Binary
Nuclear
Reactions
PROBLEMS
1. A 2MeV neutron is scattered elastically by 12Cthrough an angle of 45 degrees. What is the scattered neutron's energy?
Solution:
From Eq. (6.25)
E' = ~
(A + 1)2
cfw_JEcos(s + VE(A2 1 + COS2 2 (s)
2. The first nuclear
613
18. Estimate the available DD fusion energy in an 8 ounceglassof water. For how long could this energy provide the energy needsof a house with an average power consumption of 10 kW? Solution: (a) First find the number of deuterium atoms in the glass
ECE426
Spring 2008
APPLICATION OF SIGNAL PROCESSING
COURSE ANNOUNCEMENTS Course and Title: ECE426, Applications of Signal Processing Instructor: TA: Webpage: B. Hutchins, Rm 218 Phillips, 2554075, hutchins@ece.cornell.edu TBA http:/blackboard.cornell.edu
1012
Principles of Nuclear Reactors
Chap. 10
What is the asymptotic period resulting from a reactivity insertion of (a) 0.08$ and (b) 0.08$ ?
Solution:
By definition p($) = (keff l)/(flkeff). p($) = :1:0.08$ we find Solving this for keff and substituti
72
(a) Water:
Radiation Interactions
Chap. 7
(JLjp) = 0.07066 cm2jg and p = 1.00 g cm3. Thus,
(b) Iron: (Jl,/p)=0.05951 cm2/g and p=7.874gcm3.
Thus,
(c) Lead: (JLjp) = 0.06803cm2jg and p = 11.35g cm3. Thus,
Xl/2 = In 2/ (~ ) p = 0.898cm.
Based on the
65 6. Consider the following reactions caused by tritons, nuclei of 3H, interacting with 160 to produce the compound nucleus 19F 18F+ 170 + 180 + 16N + n d p 3He
3H + 160 + 19F*
+
For each of these reactions calculate (a) the Qvalue, (b) the kinematic
33 Using the liquid drop model, tabulate the nuclear binding energy and the various contributions to the binding energy for the nuclei 40Caand 2o8Pb. Solution: A BASIC program is used to evaluate the terms in text Eq. (3.16). A program listing and result
1013
19. A reactivity insertion into an initially critical reactor operating at steady state causesthe power to increase from 100 W to 10 kW in 6 minutes. What was the value of the reactivity insertion in $?
Solution:
From Eq. (10.16), which can be writt
18
Radiation Interactions
Chap. 7
(a) 27keV neutrons: The total interaction coefficient or macroscopiccross section is Et(27 keY) = NFea[e(27 keY) = 0.03397cml. Then from Eq. (P7.3), the fraction of 27keVneutrons transmitted through the slab is Fracti
76
Radiation Interactions
Chap. 7
A small homogeneous ample of mass m (g) with atomic mass A is irradiated s uniformly by a constant flux density </Jcm2 S1). If the total atomic cross ( section for the sample material with the irradiating particles is
514
Radioactivity
Chap. 5
20. Charcoal found in a deep layer of sedimentin a caveis found to have an atomic 14Cj12Cratio only 30% that of a charcoal sample from a higher level with a known age of 1850y. What is the age of the deeperlayer? Solution: Let R
79
The proton energy with the same speed as a 10MeV alpha particle is, thus, Ep = Ea/4 = 2.5 MeV. Then from rule 3 on page 196 for particles of the same speed in the same medium, we have
Ra(lO MeV) Rp(2.5 MeV)
ma z~ 14 ~  ~! 2
mp ZQ
= 1,
Thus the ran
66
Binary Nuclear Reactions
Chap. 6
The neutron threshold energy for thjs reaction is found from Eq. (6.15)
8. The isotope 18Fis a radionuclide used in medical diagnosesof tumors and, although usually produced by the 180(p,n)18F reaction, it can also be
73
4. A material is found to have a tenththickness of 2.3 cm for 1.25MeV gamma rays. (a) What is the linear attenuation coefficient for this material? (b) What is the halfthickness? (c) What is the meanfreepath length for 1.25MeV photons in this ma
Nuclear Power
Chap. 11
8. Although the steam cycle is simpler in a BWR, explain why the capital costs of BWR and PWR plants are very competitive. Solution: The simplicity of a single steam/water cycle in a BWR comparedto the double primary/secondary cycle
106
Principles of Nuclear Reactors
Chap. 10
8. Consider a homogeneous, are, spherical, sourcefree,critical, uraniumfueled b reactor operating at a power Po Explain how and why the power increases, decreases, r remains unchangedas a result of eachof th
74
Radiation Interactions
Chap.7
6. Calculate the linear interaction coefficients in pure air at 20C and 1 atm pressure for a IMeV photon and a thermal neutron (2200 m SI). Assume that air has the composition 75.30itrogen, 23.2%oxygen, and 1.4% argon b
PROBLEMS
1. In a BWR or PWR, steam is generated with a temperature of about 290 c. If river water used to receive waste heat has a temperature of 20 c, what is the maximum possible (ideal) conversionefficiency of the reactor's thermal energy into electric
92
Radiation Doses and Hazards
Chap. 9
2. A 137Cs ource has an activity of 700jLCi. A gamma photon from 137mBa ith s w energy 0.662 MeV is emitted with a frequencyof 0.845 per decayof 137CS. t A a distance of 2 meters from the source, what is (a) the exp
1011
From the previous problem, koo = 1.1647and f = 0.5632. From Table 10.2, we find rH20 = 27 cm2 and Lk2o = 8.1 cm2. The above equation thus reducesto
M235
"j;[ff;i5 NH2OAH2O'

N235A235
= 6,000g = 6.00 kg.
15. A control rod is dropped into a critical,
43
A nuclear scientist attempts to perform experiments on the stable nuclide ~Fe. Determine the energy (in Me V) the scientist will need to 1. remove a single neutron. 2. remove a single proton. 3. completely dismantle the nucleus into its individual nuc
26
Modern Physics Concepts
Chap. 2
A 1 MeV photon is Compton scattered at an angle of 55 degrees. Calculate (a) the energy of the scattered photon, (b) the change in wavelength, and (c) the recoil energy of the electron. Solution:
(a) FromEq. (2.26)
1 .1
14
Fundamental
Concepts
Chap. 1
12. Dry air at normal temperature and pressurehas a mass density of 0.0012 gj cm3 with a mass fraction of oxygenof 0.23. What is the atom density (atomjcm3) of 180? Solution: From Eq. (1.5), the atom density of oxygen is
N
13
8. Show by argument that the reciprocal of Avogadro's constant is the gram equivalent of 1 atomic mass unit.
Solution:
By definition one gram atomic weight of 12C is 12 gfmol. Thus the mass of one atom of 12Cis
M r~C) = Na12g/mol = "12 g/atom. atoms/m
PROBLEMS
An acceleratorincreasesthe total energy of electronsuniformly to 10 GeV over a 3000m path. That meansthat at 30 m, 300m, and 3000m, the kinetic energy is 108,109, and 1010 V, respectively. At eachof these distances,compute the e velocity, relativ
63
4. For each of the following possible reactions, all of which create the compound nucleus 7Li, '7Li + n 6Li + 'Y t.) In + 6Li + 7Li* +
6He+ p 5He+ d
3H+a
calculate (a) the Qvalue, (b) the kinematic threshold energy, and (c) the minimum kinetic en
57 10. How many atoms are there in a 1.20 MBq sourceof (a) 24Naand (b) 238U?
Solution:
BecauseA =>'N we have N(atoms) = A(Bq)j>.(sl). (a) For 24Na we find from Table A.4 that Tl/2 = 14.96 h = 5.385 X 104s. Then>. = In2/TI/2 = 1.287x 105 s1 Thus the nu
56
Radioactivity
Chap. 5
(b) Tl/2 = In 2/>" = 1.18 X 106 S = 326.5 h = 13.6 d = 1.94 wk. (c) t = 1/>" = 1.69 X 106 S = 471 h = 19.6 d = 2.80 wk.
8. The isotope 1321 ecays by /3 emissionto 132Xe ith a halflife of 2.3 h. (a) d w How long will it take for
(b) Similarly, from Table 9.13 (Case 2) we seethe number of cancer deaths from natural causesis 1 250 X 106 people 6 Nnat = (20,560+ 17,520) 5 1 = 47.6 x 10 deaths. 2 10 peope For a static population with an averagelife span of 73.1 years, the annual nat
(d) From Table 9.10, the radiation induced risk to the first generation, per rad gonad dose to the parents is seento be: risk(BEIR)= (6 to 43)/106 and risk(UNSCEAR)= (18)/106. Thus for a parental gonad dose of 0.95 rem (or 0.95 rad since the exposurewas f