Give a reaction between two nucleons, similar to Eq. 32-4, that could produce a lt/y w4unughdf gu91:kcff164y3- dy f:1ydn6gw lyu4 fg/19cdutyf3- hk4u $\pi^0$.

  If a proton is moving at very high speed, so that its kinetic egij;3r epr f5/nergy is much greater than its/ei5r3 ; rfgjp rest energy ($mc^2$), can it then decay via $p \to n + \pi^+$?  ----待选择----yesno 

What would an "antiatom," made up of the anti(p i8l tmxzjlc aw9fql /7w/5+particles to the constituents of normal atoms, consist of? What might happen if antimatter, made of such antiatoms, came in contact with our normal world of matt+i59/qww z /l ftx7cmp8l(ljaer?

What particle in a dec l03ya mltz*c+hhs c.k3nm *b4ay signals the electromagnetic interaction?

Does the presence of a nl91l9 .yzdcoj eutrino among the decay products of a particle necessarily meany9j z.ldo91lc that 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 interaction even though iq )eo1 w,kv-othe neutron and one of its decay products (proton) are io1,qwkv -)eostrongly interacting?

Which of the four interactio1q h2l1h+jdbe9vo4w o ns (strong, electromagnetic, weak, gravitational) does an electron take part in? A neutrid4h+qh1w v1ob9 oel j2no? A proton?

Check that charge and baryon number are cons-jv8oldho v(vmex. 8 3erved in each of the decays in Table j 3omodv (lehx .-v88v32-2.

Which of the particle decays in Tab tzf/ od8;jsd-/r9 ihtle 32-2 occur via the electromagnetic interac9-zf t/d 8;ji/h odrsttion?

Which of the particle decays in Table 32-2 oc: ,*7 s rsnko ynxue3u;cogd4(iuc(1ocur by the weak interaction?

By what interaction, and lop7 p)nz6 t3+/cqnjfwhy, 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 ahv 9qtk keb5f6n/9 pc(ag t+e62 zf3wdecays in Table 32-4 occur via the electromagnetic interactionah(6f/t 96 gek2nwq fcke bztp5v +9a3?

Which of the particle decays in Table 32-4 occur by the weak inter4hj2d l4)2 4lenvtte xaction?

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 massle:zz )dl*mb( k2pyj xz5ss, had no color charge or electrical charge, and did not feel the weak force. Could you say tz mp2lxzbz k:5* (jd)yhat this particle even exists?

  Is it possible for a partij4a lm-s(*h p:p jqy/qcle 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 chromodynamics, would it be possible to find particlycork-d5wh+--nd v7x es made up of two quarks and nov-7-x h+ry -d cwd5kon antiquarks? What about two quarks and two antiquarks?

Why do neutrons decay when they are free but not when they are inside the nucleu0xj:cb5sn 4 ve3c0d8d xwvmn*s?e4 mn jxnd 5xsb 8c:0d0v3cv*w

  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 protpguh3wjo(m5 /h/ xl5bon whose kinetic energy is 6.35 GeV?    GeV

  Calculate the wavelength of 35-GeV electt ;t7;g)sl v5k quusr6rons. E =    $\times 10^{-17}\ \text{m}$

  What strength of magnetic field is used in a cyclotron in whilq.+65tk(tryz w n3toch protons make $2.8 \times 10^7$ revolutions per second? $f$ =    T

  What is the time for one complete revolution for a very high-energy proe.s ylpsgpm 1m87v 1uyi*wk f.u5su3 8ton in the 1.0-km-radius Fermilab accel1 puiu7ysp5w..8k*mmuf1vsye3 g s8lerator? 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 Example 32db-e-)+xe 1m8y /rihzot-j kp-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 pic w 50iz66prmk49kmpm 48oep ttking out details of the nucleus: 30-MeV alpha particles or 30-MeV protons? Compare each of their wavelengths with the size of a nucleon ini m 0 rpko4p95 tmtw86k64ezpm a nucleus.  ----待选择---- alpha particles protons 

  The voltage across the dees of lrn+1gd nndkrhi /-d8v:gr 8-a cyclotron is 55 kV. How many revolutions do protons r-rin8h-n+d1/vd l :gnkd8g r make to reach a kinetic energy of 25 MeV? $\approx $    $\ \text{revolutions}$

  What is the wavelength (jbn oht ;,u6o:$\lambda$, maximum resolvable distance) of 7.0-TeV protons? E =    $\times 10^{-19}\ \text{m}$

  A cyclotron with a radius of 1.0s .r mb b,7oikuc fz0h+p5:*fu 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 th nxd48u3gvz l* (u6tdtat will be used to house the magnets for the Large Hadron Collider (LHC) calls for proton beams of energy 7.0* 4 dunz6g(vx tl38dut TeV. What magnetic field will be required? B =    T

  The 1.0-km radius Fermilab Tevatron takes about 20 seco:,cgak dh n74q0pao-gnds to bring the energies of the stored protons from 150 GeV to 1.0 TeV. The acceleration in40q7a-agpoh,c gk d: s done once per turn. Estimate the energy 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 q 9) * ze,ag-bnd/le/yd1ej mrof a 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 lwycg o8,k)s3the 1.0-km-radius Fermilab synchrotron for 1.0-TeV protons? Blc,ys3w8ko) g =    T

  How much energy is re5fvl g6a rl0dmp4bd3+v-pcm3nv 7sd /leased in the decay $\pi^+ \to \mu^+ + \nu_\mu$? See Table 32–2.    MeV

  About how much energy y jp9q ro6w m,26ll1+ezn7cs mis released when a $\Sigma^+$ decays to $n + \pi^+$? (See Table 32–2.)    MeV

  How much energy is required to produce a kt* b q;i pu3pjxg9p hn9842grneutron-antineutron pair?    MeV

  Estimate the range ou .l6t f( jzom(/yjkq.tyq j24f the strong force if the mediating particle were the kaon instead of the 6(/jyq .jt ftjm.4zy(2qulokpion. $mc^2$ $\approx$    $ \times 10^{-16}\ \text{m}$

  Two protons are heading toward each other with eqru52wu lax2neox 6r(5 ual speeds. What minimum kinetic energy must each(run5a5uwrx2olex62 have if a $\pi^0$ meson is to be created in the process? (See Table 32-2.)    MeV

  What minimum kinetic energy must two neutrl gfzyk 0yu,:7)abcn+ons each have if they are traveling at the same speed +al7bkycyu zn)0 f,g: toward each other, collide, and produce a $\pi^0$ pair in addition to themselves? (See Table 32-2.)    MeV

  Estimate the range of th,io2;/j zz9ebs6 rhm e7czx-te weak force using Eq. 32-3, given the masses of the W and Z particles as 7b/6cor;mx zi-ztzhe js,9e2about 80 to $90\ \text{GeV}/c^2$. $mc^2$$\approx $    $\times 10^{-18}\ \text{m}$

  What are the wavelengths of the two photons produced when a proton an tr) jv/n;mik(d antiproton at res)k(t n;mrv/ij t 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 momentum and energy, that it d2i4*0 3g p u-rxxt-3lsg +u4 gls shqxpk49mnis impossible for an isolated electron to radiate only a single photon. (b) With this result in mind, how can you defend the photon exch xm9gsix4pp- 4l34nh x ut0+u*srdqg2sg- k3lange diagram in (Fig. Below)?

  What would be the wavelengths of the two photons produced when an l)y:tg kdive mahtn*:/u6r+. electron and a positron, each with 420 keV of kinetic energy, annihilate head on? v* : lein u6mtg/tadyr:+.kh ) $\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 dec a3og7075wmy vkl6xxp ays are possible? For those forbidden, expagwm7v70o 635xk ylxplain what laws are violated.
(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 in the qhm.,e92 :lox; qtfn ddecay $\Xi^- \to \Lambda^0 + \pi^-$. 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 egh p q*6+7mn4u 2lmc( wj1lfrtn.ddi;lectron 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 energy width and then the lifetime of thewivu0y.ftqp.b1:) skb2a0 b l $\Delta$ resonance using the uncertainty principle.
$\Delta E$ =    MeV
$\Delta t$=    $ \times 10^{-24}\ \text{s}$

  The measured width of the08g(oh ev ogmw*w)1 ku $\Upsilon$ meson is 88 keV. Estimate its lifetime. $\Delta E$ =    $ \times 10^{-21}\ \text{s}$

  The measured width of thev2 amp2(5.gla kwue7i:-hfzd $J/\psi$ (3685) meson is 277 keV. Estimate its lifetime. $\Delta E$ =    $ \times 10^{-21}\ \text{s}$

  What is the energy width t))a n3t0j0w n5bjpq: jn :thv(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 are possible? For thos tv;snsqhpcu9x.xv;6b:m x.)yi ; t w:e that are forbidden, explain which laws areqw.v :;cxub:ht;y 6p;si.)mv xt9nsx violated.
(a) $\Xi^0 \to \Sigma^+ + \pi^-$
(b) $\Omega^- \to \Sigma^+ + \pi^- + \nu$
(c) $\Sigma^0 \to \Delta^0 + \gamma + \gamma$

What are the quark combinatbdxq+ zc *25tcions that can form (a) a neutron, (b) an antineutron, qb*d xtzcc2+5 (c) a $\pi^+$, (d) a $K^-$?

What particles do the following quark combinations produce: (alymp29p gixz5ihk y0nu q3b 65(6 9iic) $uud$, (b) $uu\bar{d}$, (c) $u\bar{s}$, (d) $\bar{d}u$, (e) $c\bar{s}$?

What is the quark coml889fxhj a9eu( o;m7ogr0u ku bination needed 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 Fig. Below) fpkn;mbo5 s7w3j)v k g7 lrf0i0or the reaction7swj kpv oi; bm3l )0nr5gfk07 $p + \pi^- \to n + \pi^0$.

Draw a Feynman diagram for the reacyc6 cl.5qloi4 tion $n + \nu_\mu \to p + \mu^-$.

  What is the total energy of a proton whose kinetic energy is 25 GeV? What is itwwxa1; gc*pwz 9dqkf(+ a;uezu8wg( -s wavelendeuc+qfw;9 azg ;k1(w8(*- uxzpaw wggth?
$\approx$    $ \ \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 injectedbi9ap*r6p qd9ic 26jp into the 1.0-km-radius Fermilab Tevatron with an energy of 150 GeV. If they are accelerated by 2.5 MV each revolution, how far pi*9j6 a p62qdb9rcpido they 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 whem)7/274 cqbo) rh0 ocrfgxzd /t ,lkazn an electron and a positron annihilate each other?o k7x)omaz)r, z /h ct7lfb0qcdr/24g $E_{\text{total}}$=    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 a,b7a3z dh;d8xi5ff lreactions are possible, and by what interaction could they occur? For those forbidden,h3a 7fblx,;i5df az8 d 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 intes)k yjyh2o vdr7tk too. 0434nraction could they occu k2 htdyy rt7ook3n40jvso). 4r? For those forbidden, 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 o 1s/hg;kwke66x zgu th3,a k9$\pi^+$ is $\pi^+ \to \mu^+ + \nu_\mu$. What would be the equivalent decay for a $\pi^-$? Check conservation rules.

  Symmetry breaking occurs in the electroweak theory at(z ;0v41arjrwh6 iwjq 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-valuec08w v7d onhx* for each of the reactions, Eq. 32-4, for producing a pion.*o8h vd cwnx07 $Q$ =   $MeV$ or $Q$ =    $MeV$

  Calculate the Q-value for the reac xj1-gvsx4g45 swi/fotion $\pi^- + p \to \Lambda^0 + K^0$ 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 areli u(py9fl6*g there in a water molecule?    fermions

  A proton and an antiproton pk; v8y69tyuj56ff,lkndaf, annihilate each other at rest and produce two pions, ;k 66 afjn fyfpdy u,vt5,kl89$\pi^-$ and $\pi^+$. What is the kinetic energy of each pion? $2m_pc^2$ =    MeV

  (a) Show that the so-called unifica;7kqq +ml a;sj/izuem / 7wdc9tion 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 Table 32-2 are in terms of proper time, measa9ri-jnrt 1q6ured in a reference frame where the particle is a 9aiqj r-1tn6rt 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 following react9h a5gzz3 d(hnions.
(a) $p + p \to p + n + \pi^+ + ?$
(b) $p + ? \to n + \mu^+ + \nu_\mu$

Use the quark model q 4jrwytq.p *4us .)cuyk*+ bgu h)nn(to describe the reaction $p + n \to \pi^+ + \pi^-$.

What fraction of the speedu-w7k +ml(ek69n8px4esh(ubl hy n r, of light $c$ is the speed of a 7.0-TeV proton?