Give a reaction between two nucleonhuz- zc9/*0:mm :lbw gk6xjqrs, similar to Eq. 32-4, that could produce a *jumxg /9 :rlq zb0- w:mhz6ck$\pi^0$.

  If a proton is moving at very high speed, so that its kila:enx4 8-q(vy ni+pknetic energy is much greater thanye (vx 4l -nqkpa8+n:i its rest energy ($mc^2$), can it then decay via $p \to n + \pi^+$?  ----待选择----yesno 

What would an "antiatom," madt9udh)* bo:sl e up of the antiparticles to the constituents of normal atoms, consist of? What odlsth:9 u)*bmight happen if antimatter, made of such antiatoms, came in contact with our normal world of matter?

What particle in a decay signals the electromagnetic interac+512cu uijnlntion?

Does the presence of a neutrino among the decay produc.xizt7.j fz c-xu 7 mso m1r+v8u2s9r+;epfsats of a particle necessarily mean that the decay occurs via the weak interaction? Do all decays via the weak interaction pr7st7+;f+ru 2 uerx xm jop.c.asvzsf98 1zi -moduce a neutrino? Explain.

Why is it that a neutron decays vigqu- oy7fm oh5a //s,xa the weak interaction even though the neutron and one of its decay products (pros/7x/u,foaqoy5 g -hmton) are strongly interacting?

Which of the four interactions (stromhx48d4 4z/p a *r2bhprs(ahtng, electromagnetic, weak, gravitational) does an electron th hp rd4zx 4b/tm*8rspa(4h2aake part in? A neutrino? A proton?

Check that charge and baryon number are conserved in each of the diz ;kv25 7guu4s*hc35 gpmcd fecays in Table 32-2.k pg5zu23vd;ig5 mhu* sfc4c7

Which of the particle decays in Table 32-2 occur via the electromk n:a.rv;ri1u gm(lr;.wo :3/ei)qcpj1psavagnetic interaction?:p) ;.r/ ngk.w;1cjasvi or ma:rqeu(13 piv l

Which of the particle decays in Table 3iwm1vb 8wk -,q2-2 occur by the weak interaction?

By what interaction, jm o so13fo:ws 0t;2h 4zfni+aand why, does $\Sigma^0$ decay to $\Lambda^0 + \gamma$? What about $\Xi^-$ decaying to $\Lambda^0 + \pi^-$?

The $\Delta$ baryon has spin $\frac{3}{2}$, baryon number 1, and charge states $Q = +2, +1, 0, -1$. Why is there no charge state $Q = -2$?

Which of the particle dec;eijz-ls:p ow.f,q 0s /u+uy tays in Table 32-4 occur via the electromagnetic interacu u/pw f zsy0j. oi;-,q:tels+tion?

Which of the particle decays in Table 32-4 occur by the weake +shch,n+6)9n;tml;gdt cb gh5t 9hb interaction?

Quarks have spin $\frac{1}{2}$. How do you account for the fact that baryons have spin $\frac{1}{2}$ or $\frac{3}{2}$, and mesons have spin 0 or 1?

Suppose there were a poskq0 xt1/f+6c/rldkind of "neutrinolet" that was massless, had no color charge or electrical charge, and did not feel the weak force. Could you say that this particle evenrtqpok/s lf/+d 6 xc01 exists?

  Is it possible for a partiom zpsa8:t( g.cle to be both
(a) a lepton and a baryon?  ----待选择----yesno 
(b) a baryon and a hadron? ----待选择----yesno 
(c) a meson and a quark? ----待选择----yesno 
(d) a hadron and a lepton?  ----待选择----yesno 
Explain.

Using the ideas of quantum ch*8g uczlx6h 5o0teb4j .q2p ohromodynamics, would it be possible to find particles made up of two quarks and no antiquarks? What abcp *zhu.ql 8hego506xtj2ob4out two quarks and two antiquarks?

Why do neutrons decay when they are free but not when they are insideapw(p3tztf bi; )(zh7 the nucleus?tp 7z3pfb(( ziht;aw)

  Is the reaction $e^- + p \to n + \nu_e$ possible? Explain.  ----待选择----yesno 

Occasionally, the $\pi^+$ will decay by the following reaction: $\pi^+ \to e^+ + \nu_e$. Which of the four forces in nature is responsible for this decay? How do you know?

  What is the total energy of a proton whose kinetic energy is93p zl-jcvs6i 6.35 GeV?    GeV

  Calculate the wavelength of 35-GeV electrons. Eh++d eq -:a8(kimlwzo7ytyj app7:l ( =    $\times 10^{-17}\ \text{m}$

  What strength of magnetic field is used in a cyclotron in which protons u-6kzv82vakvj4+g v kf:se y/make $2.8 \times 10^7$ revolutions per second? $f$ =    T

  What is the time for one complet luidju1 t4no6prn81yl.t:;*aey v7m e revolution for a very high-energy proton in the 1.0n; nyt:p io1yej7.84u d1a rutl*6vlm-km-radius Fermilab accelerator? T =     $ \times 10^{-5}\ \text{s}$

  If $\alpha$ particles are accelerated by the cyclotron of Example 32-2, what must be the frequency of the voltage applied to the dees? $f$ =    $ \times 10^7\ \text{Hz}$

  (a) If the cyclotron of Examplel7f;l9oh3n *advgrb 4 zbd9)g 32-2 accelerated $\alpha$ particles, what maximum energy could they attain? What would their speed be? KE =    v =    $ \times 10^7\ \text{m/s}$
(b) Repeat for deuterons ($^2\text{H}$).KE =    v =    $ \times 10^7\ \text{m/s}$
(c) In each case, what frequency of voltage is required? $f$ =    Hz

  Which is better for pickin3d+bey ,o,4njv yx6q3q7klx d g out details of the nucleus: 30-MeV alpha particles or 30-MeV protons? Compare 6oy4x,d7 e3xqvlkb n 3,+qydjeach of their wavelengths with the size of a nucleon in a nucleus.  ----待选择---- alpha particles protons 

  The voltage across the dees of a cba yqwyvo+: 58sahn, :yclotron is 55 kV. How many revolutions do protons make to reach a kinetic energya58:+qv yyan :o,bs hw of 25 MeV? $\approx $    $\ \text{revolutions}$

  What is the wavelengthxfa9.o) 2ha th ($\lambda$, maximum resolvable distance) of 7.0-TeV protons? E =    $\times 10^{-19}\ \text{m}$

  A cyclotron with a radius of 1.0 m is to a jic)fbe 7h1e3ccelerate deuterons ($^2\text{H}$, mass $= 2.014$ u) to an energy of 12 MeV.
(a) What is the required magnetic field?$\approx $    T
(b) What frequency is needed for the voltage between the dees?$\simeq $    Hz
(c) If the potential difference between the dees averages 22 kV, how many revolutions will the particles make before exiting?$\approx$    $\ \text{revolutions}$
(d) How much time does it take for one deuteron to go from start to exit? $\Delta t$ =    $ \times 10^{-6}\ \text{s}$
(e) Estimate how far it travels during this time. distance =    m

  The 4.25-km-radius tunnel that will be used to house the magnets for the u6dm82vq ha;jj(s 0vv Large Hadron Collider (LHC) calls for proton beams of energy 7.0 TeV. What magnetv2hv(vq68jjs 0;d umaic field will be required? B =    T

  The 1.0-km radius Fermilab Tevatron takes about 20 sea.n9 38p kkckfconds to bring the energies of the stored protons from 150 GeV to 1.0 TeV. The acceleration is done once per turn. Estimate the energy given to the protons on each turn. (You can assume that tc9k . p3fa8kknhe speed of the protons is essentially $c$ the whole time.) Energy/revolution =    MeV/rev

Show that the energy of ayk-)pvjt:e2/ywq c 0nm*g /os particle (charge $e$) in a synchrotron, in the relativistic limit ($v \approx c$), is given by $E\ (\text{in eV}) = Brc$, where $B$ is magnetic field strength and $r$ the radius of the orbit (SI units).

  What magnetic field intensity is needed at the5 3)q*nmww kulup3j0h.nco *x 1.0-km-radius Fermilab synchrotron for 1.0-TeV protons? Buwn 5kj3p0ch u.oq3mx)ln**w =    T

  How much energy is released in the dem)0q.1 n s7mufs2 r,nx h oj1z+av6fdjcay $\pi^+ \to \mu^+ + \nu_\mu$? See Table 32–2.    MeV

  About how much energy is fbmb c6-2op g3s(z+ ntreleased when a $\Sigma^+$ decays to $n + \pi^+$? (See Table 32–2.)    MeV

  How much energy is required to produce a neutron-antinw,05w9o0 qv7nisz-ea(yb3 zvr ty* xeeutron pair?    MeV

  Estimate the range of the strong force if the mediavrq*1;8 r fj)nur ibr/ting particle were the kaon instead of the pion.j*f1) uvnq ir;r rr8b/ $mc^2$ $\approx$    $ \times 10^{-16}\ \text{m}$

  Two protons are heading tow e3dw bu 4b2(6qv(1lc(d6m lyszi4jn iard each other with equal speeds. What minimum kinetic energy must each have if a ( 2( bdnli lz 64u3jedwyvcqb6(sm4i1$\pi^0$ meson is to be created in the process? (See Table 32-2.)    MeV

  What minimum kinetic energy must two ne; ;,2x oys*wfmgyvh5 zutrons each have if they are traveling at the same speed;sx zh;g yv,5 m*wyf2o toward each other, collide, and produce a $\pi^0$ pair in addition to themselves? (See Table 32-2.)    MeV

  Estimate the range of the weak forceqiohv hqe5)f7+/gq n53rwbn* using Eq. 32-3, given the masses of the W and Z par*)fg 5vobnqni+57 q/hhw qe 3rticles as about 80 to $90\ \text{GeV}/c^2$. $mc^2$$\approx $    $\times 10^{-18}\ \text{m}$

  What are the wavelengths of the two p,l h,w- gm gwv:6,i7w ygjshlwi 3jb:,hotons produced when a proton and antiprotow sw6l, -yih,,wjh:jigwg7l3g :v ,m bn at rest annihilate? $2m_0c^2$$\approx $    $ \times 10^{-15}\ \text{m}$

The $\Lambda^0$ cannot decay by the following reactions. What conservation law is violated in each of the reactions?
(a) $\Lambda^0 \to n + \pi^0$
(b) $\Lambda^0 \to p + K^-$
(c) $\Lambda^0 \to \pi^+ + \pi^-$

  For the decay $\Lambda^0 \to p + \pi^-$, calculate (a) the Q-value (energy released),Q=    MeV
(b) the kinetic energy of the p and $\pi^-$ assuming the $\Lambda^0$ decays from rest. (Use relativistic formulas.)
$KE_p$ =    MeV
$\text{KE}_{\pi^-}$ =    MeV

Show, by conserving momentu 1m0d qdkjjc71n3z94gd itkl8m and energy, that it is impossible for an isolated electro18ckqjdj l10z394 7gdntkidm n to radiate only a single photon. (b) With this result in mind, how can you defend the photon exchange diagram in (Fig. Below)?

  What would be the wavelengths o 4y4+srndta hyy7)2 le b*cy1/m,dxgjf the two photons produced when an electron and a positron, each with 420 keV of d17/yb+y4x)yts4 d g2e hrn,yjmc *lakinetic energy, annihilate head on? $\lambda $ $\approx $    $ \times 10^{-12}\ \text{m}$

  In the rare decay $\pi^+ \to e^+ + \nu_e$, what is the kinetic energy of the positron? Assume the $\pi^+$ decays from rest. $\text{KE}_{\text{e}^-}$ =    MeV

Which of the following r;gcpex)c a*p ,eactions and decays are possible? For those forbidden, explain what laws are vioc;xc, *p)egap lated.
(a) $\pi^- + p \to n + \pi^0$
(b) $p \to e^+ + \nu_e$
(c) $p + p \to p + e^+ + \pi^+$
(d) $\pi^- \to e^- + \bar{\nu}_e$
(e) $\mu^+ \to e^+ + \nu_\mu$
(f) $p \to n + e^+ + \nu_e$

  Calculate the kinetic energy of each of the29 qlnb3fwk.3fc ) 9fswvg 3qd two products in the decay $\Xi^- \to \Lambda^0 + \pi^-$. Assume the $\Xi^-$ decays from rest.
$\text{KE}_{\Lambda^0}$   MeV
$\text{KE}_{\pi^-}$   MeV

  Could a $\pi^+$ meson be produced if a 100-MeV proton struck a proton at rest? What minimum kinetic energy must the incoming proton have? $\text{KE}_{\pi^-}$ =    MeV

  Calculate the maximum kinetic energy of the electron igd2b5 ;axbq 8in the decay $\mu^- \to e^- + \bar{\nu}_e + \nu_\mu$. [Hint: In what direction do the two neutrinos move relative to the electron in order to give the latter the maximum kinetic energy? Both energy and momentum are conserved; use relativistic formulas.] $\text{KE}_{\text{e}^-}$    MeV

  Use (Fig. Below) to estimate the energy width and then the li0obg6 k zo+alky:p6 ,bfetime of the $\Delta$ resonance using the uncertainty principle.
$\Delta E$ =    MeV
$\Delta t$=    $ \times 10^{-24}\ \text{s}$

  The measured width of the9y9sze 8ay0s:ysup1 ; sixyi ; $\Upsilon$ meson is 88 keV. Estimate its lifetime. $\Delta E$ =    $ \times 10^{-21}\ \text{s}$

  The measured width o;ws okc qtg1.8f the $J/\psi$ (3685) meson is 277 keV. Estimate its lifetime. $\Delta E$ =    $ \times 10^{-21}\ \text{s}$

  What is the energy wiuv l;a(ur: 4dk. .)upfash)u itio63(sa ji1jdth (or uncertainty) of
(a) $\pi^0$, $\Delta E$$\approx$    keV
(b) $\Sigma^0$? (See Table 32-2.) $\Delta E$$\approx$    keV

The $B^-$ meson is a $b\bar{u}$ quark combination. (a) Show that this is consistent for all quantum numbers. (b) What are the quark combinations for $B^+$, $B^0$, $\bar{B}^0$?

Which of the following decays-xi: 2m*lxul3 atv4w ,5anup4 ek8uoy are possible? For those that are forbidden, explain which laws are violated. *anm53wu:uu4 l2xtel k-4oi,8xvp ya
(a) $\Xi^0 \to \Sigma^+ + \pi^-$
(b) $\Omega^- \to \Sigma^+ + \pi^- + \nu$
(c) $\Sigma^0 \to \Delta^0 + \gamma + \gamma$

What are the quark combinations that can form (a) a neutron, (b) an antinipo(e)dau 4uqk6. (nheutron, 6u.e)4(hn oi apuqk(d(c) a $\pi^+$, (d) a $K^-$?

What particles do the followinnc7 -cw2mplu -g quark combinations produce: (a) $uud$, (b) $uu\bar{d}$, (c) $u\bar{s}$, (d) $\bar{d}u$, (e) $c\bar{s}$?

What is the quark combination needed - vv -ue ( epgpavhcrn1ke-/rha14x;4to produce a $D^+$ meson ($Q=B=S=0, c=+1$)?

The $D_s^+$ meson has $S=c=+1, B=0$. What quark combination would produce it?

Draw a possible Feynman diagram using quarks (as ilkzhud q*go3f2 h98 ;on Fig. Below) for the reaction;h u*zlq93ho2fk 8dg o $p + \pi^- \to n + \pi^0$.

Draw a Feynman diagram for e*u4f gw*z9u.i ievc1 the reaction $n + \nu_\mu \to p + \mu^-$.

  What is the total energy of a proton whose lmm+3(lxq+ dcf .+hhyypdm63kinetic energy is 25 GeV? What is its wavelength?hl . +6 +mmyqh+xdm p(dl3fcy3
$\approx$    $ \ \text{GeV}$
$\lambda$ $= $    $ \times 10^{-17}\ \text{m}$

  Assume there are $5.0 \times 10^{13}$ protons at 1.0 TeV stored in the 1.0-km-radius ring of the Tevatron.
(a) How much current (amperes) is carried by this beam?I =    A
(b) How fast would a 1500-kg car have to move to carry the same kinetic energy as this beam? v $\approx $    $ \times 10^2\ \text{m/s}$

  Protons are injected into the 1.0-km-radius Fermi8vlm yhz ::w )f3*9tq.asm ofelab Tevatron with an energy of 150 GeV. If they are accelerated by 2.5 MV each revolution, how far do they 3t o fayle)zsvhqm8 .wm:*f9: travel and approximately how long does it take for them to reach 1.0 TeV? d$\approx $    $ \times 10^9\ \text{m}$

  (a) How much energy is released when an electron and a positropnlwsg a t,p;/8q0a a;n annihilate each other? pap;w, at;a ql/0gs8n$E_{\text{total}}$=    MeV
(b) How much energy is released when a proton and an antiproton annihilate each other? (All particles have $KE = 0$.) $E_{\text{total}}$ =    MeV

Which of the following reactions are possible, and by wgny 5a1ueuyk i3eb t6 d)d+w+9hat interaction could they occur? For those forbidden, )ydu+d+a1 9g3eiwuye tk6 b5nexplain why.
(a) $p + \pi^- \to K^+ + \Sigma^-$
(b) $p + \pi^+ \to K^+ + \Sigma^+$
(c) $p + \pi^- \to \Lambda^0 + K^0 + \pi^0$
(d) $p + \pi^+ \to \Sigma^0 + \pi^+$
(e) $p \to \pi^+ + e^- + \bar{\nu}_e$

Which of the following d(ob nqgx; xk9df3/c;reactions are possible, and by what interaction could they occur? For those forbidd(f9/;bx3 dgkdqnx oc;en, explain why.
(a) $p + \pi^- \to K^0 + p + \pi^0$
(b) $p + K^- \to \Lambda^0 + \pi^0$
(c) $n + K^+ \to \Sigma^+ + \pi^0 + \gamma$
(d) $K^- \to \pi^- + \pi^0 + \pi^+$
(e) $\pi^+ \to e^+ + \nu_e$

One decay mode for a z(ayagw(mh 0*9nyf 47 mxpp+i$\pi^+$ is $\pi^+ \to \mu^+ + \nu_\mu$. What would be the equivalent decay for a $\pi^-$? Check conservation rules.

  Symmetry breaking occurs axe*4yc5ke629j w vaxin the electroweak theory at about $10^{-18}\ \text{m}$. Show that this corresponds to an energy that is on the order of the mass of the W boson ($M_W c^2 \approx 80\ \text{GeV}$). $mc^2$$\approx$   GeV

  The mass of a $\pi^0$ can be measured by observing the reaction $\pi^- + p \to \pi^0 + n$ at very low incident $\pi^-$ kinetic energy (assume it is zero). The neutron is observed to be emitted with a kinetic energy of 0.60 MeV. Use conservation of energy and momentum to determine the $\pi^0$ mass. $E_{\pi^0}$ =    $MeV/c^2$

  Calculate the Q-value for each of the reactions, Eq. 32-4, for produci* npcd7:k p7+ )omjwgbng a pion. pd)7 7wn:*mk pc+g boj$Q$ =   $MeV$ or $Q$ =    $MeV$

  Calculate the Q-value fo (aqi-j5ru*yb r the reaction $\pi^- + p \to \Lambda^0 + K^0$ when negative pions strike stationary protons. Estimate the minimum pion kinetic energy needed to produce this reaction. [Hint: Assume $\Lambda^0$ and $K^0$ move off with the same velocity.]
Q =    MeV
$\text{KE}_{\pi^-}$ =    MeV

  How many fundamental fervza pitd02/9 umions are there in a water molecule?    fermions

  A proton and an antiproton annihilate each other at rest and produce3eo5mhppu q6kc sjta0 ;zg11n7xe(q- two pions, zc16e3q10gtuoh-spk n 5pqjax( 7; me$\pi^-$ and $\pi^+$. What is the kinetic energy of each pion? $2m_pc^2$ =    MeV

  (a) Show that the so-called unifqsa9h)vuaa2x h*; jr *ication distance of $10^{-31}\ \text{m}$ in grand unified theory is equivalent to an energy of about $10^{16}\ \text{GeV}$. Use the uncertainty principle, and also de Broglie's wavelength formula, and explain how they apply. $\Delta E$ =    $ \times 10^{16}$GeV E =    $ \times 10^{15}$
(b) Calculate the temperature corresponding to $10^{16}\ \text{GeV}$. E =    $10^{28} K$

For the reaction $p + p \to 3p + \bar{p}$, where one of the initial protons is at rest, use relativistic formulas to show that the threshold energy is $6m_p c^2$, equal to three times the magnitude of the Q-value of the reaction, where $m_p$ is the proton mass. [Hint: Assume all final particles have the same velocity.]

  The lifetimes listed in Tabl0nl l,x*pvw a.od-p9a xkz1 rx7f e)6te 32-2 are in terms of proper time, measured in a reference frame where the par xxre .o7ppxv0k an ,9tld*f a1zl6)-wticle is at rest. If a tau lepton is created with a kinetic energy of 450 MeV, how long would its track be as measured in the lab, on average, ignoring any collisions? $\Delta x_{\text{lab}} = $    $ \times 10^{-5}\ \text{m}$

Identify the missing particle in the foc)m4b:d x w /.5dr w9;hwqhmtwkc1o)tllowing reactions.
(a) $p + p \to p + n + \pi^+ + ?$
(b) $p + ? \to n + \mu^+ + \nu_\mu$

Use the quark model to describe po;k t11 ifm/so+u-fo the reaction $p + n \to \pi^+ + \pi^-$.

What fraction of the speed ofr6c u;r/n /ad4 t/aijr light $c$ is the speed of a 7.0-TeV proton?