Give a reaction between two nucleondxtobx0s+* +ds, similar to Eq. 32-4, that could produce a +bx0 *s+odxtd $\pi^0$.

  If a proton is moving at very high speed,ko0 tt su k;qp73ijp:3 so that its kinetic energy is much greater than its rest energuj37pktpi: ;k3s0 qt oy ($mc^2$), can it then decay via $p \to n + \pi^+$?  ----待选择----yesno 

What would an "antiatom," made up of t* c3li08lo 2zp ..p jqi4ftszkhe antiparticles to the constituents of norm2*zt.i ci3js.48 fozqppl 0klal atoms, consist of? What might happen if antimatter, made of such antiatoms, came in contact with our normal world of matter?

What particle in a decay signals the electromagnetiory a u-jw- +3(xp-ckd5hpa+nc interaction?

Does the presence of a neutrino among the decay products of a particle zx- 5 u*ynd*ay7m+alfehc ,9jlen.g -necessarily mean that the decay occurs via the weak intere yad*9- + .hfx-5l7ula,ynnmzg *ecjaction? Do all decays via the weak interaction produce a neutrino? Explain.

Why is it that a neutf4k ,e(d (tv3gwuqfg ;ron decays via the weak interaction even though the neutron and one of its decay products (protodetg4k fuwqgv;f(( 3,n) are strongly interacting?

Which of the four interactions (strong,uuwi*x* :k3s9d 2ksxr/ g7zgz electromagnetic, weak, gravitational) does an electron take part in? A neutrino? gs 2 sudxk:w*i7 xr 9gzu*/zk3A proton?

Check that charge and baryon numw. ei6migtuh6bv .59z9sup7 pber are conserved in each of the decays in Tablems.bp wut5hgu 9 976zv i6e.pi 32-2.

Which of the particle decays in Table 32-2 occur v k1fe- a:p qpty+.plj3ia the electromagnetic interac-fppkptyqe1 a .l+:3j tion?

Which of the particlkgzr qk/s+r s,5bw)h ;e decays in Table 32-2 occur by the weak interaction?

By what interaction, and w4a (2 k7r+u8ki0yh ethso4jwm hy, 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 Tableja.4h cu,alds: e(t 1h tqmn97 32-4 occur via the electromagnetic interactehjh sqnt9m (4aca7u1t,l .d :ion?

Which of the particle decays ieu8 sinkx2 fz4f1z;yrwp: ac hj,w)rih1(6a -n Table 32-4 occur 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,ly j6t5)ys1 kzulayh z;8trw3f4+ x e6 had no color charge or electrical charge, and did not feel the weak f4yr)fz538 1 6 yt yk+;wl6txeuaszjhlorce. Could you say that this particle even exists?

  Is it possible for a particle to be botr:zjk ds1o 7jlx.i+, bh
(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 chromodynamice s8hjulja5 9jat qt e92,y d8r0)gj5es, would it be possible to find particles made up a08r2 )5q se9d5ttjyh9e jal jej,gu8 of two quarks and no antiquarks? What about two quarks and two antiquarks?

Why do neutrons decay when they are free but not when the -yj*f-nh2 golblk q+4zo.ao xk; 7*spy are inside the nucleus?oa-kxj pq*by7 k;* z2hso n4lf+.-gl o

  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 pr1hq 1kq3sk ;,lw q1hozoton whose kinetic energy is 6.35 GeV?    GeV

  Calculate the wavelength of 35-GeV electrons. d-8g7 , exsr,gczsf8xE =    $\times 10^{-17}\ \text{m}$

  What strength of magnetic field is used in a cyclotron in wiu4bwn6y,f(i c l9wo/hich protons make $2.8 \times 10^7$ revolutions per second? $f$ =    T

  What is the time for one )bn3 dacprah31j-- u -a,m:ydzi-y excomplete revolution for a very high-energy proton in the 1xa-m3pa)dczn-ir y- :1 dhb-a,ye3 uj.0-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 Exampletw x(bfjmm5 pm+y4/-xr1r l9n 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 picking out details of the nucleus: 30-Metkdqh4.1cg1 zfmafv u)2gy 1:wdif*/lr s 5n/V alpha particles or 30-MeV pgmy5: .k1 ws1cd rh ff/)ndt42augql* i1v/zfrotons? Compare each 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 cyclotron imd3b id0rqh ;-s 55 kV. How many revolutions do protons make to rerm3b;d-h i 0dqach a kinetic energy of 25 MeV? $\approx $    $\ \text{revolutions}$

  What is the wavelength 9*nljc d:fy5g ($\lambda$, maximum resolvable distance) of 7.0-TeV protons? E =    $\times 10^{-19}\ \text{m}$

  A cyclotron with a radius of 1.0 m iyob ;8n;4pyp js9p ib+s 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 tq hqlfg1(w0;zn 7xz z/he Large Hadron Collider (LHC) calls for proq0z(znwlh1f7z g /q x;ton beams of energy 7.0 TeV. What magnetic field will be required? B =    T

  The 1.0-km radius Fermilab Tevatron takes about 20 seconds to bri d;: feabxtx0)ng 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 a0afx: d)teb ;xssume that the speed of the protons is essentially $c$ the whole time.) Energy/revolution =    MeV/rev

Show that the energy of a)x lyl*1y s-ju 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 p 3s7iq1f6aawc- h;dfneeded at the 1.0-km-radius Fermilab synchrotron for 13;-is p ca1qwhaf7d 6f.0-TeV protons? B =    T

  How much energy is released in the decadv v y;)-nq0udh +sb21u (/d tlaz2rgmy $\pi^+ \to \mu^+ + \nu_\mu$? See Table 32–2.    MeV

  About how much energy m ks0ivh4mfb46k 0i2 pis released when a $\Sigma^+$ decays to $n + \pi^+$? (See Table 32–2.)    MeV

  How much energy is required to producy m)5rppliycdtt 9 /;,e a neutron-antineutron pair?    MeV

  Estimate the range of the mp6 qf9) d -0hjikg:yustrong force if the mediating particle were the kaon instead of thekfjh90 gy6up q)im d-: pion. $mc^2$ $\approx$    $ \times 10^{-16}\ \text{m}$

  Two protons are heading toward each other with equal speeds. What minimum ;lgydpp*d:sw 0 9yvaecje 0d 5wl7g/5kinetic energy must each have wp*sypjea: lc yd 0 g;wl7d905e/dg 5vif a $\pi^0$ meson is to be created in the process? (See Table 32-2.)    MeV

  What minimum kinetic energy must twom ouff9qse6)uh)/au) bkpy4- neutrons each have if they are traveling at the same speed towar eq/4ub-a)m uuo) kp)fs96fh yd each 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. 32-3, givenbvc 4 -hba5mn6 the masses of the W and 46-vbch m5 bnaZ particles as about 80 to $90\ \text{GeV}/c^2$. $mc^2$$\approx $    $\times 10^{-18}\ \text{m}$

  What are the wavelengths 5ap5jw ngk0k w ):l;0nya pok,of the two photons produced when a proton and antiprotoaj) py :5a ,5lnnw00w;kpokkgn 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 momentum and enef*1h zx4hw -yc93eamtrgy, that it is impossible for an isolated electron to radiate only a single photon. (b) With this result in mind, h3hxfa9w 4t1zec-*ym how can you defend the photon exchange diagram in (Fig. Below)?

  What would be the wavelengths of the two photons produced when an electron . mz *(gvmc6c r/b.5u-jl aqsf h8zix4and a positroxq.-rla 6bs g c*j8h uv4zi5fz .mcm(/n, each with 420 keV of kinetic 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 reactions and decays ba n1di;3d n+xare possible? For those forbidden, explain what laws are violab+i31a;xnn d dted.
(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 tjrd /q( oir3z.he 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 kinec78i ).zoi/x + lyumdc:euz a(tic energy of the electron 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 th,g mvv (*,fbwben the lifetime of the $\Delta$ resonance using the uncertainty principle.
$\Delta E$ =    MeV
$\Delta t$=    $ \times 10^{-24}\ \text{s}$

  The measured width of th.rgho km;fr()e $\Upsilon$ meson is 88 keV. Estimate its lifetime. $\Delta E$ =    $ \times 10^{-21}\ \text{s}$

  The measured width of the8bokz/ dxc s478.6d dkgw-t ao $J/\psi$ (3685) meson is 277 keV. Estimate its lifetime. $\Delta E$ =    $ \times 10^{-21}\ \text{s}$

  What is the energy width (or uncertak6+l-bkgvgc;92k-c d7o b85t aqylbmmvhv 8,inty) 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 decayshg)pf0dtfo;5bax0 l3 are possible? For those that are forbidden, explain whic xfplg 0dho )a;30b5tfh laws are 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 combinations that can 5 z s, kqdob*6,swmrt4hulm7x:/qai 1form (a) a neutron, (b) an antineutron, (ms1dq,ia5 w *h7 4r q6t/s: mzxku,bloc) a $\pi^+$, (d) a $K^-$?

What particles do they3q z ap)-8oer following 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 to produce abtrj2(z6*rq miq7ut 6 $D^+$ 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 (a0 8qs;hbdbe .bs in Fig. Below) for the reactionb8eqh0d b.;sb $p + \pi^- \to n + \pi^0$.

Draw a Feynman diagram for the reac8 kbra+y5 6wvzh n,*cxtion $n + \nu_\mu \to p + \mu^-$.

  What is the total energy of a proton whose kinetic energy i(fmd+ sxx)yp 5yqqn 68eg5jx( s 25 GeV? What is its wavelee nm+q5xq )56(xjy(g sy pd8xfngth?
$\approx$    $ \ \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 Fermilabl0/og- whll o( Tevatron with an energy of 150 GeV. If they are accelerated by 2.5 MV each revolutoh(/ oll0 lgw-ion, how far do 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 when an electron 8 b0;y8qyim5- .pug6uxrxrvj and a positron annihilate each othqxu ryp8gixym.u8;v05 rb -j 6er? $E_{\text{total}}$=    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 inte j/ifp i2uq.*nraction could they occur? For thpn2 uj fiq/.*iose 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 posza1dqq(ok.wll.b /( c sible, and by what interaction could they occur? For those forbz k(la.loq(d/wq. 1b cidden, 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 lzjlms72nq6(qz )ad hj2 v;1h$\pi^+$ 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 xdsh402 3)pczys3 yvqat 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. 3c 3yhtb2nyx .6z( z)zt2-4, for producing a pion.yn.2z3zc yxt6t zh) b( $Q$ =   $MeV$ or $Q$ =    $MeV$

  Calculate the Q-value forgp c+cfmdw 6 nrsvgj: +*p8n5. 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 fermions are there in a water moleculkjc1a59f8(eccd:r v re?    fermions

  A proton and an antiproton annihilate each other de)5o q( sd.lu;me*mqat rest and produce two pions, qmm. lo eudd*);sq5e($\pi^-$ and $\pi^+$. What is the kinetic energy of each pion? $2m_pc^2$ =    MeV

  (a) Show that the so-calldss / m+5vnaw9ed unification 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, measured /ibiv1:1u.s n4s5ql9pb agyd 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 as1vs uq:g/4 15 nsb dili9pyb.a 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 reactions. 84iub hzopt4)
(a) $p + p \to p + n + \pi^+ + ?$
(b) $p + ? \to n + \mu^+ + \nu_\mu$

Use the quark model tzrohqivm c-g-ti7(pr5c8 c 87o describe the reaction $p + n \to \pi^+ + \pi^-$.

What fraction of the speed of light yuhv 09( l azu*7eyn-f$c$ is the speed of a 7.0-TeV proton?