Give a reaction between two nucleons, similar to Eq. 32-g*icuq +(3p mv4, that could produce a 3 q+vu(mcgp*i$\pi^0$.

  If a proton is moving ov3rv9ji i;;hat very high speed, so that its kinetic energy is much greater thai voi ;9h3rjv;n its rest energy ($mc^2$), can it then decay via $p \to n + \pi^+$?  ----待选择----yesno 

What would an "antiatom," made up of th cx:f vc9nox9cv9-x/ se antiparticles to the constituents of normal atoms, consist of? What might happen if antimatter, made of such antiatoms, came in contact with our normal worxs9:c x9/xvc f -9nocvld of matter?

What particle in a decay signals the electromagnetic interaibv5 q7urq7 vx5mer-7 ction?

Does the presence of a am fg7hi w*pgv(k ui6a1 zs,s(l88 pt(neutrino among the decay products of a particle necessarily mean thag fh68k,vzs 7*ip gua1 i8at m((lwps(t the decay occurs via the weak interaction? Do all decays via the weak interaction produce a neutrino? Explain.

Why is it that a neutron decays via the weak i b8f2h eoza),-6vgwm unteraction even though the neutron and one of its decay products (proton) are stron- ,ae )hbo28vmuwf6g zgly interacting?

Which of the four interactions (strong, e 0p;q7m8sst 0omsb :qjlv 61x-(q cyaelectromagnetic, weak, gravitational) does an electron take part in? A c - a6m;jybemss1(7ql qo:0tvx 8q s0pneutrino? A proton?

Check that charge and baryon number are conserved in each of thely + pey8y;o)e decays in Table 32+ee y ;lyy8p)o-2.

Which of the particle decays in Table 32-2 occur via the electromagnetic interac7 a zjiv.*i6m pcd1le7qj8d+ctio*8 cd.d m 7ij+1l zaepvjiq6c7n?

Which of the particle decays in Table 32-2 occur by the ep,s0erfb3ckyxj ok,h 209s g6ygj6 6weak interaction?

By what interaction, a *q8n0m,;si6wo 7x bmafwg: bund 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 decays in Table 32-4 occur via the electromagnd9:ce y )i*bj((oekdxetic interactio 9jcyi(ddeo :b )ekx*(n?

Which of the particle decays in Table 32-4 occurw was*/5dbk4d by the weak 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 kind of "neutrinolet" that was massless, had no cor fwvu03sn9,j lor charge or electrical charge, and did now9rsu0n3jv ,f t feel the weak force. Could you say that this particle even exists?

  Is it possible for a particle tff) juyd +)y5ro 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 chromodynamics, would it be possible to find particle 6jnkev81: hj2 f,obb gf,p)yrs made up of two quarks and np,b h2r) k1 8fgyj6jbfeo, vn:o antiquarks? What about two quarks and two antiquarks?

Why do neutrons decay when thet5n45 gy q 9obbz3u)usy are free but not when they are inside the nucleus?o g sb5u 3t5nqu)by4z9

  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 energ3va/en69i iivj ;kfh4 y is 6.35 GeV?    GeV

  Calculate the wavelength of 35-Gejby zuwtv;: le3 ;h47eV electrons. E =    $\times 10^{-17}\ \text{m}$

  What strength of magnetic field is used nof 8,8czmvux86- 6naidez5 nin a cyclotron in which protons make $2.8 \times 10^7$ revolutions per second? $f$ =    T

  What is the time for one complete revolution for a very high-en:zr*g8m y(o2cv a0zxsergy proton in the 1.0-km-radius Fermilab accelerator? T =0zzcgxa * 8(ysr2vo: m     $ \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 Example 32-ej/pd h5k.lgw/k.yc z(.2 fbo2 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 picking out details of the nucleus: 30-MeV alpha parq8g;dz:j5ishzf4l) l ticles or 30-MeV protons? Compare each of their wavelengths with the size of a nucl g;ljs:h lq)58 z4zdifeon in a nucleus.  ----待选择---- alpha particles protons 

  The voltage across the dees of a cyclotronvw9 z - ndq *4zgk:mspadf1x+2 is 55 kV. How many revolutions do protons make to reach *p1g92:amf-d4wns k z qvd+xza kinetic energy of 25 MeV? $\approx $    $\ \text{revolutions}$

  What is the wavelengt) m5 g74q s6m ka9e(mwbrx+* bjwgreg:h ($\lambda$, maximum resolvable distance) of 7.0-TeV protons? E =    $\times 10^{-19}\ \text{m}$

  A cyclotron with a r- h2trqb3e+-:i wahi) w1t cmwadius of 1.0 m is to accelerate 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 thxe.b6e85s,x/r kx qy de Large Hadron Collider (LHC) calls for proton beams of energy 7.0 TeV. What magnetic field will be requx ,.8sedkerxyq/65 xbired? B =    T

  The 1.0-km radius Fermilab Tevatron t/r)xch5s6gu) sxd+ aoakes about 20 seconds 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 arogh c)56x d+s/ usx)given to the protons on each turn. (You can assume that the speed of the protons is essentially $c$ the whole time.) Energy/revolution =    MeV/rev

Show that the energy of a particle (chal2bk4rdu htl ,3w.v ,prge $e$) 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 t1w+apm.4*qvumdr8u 8diuz61uud -vneeded at the 1.0-km-radius Fermilab synchrotron for 1.0-TeV pdt+qm ud uup -41muiz*w1v d.8v68ar urotons? B =    T

  How much energy is releaix*i afs8*m *ksed in the decay $\pi^+ \to \mu^+ + \nu_\mu$? See Table 32–2.    MeV

  About how much energy is releas+-a *2twue ttaed when a $\Sigma^+$ decays to $n + \pi^+$? (See Table 32–2.)    MeV

  How much energy is re;4-cwux y csa9quired to produce a neutron-antineutron pair?    MeV

  Estimate the range of the sdesyu5)/88kbx zxf +itrong force if the mediating particle were the kaon instead of the p sdxxiub)58+y8/ kef zion. $mc^2$ $\approx$    $ \times 10^{-16}\ \text{m}$

  Two protons are heading toward each o/.g x5q.oy s-vrg,tujfho e4)ther with equal speeds. What minimum kinetic energysg )t4 rfoq/jxeyh.g.u ov5,- must each have if a $\pi^0$ meson is to be created in the process? (See Table 32-2.)    MeV

  What minimum kinetic energy must two neutrons each have if oaku3 nag jc 3 mkz6ko8c,3+7cthey are traveling at the same speed toward ek+ caj36cu,kk n87zmo g3oc3a ach other, collide, and produce a $\pi^0$ pair in addition to themselves? (See Table 32-2.)    MeV

  Estimate the range of the weak force using Eq. 6t8av+0)vijwdi jfk;4l 9 tts32-3, given the masses of the W and Z particles as aboutt9 vv aiks6jt)8it+;w4dlj 0f 80 to $90\ \text{GeV}/c^2$. $mc^2$$\approx $    $\times 10^{-18}\ \text{m}$

  What are the wavelengths of the two photons produced whe, g +y9knu*70 kk9evq8co qsnin a proton and antiproton at rest anni v7n *y,q kkk9g80nu9q soiec+hilate? $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 momentum and energy, that it is impossiblev ) 7 zjqj.z ev cr9b ;,h8/yxmqg1xo1icu4da2 for an isolated electron to radiate only a single photon. (b) 8 ,ed12rbmajcv;jxi/yc).q h 9uv xz74gozq1With this result in mind, how can you defend the photon exchange diagram in (Fig. Below)?

  What would be the wavelengths of the two photons produced when an elen kxdsb t.ixl; s4/g0/ctron and a positron, each with 420 keV of kinetic energy, annihil/b4dxk ;gt /is .nsxl0ate 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 reactions and decays are possiblnv5)h tpei b+ryrf8 ke2 91;rce? For those forbidden, explain what laws are viola1 ek)9;fe+ptn rh rcr 582yibvted.
(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 the two products s-.z3gctk( s,cbk wh-z:2t hoin 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 evkivcwp6x8 71lectron in 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 pjbmv140 4cv es1av v8energy width and then the lifetime of the $\Delta$ resonance using the uncertainty principle.
$\Delta E$ =    MeV
$\Delta t$=    $ \times 10^{-24}\ \text{s}$

  The measured width of 1ehzbf; jpu.32,hye t;x 1qjsthe $\Upsilon$ meson is 88 keV. Estimate its lifetime. $\Delta E$ =    $ \times 10^{-21}\ \text{s}$

  The measured width ofn,7s4svyjxgv1 4;ad, r(ydojlr7 e4 imy* o5j the $J/\psi$ (3685) meson is 277 keV. Estimate its lifetime. $\Delta E$ =    $ \times 10^{-21}\ \text{s}$

  What is the energy width (or un r4ixagf 0py-/certainty) 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 are possible? For those that dc+sa,h(p)*hrrl 6(t t8ycapare forbidden, explain which laws are violated. ttc (a 6hly)rr*d, pap sc(8h+
(a) $\Xi^0 \to \Sigma^+ + \pi^-$
(b) $\Omega^- \to \Sigma^+ + \pi^- + \nu$
(c) $\Sigma^0 \to \Delta^0 + \gamma + \gamma$

What are the quark combinationsc()l1ud :vlrt that can form (a) a neutron, (b) an antineutron, tcd)rullv1(: (c) a $\pi^+$, (d) a $K^-$?

What particles do the following quark cowik.ova1xp04 ( llm nj (f37p;*qqe owmbinations produce: (a) $uud$, (b) $uu\bar{d}$, (c) $u\bar{s}$, (d) $\bar{d}u$, (e) $c\bar{s}$?

What is the quark combination nelo)xhb*) sk c-eded to 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 in Fignegi;8rn bt;yl 5,yk). Below) for the reaction nl,r k5tg i ;y;yen8)b$p + \pi^- \to n + \pi^0$.

Draw a Feynman diagram for the nsdp1tq hab x-zzhjju2(y+yd:6q 59. reaction $n + \nu_\mu \to p + \mu^-$.

  What is the total energy of a proton whose kinetic energy 905uyxbe f ,jdis 25 GeV? What is its wa fdb uyjx9e,50velength?
$\approx$    $ \ \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 Fermilab Tevatron with an en n0xmsgr:6 eu(ergy of 150 GeV. If they are accelerated by 2.5 MV each revolution, how far do they travel and approximately how long does it take for ugr( 0:sxe6mn them to reach 1.0 TeV? d$\approx $    $ \times 10^9\ \text{m}$

  (a) How much energy is released when an electron and a pn1* hxq (p)rqw54ucpf ositron annihilate each other(* n)4wpq cuhfrpqx15? $E_{\text{total}}$=    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 what 7a5(mjl(o,8rgq.jy 5jqt y lginteraction could they (t85 (q o7a,rqyggyjjlj .m5loccur? For those forbidden, explain 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 reactions are possible, and by what interaction cou+c u2 v l//ar7j-qdga+fd+l yuld they occur? For those forbidden, exgy la+ar7u+ //fd v-luqd+c2jplain 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 vi ;07w+6cfxap ku3l7xma*hy $\pi^+$ is $\pi^+ \to \mu^+ + \nu_\mu$. What would be the equivalent decay for a $\pi^-$? Check conservation rules.

  Symmetry breaking occurs incj15 yebxp. ,n 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 theq. -jf.vf2as a reactions, Eq. 32-4, for producing a pion. s-fj2. afq.av $Q$ =   $MeV$ or $Q$ =    $MeV$

  Calculate the Q-value for the reactio.pxm h(59zd mij0,hwf n $\pi^- + p \to \Lambda^0 + K^0$ 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 fermions are there in a wat9r r wy*n),zyua4s 9guer molecule?    fermions

  A proton and an antiproton annihilate each other at rest and produce two i;mnsijdh. (6jh,(0ug r+drupions, dhjri; 6d, nj (0sh rum+u(.ig$\pi^-$ and $\pi^+$. What is the kinetic energy of each pion? $2m_pc^2$ =    MeV

  (a) Show that the so-called unification distance+ vjcsr)(6gxgt ;-ce.r+wu es 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 Table 32-2 are in terms of proper time, measineqm yqt457 0ured in a reference frame where the particle is at rest. If a tau lepton is created with a kinetic energy of 450 MeV, how long would its track be as measuredq074iemtnyq 5 in the lab, on average, ignoring any collisions? $\Delta x_{\text{lab}} = $    $ \times 10^{-5}\ \text{m}$

Identify the missing particle in the following reactions.gy ;g5. )4zbz8ju:nadj3j qge
(a) $p + p \to p + n + \pi^+ + ?$
(b) $p + ? \to n + \mu^+ + \nu_\mu$

Use the quark model to debjtdeh671n p: scribe the reaction $p + n \to \pi^+ + \pi^-$.

What fraction of the speed of68. svbowm+9.fe 9xh; p pfbhv light $c$ is the speed of a 7.0-TeV proton?