What do different isotopes of a given element have in common? How are theii-e )(vbctaq +5d)o jy different?qj5cbe ()-to) +i aidv

What are the elements represented by the X in the following: (a ptwa.b /xf+;z) $_{2}^{4}\text{He} + \text{X} \to _{7}^{14}\text{N}$ (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 isotopes in Question 2 havioru gce9pe +/8 -i vmwd1bu-m1:o6tmv6/i d1p8:mi ob eu m-9ermt+o-cg1uwe?

Identify the element that has 88 nucleons and 50 .z0 gw1m40kfgib emp zfmt fu752 n(c.neutrons.

Why are the atomic masses of many elements (see the periodic table,fs .mp6(bov,x fuf49zu n4xl ) not close to wx4v b ,p9u(f4f.zfmo6ul ,x nshole numbers?

How do we know there is such a thing as the strong nuclear fo8f2oxrs*w j2e+so k (,2szxujrce?

What are the similarities and the6n nrj-w( z9bsq jbbw.g74vn/ differences between the strong nuclear force and v67 jr/bbg4.j (q-znbn9 snwwthe electric force?

What is the experimentau99cif* s3 7f0ahg pnsl evidence in favor of radioactivity being a nuclear proce uah9gis3f pnf*sc907ss?

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 difference betw/+0 ifjqymi:f een $\alpha$, $\beta^-$, $\beta^+$, and $\gamma$ rays.

What element is formed ,-nvb,pb h rkd:. gco;yz1:kb ;2iwor by the radioactive 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 the d tvt1j8/b om(decay of (a) $_{15}^{32}\text{P}\ (\beta^-)$ (b) $_{16}^{35}\text{S}\ (\beta^-)$ (c) $_{83}^{210}\text{Bi}\ (\alpha)$?

Fill in the missing afg*usosvzv 3f5 a3 6.)ptz (c0r1v qjparticle 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 kdzdj1p 21 0zr$_{92}^{238}\text{U}$ nucleus decays to $_{90}^{234}\text{Th} + _{2}^{4}\text{He}$, the daughter thorium nucleus still has 92 electrons circling it. Since thorium normally holds only 90 electrons, what do you suppose happens to the two extra ones?

When a nucleus undergo 8)1a4 ihiw.zvet9jpbes 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 generally monoenergs 6camwhfn-(4etic; that is, they all have the same kinetic energy. But the beta particles from a beta(4ca6 wmfs nh--emitting nuclide have a spectrum of energies. Explain the difference between these two cases.

Do isotopes that undergo electron capture generally lie above o t* 9 2ykkw9e1wg bhiqyd7t*w:r below the line of stability* tt 92kwyqe9h1w7:gb yw *ikd in (Fig. Below)?

Can hydrogen or deuteriutyplbd um/5s vn7 1+w:m emit an $\alpha$ particle? Explain.

Why are many artificially produced radioactive isotopes rare hcwypo0n50l *9 v sgv;ys1o v:in nature?

An isotope has a half-life of one month. After two months, will pj61a r;xjpzr-; o4riinw 6m3 a given sample of this isotope have completely wrj-opam;4z1 i rpx6j3; 6ri ndecayed? If not, how much remains?

Why are none of the elements txz z7g0xh+/mwith $Z>92$ 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 conversionv06t/ do ed0v8r0+br-pdd i7 q xa/fiu and $\beta^-$ decay, an electron is emitted. How could you determine which decay process occurred?

  A pi meson has a mass ofjnlb /nif+,;z $139\ \text{MeV}/c^2$. What is this in atomic mass units? m =    u

  What is the approximate radius of)uf ,+kou xot0 an alpha particle $(_{2}^{4}\text{He})$?r =    $ \times 10^{-15}\ \text{m}$

  What is the rest mass )0wcrs2ur jelc j0,4gof a bare $\alpha$ particle in $\text{MeV}/c^2$? $m_{\alpha}$ =    $\ \text{MeV}/c^2$

  (a) What is the approuhs5*rc8 )aj /n aiqj5gti; g8ximate radius of a $_{6}^{12}\text{C}$ nucleus? r =    $ \times 10^{-15}\ \text{m}$
(b) Approximately what is the value of A for a nucleus whose radius is $7.0\ \text{fm}$? A =   

  (a) Show that the density of nuclear matter is essentially the same for alln/+pfm)) qc xu e3dz82hxf3v n nuclei. vzex fn3xfd2u/ m8nq+3)p )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 t91t pfvkj5ao6. je*st he hydrogen atom's mass that is in the nucleus? $\dfrac{m_{\text{p}}}{(m_{\text{p}} + m_{\text{e}})}$ =   
(b) What is the fraction of the hydrogen atom's volume that is occupied by the nucleus? $\left( \dfrac{r_{\text{nucleus}}}{r_{\text{atom}}} \right)^3$ =    $ \times 10^{-14}$

  Approximately how many nucleons are there in a 1.0-kg object? Does it matter wh/e6cb x92:lzgp3p a wnat the object is made of? Why or why noabxp3e9c/ nwg6:p lz2t? N $\approx $    $\times 10^{26}$ nucleons

  How much energy musty gfga /*qas1, an $\alpha$ particle have to just "touch" the surface of a $_{92}^{238}\text{U}$ nucleus? $\text{KE}$ =    $MeV$

  Use (Fig. Below) to estimatjf sn,o;da0r*r e y1a kqi,9p5e the total binding energy of
(a) $_{92}^{238}\text{U}$    $ \times 10^{3}\ \text{MeV}$
(b) $_{26}^{56}\text{Fe}$.    MeV

  Use Appendix B to calculate the binding ei4:v* : 1hkof;j hf l/ xtxlct5pnw3v+nergy of $_{1}^{2}\text{H}$ (deuterium). Binding energy =    $MeV$

  Calculate the binding energy per vsiak /wfg czz b:7.4i;yc(n*nucleon for a $_{26}^{56}\text{Fe}$ nucleus.    $MeV$

  Determine the binding enlplw(r l4 bq494tjag7 ergy of the last neutron in a $_{19}^{40}\text{K}$ nucleus. Binding energy =    $MeV$

  Calculate the total bindbj3 evp 3)vyo4ing 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 binding gsmw vq07* j;rg;kn9 1mewk-senergy 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 ree.z*7eqz- e/ c/tqt*-lpcnfl quired to remove (a) a proton, Energy(p) =    $MeV$
(b) a neutron, from $_{8}^{16}\text{O}$? Energy(n) =    $MeV$
Explain the difference in your answers.

  (a) Show that the nucleus k:kp fguw3(.jk7ws) n/a2evpmr)2 l d)m6sbl$_{4}^{8}\text{Be}$ (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 br41 /ry 8 x1ap7vaqpktritium, $_{1}^{3}\text{H}$, decays by $\beta^-$ emission? Q =    $MeV$

  What is the maximum kk aiqa lby+.yz 06-uf.4kk:f iinetic energy of an electron emitted in the $\beta^-$ decay of a free neutron? $\text{KE}$ =    $MeV$

Show that the decay p;g,)y-y*u fr*mca 8qfff b/l$_{6}^{11}\text{C} \to _{5}^{10}\text{B} + \text{p}$ 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 calculcdn3 /hfjjo(+kxc7o+,av0h y, p jbvk(a7kr6ation that shows whether or not the following decays are poav7cr(oky0d6n( v,k/h+ po3x,7fahjjc b+ kj ssible:
(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 igm(.kd)+ zlmx sc2i4/p8ijvan $\alpha$ 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 eix9c g(c qy c+.b2puk*/tc t.imitted $\beta^-$ 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 b - ynpudrt.l1x,4t0gin electron capture by beryllium: $_{4}^{7}\text{Be} + \text{e}^- \to _{3}^{7}\text{Li} + \nu$? Q =    $MeV$

  A photon with a wavelength of s3 z52+ mifjot$1.00 \times 10^{-13}\ \text{m}$ 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 kinw8 s/efd zm*i2etic 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 does a zm4-*mp,f ucw$_{19}^{40}\text{K}$ nucleus get when it emits a 1.46-MeV gamma ray? $\text{KE}_{K}$ =    $eV$

  What is the energy ofm5)oq4oip f9h/9f vej the $\alpha$ particle emitted in the decay $_{84}^{210}\text{Po} \to _{82}^{206}\text{Pb} + \alpha$? Take into account the recoil of the daughter nucleus. $\text{KE}$ =    $MeV$

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

Show that when a nucleus decays by,zf) 2 dd1fuuy $\beta^+$ 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.g j(xefm;bvqa16mn 6 minute at one time, and 4.6 h later produces320 decays per minute. What;1mqgbv 6xjna.e f6 (m is its half-life? $T_{\frac{1}{2}}$=    $h$

  (a) What is the decay 1f sbibu+ew )+tlwq54c d w;oxxy)i 0+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 sample ofn1 1+a*qzryg)bi av4d $_{6}^{14}\text{C}$ that contains $3.1 \times 10^{20}$ nuclei? $\dfrac{\Delta N}{\Delta t}$ =    $ \times 10^{9}\ \text{decays/s}$

  What fraction of a sample of2si;qjh2++k u1;ck7zf d+ x6brhq tbm $_{32}^{68}\text{Ge}$, 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 hnrbnql 3-p/5gyfhjd dw 6e8g(;kds/ :alf-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 decay6g)qp-(wsgh/le, cdc lnbu fz i)1w,, s, 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 s h92yjdlq ;-kuample 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 activitytkfw.9mxj)vuz 53gw. of a pure $9.7-\mu\text{g}$ sample of $_{15}^{32}\text{P}\ (T_{1/2}=1.23 \times 10^6\ \text{s})$. $\lambda N$ =    $ \times 10^{11}\ \text{decays/s}$

  The activity of a sample ,6 z)cqak4fnuy)f 9pg 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 fa x8p yj.sav.q/n x6r+fctor of 10 in 8.6 minutes. What is its half-/.n6r+a xv p8qjxs.y flife? $T_{\frac{1}{2}}$ =    $min$

  A 285-g sample of pure carbon contains 1.3 parts i/h qjwuo cf/cef* 6o9t* /5ofwjg) y)un $10^{12}$ (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 isotopegzhc, zzu 66-i $_{37}^{87}\text{Rb}$, 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 raten1n;wmb x3w ,,ubb1zi s 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 sequences1-3:q,dvr edwy .dfyd 6)yvq z 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 ofof2g5tvfx :5k,q9 x ja(os0uh carbon and has an activity of 8.0 deca9fxxku v5:0ohaj gof t2q (s,5ys 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 lz(m5ctxq s**is being produced in a reaction where the measured activity of a sample drops to 1.050% of its original activity q*xsl(tcz *m5 in 4.00 h?

  An old wooden tool is found to co. u0fnqi3,z i;7n.hogsx-o m qntain 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 nuclear density. Estimakdjpn 80 v6ox0te, for a 10-km-diameter neutron star, 80dn6vpj ok0x
(a) its mass number, A =    $ \times 10^{55}$
(b) its mass (kg),m =    $ \times 10^{29}\ \text{kg}$
(c) the acceleration of gravity at its surface. g =    $ \times 10^{11}\ \text{m/s}^2$

  The $_{1}^{3}\text{H}$ isotope of hydrogen, which is called tritium (because it contains three nucleons), has a half-life of 12.33 yr. It can be used to measure the age of objects up to about 100 yr. It is produced in the upper atmosphere by cosmic rays and brought to Earth by rain. As an application, determine approximately the age of a bottle of wine whose $_{1}^{3}\text{H}$ radiation is about $\frac{1}{10}$ that present in new wine. t =    yr

  Some elementary particle theories suggest that the proton may be unstable, wa(fqw,yx. um e7 ps.6rith a.w,y.mxa r s(67pfu eq half-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 t2 ndk;x2hlplyy) l)wjb; i(.ho drop to 1.00% of its originaly()d;n i;lw x)bkhj2 2llh yp. activity?    $T_{\frac{1}{2}}$

  If the potassium isotopxa4sq v5q8yjz - g42jme $_{19}^{40}\text{K}$ 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 ajt du;ovnwsry.3/a zxg(z :.3nz/ 4r b/l:zwes a nuclear fission product of uranium in both reactors and atomic bombs. Look at its location in the periodic table to see what otherz3 /d:bnv/xn e gs3 yrwato4:r zjw/;..(zlzu 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 activitie80 rlzdflz;4 xs 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 copper and then estimate the energy, in j0+ch kqg it627nuqfy+q, oo.p. q ktnfy3/g* toules, needed ttcthk iq.ggf32y q7 *q n 0,6fq.tky/+ouon+po 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 as in Appen9hps ,ph;yh)n dix B, some Tables give the my;,hpsh9 h )npass 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 natural carbon contains the usual fractioo+lo5s0dm 0 nwn 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 t 55113reqk cq9b*t/ow uwfx lgo the mass of the neutron, the followi1ew9x/o g5*w 53 ulkqbqfcrt 1ng 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 kinetic energies for an alpha particle and x vri.h1fgx. 4ogk8+v a beta particle if both make tracks with the same radius of curvature in a magnetic field, oriented perpendicular to thxhi+vf8x g . g.rkv4o1e paths of the particles.    $T_{\frac{1}{2}}$

  A 1.00-g sample of naturalo 770 t rzg.wdmd*r33dm7kwk o.tac4p 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 occo7t a k79r1iujurring 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 contgus (ai 5cn:a7n/eor/ains 400 mg of potassium, of which a small fraction is the radioactive 5/r inge asco(a7u/ n: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 carl93r+g.v2 fz .4ozfy gy 3/rlwwimlv* bon-14 dating is about 60,000 years. If a bone contains 1.0 frw. zo*i 3yr+z9/ f2l4w3v.gl ly gvmkg of carbon, and 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 l a. gq7xg6(uzg9mo8tinto four families, depending on whether the mass numbers ho (7zg.qtxlg8 g6m9auave 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.