What do different isotopes of a gisxbf) 4 8; eq-umgqt:tven element have in common? How are they differen;qt-x4 sbt8f :g umq)et?

What are the elements rg4k4 2fhem clpc6m11sepresented by the 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 man+i,s1sw3 jvw rz12guty neutrons do each of the isotopes in Question 2 have?+rjgi vzws1w12, 3tu s

Identify the element that) sfk xi)mc-:0.wp ude has 88 nucleons and 50 neutrons.

Why are the atomic masses of many elements (see the periodic;htla7:f .nzfu)fcf g9,p ux ) table) not close to whole numbeg,7 lx.nu 9tfz f:f )ah;p)fucrs?

How do we know there is such a thing a7h1w :p/0hoprtph;tls the strong nuclear force?

What are the similarities and the differen-m /qy ii,/.g:gzbyu *rpzj6t ces between the strong nuclear force and the electric foyz: zb/m6-q pygiut g r,*i/.jrce?

What is the experimental evidence in favor of radioactivity being a nuclear prt1thcfb pz*h+c3)+rv ocv+)r1zfbhp c+h 3tc *tess?

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 yobxhs/ f2u fx7xa2; 9 usu8kv8-3mgzetu can, the difference between $\alpha$, $\beta^-$, $\beta^+$, and $\gamma$ rays.

What element is formed by the radioactive decay of (a) )719yl/az hh i mp6 i1ikubu:v$_{11}^{24}\text{Na}\ (\beta^-)$ (b) $_{11}^{22}\text{Na}\ (\beta^+)$ (c) $_{84}^{210}\text{Po}\ (\alpha)$?

What element is formed by thaf.l/ jo;+t) lxxe+fyayt(/ qe decay of (a) $_{15}^{32}\text{P}\ (\beta^-)$ (b) $_{16}^{35}\text{S}\ (\beta^-)$ (c) $_{83}^{210}\text{Bi}\ (\alpha)$?

Fill in the missing parusej 4(/izbu9 k s37wpticle 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 xx)o3v c j7 /u gg7u5pt:qrh,p$_{92}^{238}\text{U}$ 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 undergoe c,o 9 kkpda9cxm4+jlcca;e5y)r8+mulae y64s 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 nucli y tk5exf1.(fonqr12jde are generally monoenergetic; thafj5t(eq f2k n.rx11yot is, they all have the same kinetic energy. But the beta particles from a beta-emitting nuclide have a spectrum of energies. Explain the difference between these two cases.

Do isotopes that undergo el6+mhq ah /yg2dsa 47lcectron capture generally lie above or below the line of stability in (Fig. Below)? a4gdlmqh shyc/a+76 2

Can hydrogen or deuterium em;(98 u3y;ww9h8 f fgiqlfmkjv it an $\alpha$ particle? Explain.

Why are many artificially produced radioactiveu6 udpng(2:fphrqi ab+84 af 1 isotopes rare in nature?

An isotope has a half-life of one montwhk/0rs7y9k pmrw p) /h. After two months, will a given sample of this isotope have comh) 7w/0rk kps ryw/m9ppletely decayed? If not, how much remains?

Why are none of the elecf jeh/fm rg9.dhnl3;b1w 8m.ments 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 conv k+era.( )fugsersion and $\beta^-$ decay, an electron is emitted. How could you determine which decay process occurred?

  A pi meson has a mass ;nr (fit9 ev3tof $139\ \text{MeV}/c^2$. What is this in atomic mass units? m =    u

  What is the approximate r id7 n,yrbq1vs91cj,dadius of an alpha particle $(_{2}^{4}\text{He})$?r =    $ \times 10^{-15}\ \text{m}$

  What is the rest mass of a bare mjloh/womnj, 9++- a r$\alpha$ particle in $\text{MeV}/c^2$? $m_{\alpha}$ =    $\ \text{MeV}/c^2$

  (a) What is the approximate radiuh0o 9vt i)ww2xs 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 for all nutc5*(y vvpbh ibn),n k*s82i gcl g* ihp vsv 8kt2,b(*bcny)ni5ei. $\rho$ =    $ \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 hydroic jafw-- b)l/gen 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 g6*cu0 l;iyy oare there in a 1.0-kg object? Does it matter what the object is made of? Why or why ug 6;0icoyly*not? N $\approx $    $\times 10^{26}$ nucleons

  How much energy must an 78j .f+ vroyycp k;tgv9-wqy4 $\alpha$ particle have to just "touch" the surface of a $_{92}^{238}\text{U}$ nucleus? $\text{KE}$ =    $MeV$

  Use (Fig. Below) to estimate thegklvm i(m*5+;nc 9hl o total binding energy of
(a) $_{92}^{238}\text{U}$    $ \times 10^{3}\ \text{MeV}$
(b) $_{26}^{56}\text{Fe}$.    MeV

  Use Appendix B to calculat*jr * tn1qni.bxn lah(u0 no5*e the binding energy of $_{1}^{2}\text{H}$ (deuterium). Binding energy =    $MeV$

  Calculate the bindin70/yr cd:p .0dc0pk yjzks-o vg energy per nucleon for a $_{26}^{56}\text{Fe}$ nucleus.    $MeV$

  Determine the binding energ3s v jua3wgy:;y of the last neutron in a $_{19}^{40}\text{K}$ nucleus. Binding energy =    $MeV$

  Calculate the total binding ener1frv 2z0jxh k,v7*hz agy, 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 ( b u. kj* kwkqy*jw,llf73,uvbinding 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 remove (a)pd6gpofq+s1vo-w ds;e dj 8 csj5l4,4 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 nucleu4jn 4;*tuzuu.mv aowfy g7/,rujxn*7s $_{4}^{8}\text{Be}$ (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 u;/qtek 8cg: ctritium, $_{1}^{3}\text{H}$, decays by $\beta^-$ emission? Q =    $MeV$

  What is the maximum kinetic enef10,ebvi1xy e) vt ;ndz0lv.y9 w9cgf rgy of an electron emitted in the $\beta^-$ decay of a free neutron? $\text{KE}$ =    $MeV$

Show that the decay e8zp8v;z/p5ya s)nwf9ew yp* wns-+ x$_{6}^{11}\text{C} \to _{5}^{10}\text{B} + \text{p}$ 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 the yuj.ydm/uexg8; :bc3following decays are possible: gu8ymyd:j;. xcb3ue/
(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 restoev3r + .y9tiu6zqad), 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 emitte7 falnzl 7+p7 vamz2vy2-8rke d $\beta^-$ 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 *y *)oyxmp+ w24q3tnwlb 4yircapture by beryllium: $_{4}^{7}\text{Be} + \text{e}^- \to _{3}^{7}\text{Li} + \nu$? Q =    $MeV$

  A photon with a wavelength of js13iynb2: vgb ;k+,8cy wxlb$1.00 \times 10^{-13}\ \text{m}$ 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 enn2xb1bt;-m kqc )8tdbergy 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 does as1xa *9qtpj2o0 gqc:rxpl +:q $_{19}^{40}\text{K}$ nucleus get when it emits a 1.46-MeV gamma ray? $\text{KE}_{K}$ =    $eV$

  What is the energy of2cox utjx12,w b-rsx nxx0)v 6 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 cgf,u j.vh* p5decays 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 minute at one tib;xgxr92obm23m0jz/zr5 ezq me, and 4.6 h later produces320 deca2 m2xgzxr0q; r9/boe3z m jzb5ys per minute. What is its half-life? $T_{\frac{1}{2}}$=    $h$

  (a) What is the decay constant of i d,uen77,nmq g( hd-u$_{92}^{238}\text{U}$ 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 samplew ++/i,ni4(gk txs-: pfssqle 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 f ;gv3unqxmxy9h3n29of $_{32}^{68}\text{Ge}$, whose half-life is about 9 months, will remain after 3.0 yr? $\dfrac{N}{N_0}$ =   

  What fraction of a sample is left af -t9lmtra d) h(yoc6 ; zus.y:d+k/blqter 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 nuclide l w. x:n edj9k,cp+8me$_{92}^{235}\text{U}$ 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 ofqep1xr-s0m y /gzi0c 6uty)4d a sample 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 puraszs9,vvgk7*o 1 4d ioe $9.7-\mu\text{g}$ 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 samplnnop,mxxbi5l( 6er 63e 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 factorj 9;yphk 0apj, of 10 in 8.6 minutes. What is its half-li y j0,hjapk9p;fe? $T_{\frac{1}{2}}$ =    $min$

  A 285-g sample of pure carbon contains 1yk6v19a pp* /x2vt -ghuf)mqv .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 8uy* c w9n2m qpl2 3cdmyto52j$_{37}^{87}\text{Rb}$, 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 calculateqx0u2 4p-w wli3zk ovc*kut,t0*7vj h 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 df*nbgv7 ;-jsdecay 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 and has an activ- c 8y*ugbd62vpq/s 3hpi,luxity of 8.0 decays per second. Determine its age assuming thatvi3lb6 p u-hpg8*scdq x /2,uy 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 uxh7 i*h56+m:cz/mldahv 6lzproduced in a reaction where the measured activity of a sample drops to 1.050% of its origial*d u6 5 xmhm:6 ih7hz+lvz/cnal activity in 4.00 h?

  An old wooden tool is found to contain only 6.0% ofxvid-s4r5 -a.lck )t 2;ncrs4jel q8g*pe gn3 $_{6}^{14}\text{C}$ that a sample of fresh wood would. How old is the tool? t =    $ \times 10^{4}\ \text{yr}$

  A neutron star consists of neutrons a7:*swv6m xqw it approximately nuclear density. Estimate, for a 10-km-diameter neutron stasw7w6:i*v x mqr,
(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 protonfjf2ol (9 gxc(lx6 9km may be unstable, with a jgxf(o kx9( c2l9flm6half-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) for a radioactive sample to 3xmk 0z5j,phjb 2mc,f drop to 1.00% of its original activitfjbzk , cm32m0hp, 5jxy?    $T_{\frac{1}{2}}$

  If the potassium isodgdze q. 85zlm+0i/bc 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 produced as a nuclear fission product of uranium in botq0+khad w-i+ /e88 scngz;iwqh 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 whgw;+wzdk -8iia s /+qh08qcney 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 activit/6sa*: d6s klv1ta6rpe +egkqies 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 coom2hhixb/ 6s(j)/s. z1d qoawpper and then estimate the energy, in joules, need6 h . /wq)as2moho/(1ibzsdxjed 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 nucl3j:d; 7c-xwk/aq:y ih 9y dthfides as in Appendix B, some Tables give the m-:t:fd9 y/c7xdwa q;kyh 3 hjiass 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 natu+xqk:s2*q opy.ymeg. ral 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 proton were just a gv3i,f lwmg)1zqy . :klittle closer to the mass of the neutron, the following fz, l)kivq1ymg3 .gw:reaction would be 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 the n;k bby ge46- v *l3gd3xpkob4kinetic 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 particlesx-3g4*3 eg 4dkoynbvb;p6 klb.    $T_{\frac{1}{2}}$

  A 1.00-g sample of natural samarium emits a5ay * o,nr 5*as+nrgl4r0yyu $\alpha$ 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 uranium is 2ylnu3tdox3)sb,f 1 f 6i *bne$_{92}^{238}\text{U}$ 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 n3+u,d z d 7g-f +23sozs3 t5cvssbgrumg of potassium, of which a small fraction is the radioactive isotonso5ss7 vdu-3f2drug b+ zc+sgtz ,3 3pe $_{19}^{40}\text{K}$ (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 6b7qzzmrzf9( ii1( 9a w0,000 years. If a bone contains 1.0 kg of carbon, a r i9mz7q(9bizz a(w1fnd the animal 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 lc ze0c ziv.1*into four families, depending on whether the mass numbers hav 0z1vlzc e.*ice 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.