya a hf6r all nuclei)4irt0 fyja9 t 3zido: an6+ch. $\rho$ =    $ \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 n-agrm3i 2+b ,6l75e,wtzmb xe ep0frqxl.z x8ucleus? $\dfrac{m_{\text{p}}}{(m_{\text{p}} + m_{\text{e}})}$ =   
(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? Does it matter w,+ regxj (x oe:/8ocafhat the object is made of? Why or why not? o+ xjcfor(/,eex:8g a N $\approx $    $\times 10^{26}$ nucleons

  How much energy must an 6wjw2lk ps2-be-k j6x$\alpha$ particle have to just "touch" the surface of a $_{92}^{238}\text{U}$ nucleus? $\text{KE}$ =    $MeV$

  Use (Fig. Below) to estimate the total binding energy of x74 u1/ayyhub/+u* oi vwa6ie
(a) $_{92}^{238}\text{U}$    $ \times 10^{3}\ \text{MeV}$
(b) $_{26}^{56}\text{Fe}$.    MeV

  Use Appendix B to calculat5 ljps vgsem2l.307yhp-e)o6 3bcc u ye the binding energy of $_{1}^{2}\text{H}$ (deuterium). Binding energy =    $MeV$

  Calculate the binding energy per x+nztyvi e534 nucleon for a $_{26}^{56}\text{Fe}$ nucleus.    $MeV$

  Determine the binding energy of the laso*a hv1p87 mh.+rkftct neutron in a $_{19}^{40}\text{K}$ nucleus. Binding energy =    $MeV$

  Calculate the total bi1o 6r cc sz,t0swqb9qiw3h 4mh:1 b2qdnding energy, and 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 binavx; :k0njr3k ding 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 to removee;gxdu;7 .,li mng4me2bc ,ub (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 nuwke(ccqrb08mk e 1h:6jw/sa 6w,t s)zcleus $_{4}^{8}\text{Be}$ (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 releasev*yg1a p3cjk dkk2 +s7h0 zl(sd when tritium, $_{1}^{3}\text{H}$, decays by $\beta^-$ emission? Q =    $MeV$

  What is the maximum kinetic energy of an e1kg0*g1h yp3 kcm 3hoilectron emitted in the $\beta^-$ decay of a free neutron? $\text{KE}$ =    $MeV$

Show that the decay q1l d cg(6/zqu;sm dm c2wbm24$_{6}^{11}\text{C} \to _{5}^{10}\text{B} + \text{p}$ 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 calyq;lo-i i-a;mi6tu r3culation that shows whether or not the following decays are possibliluy i6o -mtai; q;r3-e:
(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, emy+bnu :tk)rz1 its 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 emitte/0j4l0z qr8f fv0 w8oo tve2ned $\beta^-$ 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 electron capture uncsb728y5 fy by beryllium: $_{4}^{7}\text{Be} + \text{e}^- \to _{3}^{7}\text{Li} + \nu$? Q =    $MeV$

  A photon with a wavelengt*kwafh:11u./-c;h48d i dkxpsz zajdh 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 kinetid.cj0-,yosx 1*r jtfw c 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 doetk-in 2(cf9zgid+98*h;b 2fiwb/ k: oqgoyc gs 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 txg ss7tjbbjy* u/b6 04he $\alpha$ 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 byl;b vlxle2 -y6 $\beta^+$ 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 minute at og,v(sh.1ddez mx8wf8q *w(pm ne time, and 4.6 h later produces320 decays per minute. What is its ha .hez w(m1(d,*8fgd8spxmvq w lf-life? $T_{\frac{1}{2}}$=    $h$

  (a) What is the decay constant of9 dj)d.c9jpum $_{92}^{238}\text{U}$ 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 oro zny7):qd u3f 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 s/1z xh-d:c/v+x uqnm-; lgqv jample 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 after exactly 6 half4h7)h5+g c g4dvdd)fp lt *pcl-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, 930sebli6+w ,r3)b(bh4 jv ty staelu 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 pur1aa5pgjenu0v 0- l7ub4 iel8 fe $_{19}^{40}\text{K}$ 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 zqpu0t0n+5irof 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 sampf/f s61xm05 v;f lhm ,g6dkkjkle 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 i lec.-lwnh(2c 2mdc(ks its hal -ml( khn(l2wcccd2.ef-life? $T_{\frac{1}{2}}$ =    $min$

  A 285-g sample of pu6y7j -wch fpx7 c4m-jcre 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 o+jpld1ms6ml*hc7wj lp a/ 89$_{37}^{87}\text{Rb}$, 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 relatix1b z 1aqy;v,s1pmy. yve 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 radioacte1ekj:rmw)nidx-1+nw :k dw/ive 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 th lg1lpq fv( *zy*yi8k/at contains 290 g of carbon and has an activity of 8.0 decays per second. Determine its age assuming that in living trees the ratizk if(*l81/yg*v q pylo 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 prodddjvco4mr;2 i;4c8esuced in a reaction where the measured activity of a sample drodrjc4se d ci;4;28v omps to 1.050% of its original activity in 4.00 h?

  An old wooden tool is found to contain only 6.0% b a 1/y-.hbaryzgn59+;hclcwptz,2kof $_{6}^{14}\text{C}$ that a sample of fresh wood would. How old is the tool? t =    $ \times 10^{4}\ \text{yr}$

  A neutron star consi1y (5jiot q a 3lc0mj9bkpt28ests of neutrons at approximately nuclear density. Estimate, for a 10-km-diameter neutron stak2be30 t 8po5cm(1lq ij9ytj ar,
(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 pro :znp.b4zo ns2i9 qp-mton may be unstable, with a halfop:snz q49mbp 2n.zi--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 ha2ldb s sr4aeueig9kwho0ho(7 (6 bc /0lf-lives) for a radioactive sample to drop to 1.00% of its6d oawrs 7/(ge0o 0(ubh bl e24ch9kis original activity?    $T_{\frac{1}{2}}$

  If the potassium isotop a 91z-kguib6)hn sc,re $_{19}^{40}\text{K}$ 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 nits+hcq( d- x-uclear fission product of uranium in both reactors and atomic bo s+qthc(x -di-mbs. 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, 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) 1.0 ydkx dbgu8;*dhu 6 ulwy,5e2ohger7/ :l-ve *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 the energy, in y9* 7 pq ;y6bhi5l-rv-hxb2gl3jopff) c .dlbjouyf v xl.hbh5c 9lp;3- op 7j)qg-rb6l*ifyb d2les, needed to break a 3.0-g copper penny into its constituent nucleons. (Fig. Below)    $ \times 10^{12}\ \text{J}$

  Instead of giving atomic masses for nuclides ass6a-mk.s,he7+-cf ip. 4 wa2odvhkro in Appendix B, some Tables give the mass excesa-fih27r-e o.sk v6cpohasm, .w4 k d+s, $\Delta$, 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 thpfl..n9cn* 6vnt0s8krn:7 bfv p /gnu e 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 a little closer to th / )sut)66m bamoiu*rfe mass of the neutron, the following reaction would b6br)s* mmuufti6 ) ao/e possible even at low 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 t1g*;axnjr ,rs he 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 particlxj*;san ,grr1es.    $T_{\frac{1}{2}}$

  A 1.00-g sample of naturi2b2djm5si5sf. -wr bik,yu; al 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 occur4do+ ;9 ppy7k gyjr1cs m4p*yer47 azvring 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 potasz661f;0yit h8c0,mfa,;dbwqno0e9 siudio csium, of which a small fraction is the ryiftfb9 1; qhn6 ,0a 0i8ic moocw;zsd6ed,u0 adioactive isotope $_{19}^{40}\text{K}$ (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 carbon8ww;f7:lg b+ 5otu xrq-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? : forwx;ulwb58q+g t 7   $\ \text{decays/s}$

Decay series, such as that shown in(Fig. Below), can be ctjdn: sa ,1r-hh4mv :elassified into four families, depending on whe t :hevsm naj1:hr-4d,ther the mass numbers 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.