12.6 Gamma Decay- Determine the ground and lowest excited states of the thirty-
ninth proton in^89 Y with the help of Fig. 11.18. Use this
information to explain the isomerism of^89 Y together with the
fact, noted in Sec. 6.9, that radiative transitions between states
with very different angular momenta are extremely improbable. - When an excited nucleus emits a gamma-ray photon, some of
the excitation energy goes into the kinetic energy of the recoil
of the nucleus. (a) Find the ratio between the recoil energy and
the photon energy when the nucleus of an atom of mass 200 u
emits a 2.0-MeV gamma ray. (b) The lifetime of an excited
nuclear state is typically about 10^14 s. Compare the corre-
sponding uncertainty in the energy of the excited state with the
recoil energy. (See Exercise 53 of Chap. 2 to learn how the
Mössbauer effect can minimize nuclear recoil.)
12.7 Cross Section- The cross sections for comparable neutron- and proton-induced
nuclear reactions vary with energy in approximately the manner
shown in Fig.12.32. Why does the neutron cross section
decrease with increasing energy whereas the proton cross
section increases? - A slab of absorber is exactly one mean free path thick for a
beam of certain incident particles. What percentage of the
particles will emerge from the slab? - The capture cross section of^59 Co for thermal neutrons is 37 b.
(a) What percentage of a beam of thermal neutrons will
penetrate a 1.0-mm sheet of^59 Co? The density of^59 Co is
8.9 103 kgm^3. (b) What is the mean free path of thermal
neutrons in^59 Co? - The cross section for the interaction of a neutrino with matter
is 10 ^47 m^2. Find the mean free path of neutrinos in solid
iron, whose density is 7.8 103 kgm^3 and whose average
atomic mass is 55.9 u. Express the answer in light-years, the
distance light travels in free space in a year.
39. The boron isotope^10 B captures neutrons in an (n, )—neutron
in, alpha particle out—reaction whose cross section for thermal
neutrons is 4.0 103 b. The density of^10 B is 2.2 103
kgm^3. What thickness of^10 B is needed to absorb 99 percent
of an incident beam of thermal neutrons?
40. There are approximately 6 1028 atoms /m^3 in solid
aluminum. A beam of 0.5-MeV neutrons is directed at an
aluminum foil 0.1 mm thick. If the capture cross section for
neutrons of this energy in aluminum is 2 10 ^31 m^2 , find the
fraction of incident neutrons that are captured.
41. Natural cobalt consists entirely of the isotope^59 Co whose
cross section for thermal neutron capture is 37 b. When^59 Co
absorbs a neutron, it becomes^60 Co, which is gamma-
radioactive with a half-life of 5.27 y. If a 10.0-g cobalt
sample is exposed to a thermal-neutron flux of 5.00 1017
neutronsm^2 s for 10.0 h, what is the activity of the sample
afterward?
42. Natural sodium consists entirely of the isotope^23 Na whose
cross section for thermal neutron capture is 0.53 b. When^23 Na
absorbs a neutron, it becomes^24 Na, which is beta-radioactive
with a half-life of 15.0 h. A sample of a material that contains
sodium is placed in a thermal neutron beam whose flux is
2.0 1018 neutronsm^2 s for 1.00 h. The activity of the sam-
ple is then 5.0 Ci. How much sodium was present in the
sample? (This is an example of neutron activation analysis,a
very sensitive technique.)
12.8 Nuclear Reactions- Complete these nuclear reactions:
(^63) Li?S (^74) Be (^10) n
(^3517) Cl?S (^3216) S (^42) He
(^94) Be (^42) HeS 342 He?
(^7935) Br (^21) HS? 210 n
- Find the minimum energy in the laboratory system that a neu-
tron must have in order to initiate the reaction
(^10) n (^168) O2.20 MeV→ (^136) C (^42) He
- Find the minimum energy in the laboratory system that a
proton must have in order to initiate the reaction
pd2.22 MeV→ppn - Find the minimum kinetic energy in the laboratory system a
proton must have to initiate the reaction^15 N (p,n)^15 O. - A 5-MeV alpha particle strikes a stationary^168 O target. Find the
speed of the center of mass of the system and the kinetic
energy of the particles relative to the center of mass. - A thermal neutron induces the reaction of Exercise 39. Find the
kinetic energy of the alpha particle. - An alpha particle collides elastically with a stationary nucleus
and continues on at an angle of 60with respect to its original
direction of motion. The nucleus recoils at an angle of 30with
respect to this direction. What is the mass number of the
nucleus?
472 Appendix to Chapter 12
Neutron captureEnergyCross sectionProton captureEnergyCross sectionFigure 12.32Cross sections for neutron and proton capture vary
differently with particle energy.bei48482_ch12.qxd 1/23/02 12:08 AM Page 472 RKAUL-9 RKAUL-9:Desktop Folder: