Exercises 505
energy of the ^0. How long does the uncertainty principle
allow the virtual nucleon-antinucleon pair to exist? Is this long
enough for the process to be observed?- A neutral pion whose kinetic energy is equal to its rest energy
decays in flight. Find the angle between the two gamma-ray
photons that are produced if their energies are the same.
13.4 Elementary Particle Quantum Numbers- Why does a free neutron not decay into an electron and a
positron? Into a proton-antiproton pair? - Which of the following reactions can occur? State the conser-
vation principles violated by the others.
(a)
0 →
(b)p→n^0
(c)p→p^0
(d)n→p - Which of the following reactions can occur? State the conserva-
tion principles violated by the others.
(a)pp→np
(b)pp→p
^0
(c)ee→
(d)pp→pK^0
^0 - According to the theory of the continuous creation of matter
(which has turned out to be inconsistent with astronomical
observations), the evolution of the universe can be traced
to the spontaneous appearance of neutrons and antineutrons in
free space. Which conservation law(s) would this process
violate? - The products of a collision between a fast proton and a neutron
are a neutron, a ^0 particle, and another particle. What is the
other particle? - A muon collides with a proton, and a neutron plus another
particle are created. What is the other particle? - A positive pion collides with a proton and two protons plus an-
other particle are created. What is the other particle? - A negative kaon collides with a proton and a positive kaon and
another particle are created. What is the other particle? - The hypercharge Yof a particle is defined as the sum of its
strangeness and baryon numbers: Y SB. Verify from
Table 13.3 that the hypercharge Yof each hadron group is
equal to twice the average charge (in units of e) of the members
of the group.
13.5 Quarks- Why must the quarks in a hadron have different colors? Would
they have to have different colors if their spins were 0 or 1
rather than ^12 ? - The particle consists of a uquark, a dquark, and an squark.
What is its charge? - A member of the group of particles consists of two uquarks
and an squark. What is its charge? - Which quarks make up the negative pion? The hyperon?
- What particle in Table 13.3 corresponds to the quark composi-
tions uus? - One kind of Dmeson consists of a cand a uquark. What is its
spin? Its charge? Its baryon number? Its strangeness? Its charm?
13.6 Fundamental Interactions- All resonance particles have very short lifetimes. Why does this
suggest they must be hadrons? - The gravitational interaction is the weakest of all by far, yet it
alone governs the motions of the planets around the sun and the
motions of the stars of a galaxy around the galactic center. Why? - The initial reaction of the proton-proton cycle that provides
most of the sun’s energy is
(^11) H (^11) H→ (^21) He
This reacton occurs relatively infrequently in the sun for two
reasons, one of which is the coulomb “barrier” the protons
must overcome if they are to get close enough together to react.
What do you think the other reason is?
- The “carriers” of the weak interaction are the W, whose mass
is 82 GeV/c^2 , and the Z^0 , whose mass is 93 GeV/c^2. Use the
method of Sec. 11.7 to find an approximate figure for the range
of the weak interaction.
13.9 The Future- Figure 1.8 shows the expanding-balloon analogy of the expand-
ing universe. As the balloon expands, the angular separations of
the spots (as measured from the center of the balloon) remain
constant. (a) If sis the distance between any two spots, show
that the recession speed dsdtis proportional to s, which is the
equivalent of Hubble’s law in this situation. (b) Find an expres-
sion for Hubble’s parameter Hfor the expanding balloon. Is H
necessarily constant?
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