Nuclear Chemistry

Report
Chapter 24 Nuclear Chemistry
24.1 Nuclear Radiation
24.2 Radioactive Decay (includes decay
rates & radiochemical dating)
24.3 Nuclear Reactions (Transmutation
Part only)
24.4 Applications & Effects of Nuclear
Reactions (except for radiation dose and
intensity/distance)
Section 24.1 Nuclear Radiation
Under certain conditions, some nuclei can
emit alpha, beta, or gamma radiation.
• Summarize the developments that led to the discovery and
understanding of nuclear radiation, including the names of
the important scientists and the nature and significance of
their contributions.
• Distinguish between chemical and nuclear reactions.
• Identify alpha, beta, and gamma radiations in terms of
composition and key properties.
• Rank the penetrating power of the various types of radiation.
• Predict the effect of an electric field on the path of the
various types of radiation.
Section 24.1 Nuclear Radiation
Key Concepts
• Wilhelm Roentgen discovered X rays in 1895.
• Henri Becquerel, Marie Curie, and Pierre Curie pioneered
the fields of radioactivity and nuclear chemistry.
• Gamma radiation has the most and alpha particles the least
penetrating power of the 3 basic types of nuclear radiation.
Chemical vs Nuclear Reactions
Chemical
Nuclear
Bonds broken & formed Nuclei emit particles
and/or rays
Atoms remain
Atoms often changed
unchanged – may be into atoms of new
rearranged or ionized element
Involve only valence May involve protons,
electrons
neutrons, & electrons
Small energy changes Large energy changes
Chemical vs Nuclear Reactions
Chemical
Reaction rate influenced
by temperature,
pressure, concentration,
and catalysts
Nuclear
Rate not normally
affected by
temperature, pressure,
or catalysts
Classifying
Classify each of the following as a
chemical reaction, a nuclear reaction,
or neither:
?
• Thorium emits a beta particle
Nuclear
• Two atoms share electrons to form a
Chemical
bond
• A sample of pure sulfur releases heat as
Neither
it slowly cools
• A piece of iron rusts
Chemical
Discovery of Radioactivity
Wilhelm Roentgen (Germany),
1895: invisible rays emitted
when electrons bombarded
surface of certain materials
Rays caused photographic
plates to darken
Roentgen called these high
energy rays called X rays
Roentgen in 1901 became first
Nobel laureate in physics for
this discovery
Discovery of Radioactivity
Antoine-Henri Becquerel 1896 (France) experiment to determine if phosphorescent
minerals also gave off X-rays
Image of Becquerel's
photographic plate which
has been fogged by
exposure to radiation from
a uranium salt. The
shadow of a metal Maltese
Cross placed between the
plate and the uranium salt
is clearly visible.
http://en.wikipedia.org/wiki/Henri_Becquerel
Discovery of Radioactivity
Becquerel discovered that certain minerals
were constantly producing penetrating
energy rays he called uranic rays
• like X-rays, but not related to fluorescence
Determined that
• all minerals that produced these rays
contained uranium
• rays were produced even though mineral
was not exposed to outside energy
Energy apparently being produced from
nothing??
Discovery of Radioactivity
Henri Becquerel
uranium salt
K2UO2(SO4)2
Darkened photographic
plates– even when not
exposed to light –
Discovery of Radioactivity
Marie Curie (Polish born
French physicist/chemist)
~ 1896-1898
Named process by which
materials give off such
rays radioactivity
Emitted rays and particles
she named radiation
Developed device to
measure radioactivity
Detecting Radiation: Electroscope
When When
exposed
positively
to ionizing
charged,
radiation,
metal
radiation
knocks
foils in
electrons
electroscope
off airspread
molecules,
apartwhich
due tojump
onto foils andlike
discharge
charge repulsion
them, causing them to
drop down
Madam Curie
Used electroscope to detect uranic rays
in samples
Discovered new elements by detecting
their rays
• radium named for its green
phosphorescence
• polonium named for her homeland
Since these rays were no longer just a
property of uranium, she changed
name from uranic rays to radioactivity
Discovery of Radioactivity
Curies in 1898, by processing several
tons of uranium ore (pitchblende),
identified 2 new radioactive elements:
polonium, radium
Curies shared 1903 Nobel prize in
physics with Becquerel
Marie awarded 1911 Nobel prize in
chemistry for work with polonium &
radium
Died in 1934 from effects of radiation
Discovery of Radioactivity
Name, Date
Contribution
Wilhelm
Discovery of X-Rays
Roentgen, 1895
Henri Becquerel, Uranium salt darkens
1896
photographic plate
Marie Curie,
1896-1898
(up to 1934)
Pierre & Marie
Curie, 1898
Introduced terms radioactivity &
radiation; developed device to
measure radioactivity
Isolated polonium and radium
& continued study of radiation
Properties of Radioactivity
Can ionize matter (cause uncharged
matter to become charged)
• basis of Geiger Counter and
electroscope
Has high energy
Can penetrate matter
Causes phosphorescent materials to
glow
• basis of scintillation counter
3 Common Types of Radiation
Alpha particles
Beta particles
Gamma rays
(two more types described in next
section)
Alpha Radiation
Alpha particle
4 He+2
2
• 2 protons & 2 neutrons = nucleus of
helium-4 atom
• +2 charge
+
Beta Radiation
0 b
-1
Beta particles – fast moving
electrons
Originate from decay of a neutron
+
b
Beta Decay In Neutron
neutron
Particle Symbol
proton
Relative mass
Electron
e1/1840
Proton
p+
1.000
W– boson
Neutron
n0
1.001
Matter changed to energy plus other matter
neutrino
electron
Neutron (made of quarks - fundamental) does not
Example
of weak
force,
of which W– is a boson
“contain” an
electron
(a lepton)
Gamma Radiation
0 g
0
High energy radiation; massless
Except for very unusual cases, gamma
radiation always accompanies alpha
and beta decay – few “pure” gamma
emitters
Characteristics of Alpha, Beta,
and Gamma Radiation
Alpha, Beta, Gamma Properties
Particle
Energy
alpha
~5
MeV
beta
gamma
Penetrating Power
Blocked by paper
0.05 to Blocked by thin metal foil
1 MeV (aluminum foil)
~1
MeV
Blocked only by thick layers
of lead or concrete
Penetrating Ability of Radioactive Rays
a
g
b
0.01 mm
1 mm
100 mm
Thickness of Lead
Effect of Electric Field on Trajectory
of Subatomic Particles
Lead
Block
Hole
Positive plate
b 1charge
g 0 charge
Radioactive
Source
a 2+
charge
Negative plate
X-Rays
Not generated by nuclear processes
(get by bombarding materials with
electrons)
Like gamma rays – form of high energy
electromagnetic radiation (gamma has
higher energy)
Both X and gamma rays highly
penetrating & can be very damaging to
living tissue
Practice
Nuclear Radiation
Problems 1-5, page 864
Problems 34-41, page 894
Chapter 24 Nuclear Chemistry
24.1 Nuclear Radiation
24.2 Radioactive Decay (includes decay
rates & radiochemical dating)
24.3 Nuclear Reactions (Transmutation
Part only)
24.4 Applications & Effects of Nuclear
Reactions (except for radiation dose and
intensity/distance)
Section 24.2 Radioactive Decay
Unstable nuclei can break apart
spontaneously, changing the identity of
atoms.
• Explain why certain nuclei are radioactive while others are
stable.
• Predict the type of radiation an unstable nucleus will emit.
• Apply your knowledge of radioactive decay to write
balanced nuclear equations.
• Solve problems involving radioactive decay rates.
• Explain the basis for the technique of radiochemical dating,
especially carbon dating.
• Describe the decay processes of positron emission and
electron capture.
Section 24.2 Radioactive Decay
Key Concepts
• Radioisotopes emit radiation to attain more-stable atomic
configurations.
• Atomic number and mass number are conserved in nuclear
reactions.
• Radiochemical dating is a technique for determining the age
of an object by measuring the amount of certain
radioisotopes remaining in the object.
Section 24.2 Radioactive Decay
Key Concepts
• A half-life is the time required for half of the atoms in a
radioactive sample to decay. The number of nuclei N
remaining after a certain number of half-lives n or after
some time t can be calculated from:
Nuclear Reactions
Involve a change in atom’s nucleus
Radioactive materials spontaneously
emit radiation
• Called radioactive decay
• Do this because a radioactive nucleus is
unstable

Gain stability by losing energy
Pencil Analogy for Stability
Gravitational Potential Energy
Forces Between Nucleons
Green:
Strong
Force
(attractive)
Purple:
EM Force
(repulsive
for protons)
Nuclear Stability - Forces
Nucleons (protons, neutrons) held together
by strong force
Overcomes electrostatic repulsion by
protons
Neutrons don’t have repulsion
Stability tied to neutron/proton ratio (n/p)
High atomic number nuclei need relatively
more neutrons for stability
Range for stable nuclei: 1:1 light to 1.5:1
heavy (Pb, AN 82)
Neutron-toProton Ratio
Shaded region
corresponds to
“band” or “belt” of
stability
Nuclear Stability
Radioactive nuclei are found outside
band of stability – above/below/beyond
Undergo decay to gain stability
All elements with atomic number (AN) >
82 (lead) are radioactive
Isotopes of elements with AN ≤ 82 but
outside band of stability are radioactive
Nuclear Stability – Decay Series
Various decay types change n/p in
different ways
Unstable nuclei lose energy through
radioactive decay in order to form a
nucleus with a stable n/p ratio
Eventually, radioactive atoms undergo
enough decays to form stable atoms
• Lead-206 is final decay product of
Uranium-238 (14 steps)
Decay of
238U
to
206Pb
Practice
Nuclear Stability
Problems 12 - 14 page 874
Problems 42, 45 – 48, 50 page 894
Nuclear Equations
Atomic number (AN) and mass
numbers (MN) are shown
Atomic and mass numbers are
conserved
AN: 88 = 86 +2
MN: 226 = 222 + 4
5 Types of Radiation
Alpha
Beta
Positron Emission *
Electron Capture *
Gamma
* New in this section
Alpha Radiation
Alpha particle emission changes the
element
Leaves n/p about the same (for heavier
elements)
In example below, start with radium, end up
with radon
n/p: 138/88=1.57
136/86 =1.58
Beta Radiation
0 b
-1
Beta particles – fast moving electrons
Originate from decay of neutron
Beta emission changes element
Lowers n/p
In example below, start with carbon, end up
with nitrogen
n/p: 8/6=1.43
7/7 =1.00
Positron Emission (b+ Decay)
Positron Emission
+
(b
Decay)
Neutron-deficient isotopes can decay by
proton decay (emitting positrons –
antiparticle of electron)
+
anti-neutrino
+
+
+
+
+
+
+
+
+
Net effect: one
proton
replaced by
positron
• neutron
• anti-neutrino
• positron
Electron Capture
Like positron emission, also reduces
number of protons (increase n/p)
Nucleus draws in surrounding electron
(usually from lowest energy level)
Electron combines with proton to form
neutron with X-ray emission
1 p + 0 e  1 n + X-ray
1
-1
0
81 Rb
37
+ 0-1e  8136Kr + X-ray
Decay Processes that Increase n/p
Positron Emission
Electron Capture
+
b
Particle Changes
Beta Emission: neutron  proton
1
0
n p b
1
1
0
1
Positron Emission: proton  neutron
1
1p

1
0
0 n  1b
Electron Capture: proton  neutron
1
1p

0
-1e

1
0n
Decay Process Summary
Decay
alpha
beta
Positron
Emission
Electron
Capture
gamma
Particle
Mass #
Change
AN
Change
2He
-4
-2
-1b
0
+1
1b
0
-1
X-Ray
Photon
0
-1
0g
0
0
4
0
0
0
Nuclear Equations
Atomic number (AN) and mass
numbers (MN) are shown
Atomic and mass numbers are
conserved
AN: 88 = 86 +2
MN: 226 = 222 + 4
Nuclear Equations
60 Co
27
 6028Ni + ?
Conserve mass number:
60 = 60 + 0
Conserve atomic number:
27 = 28 + (-1)
Particle must be 0-1b
241 Am
95
 23793Np + ?
Conserve mass number: 241 = 237 + 4
Conserve atomic number: 95 = 93 +2
Particle must be 42He
Practice: Write Nuclear equation for
each of Following
Alpha emission from U-238
238
92
U He
4
2
234
90
Th
Beta emission from Ne-24
24
10
Ne b 
0
-1
24
11
Na
13
6
C
Positron emission from N-13
13
7
Electron capture by Be-7
7
4
N  b 
0
1
Be  e  Li
0
1
7
3
Practice
Writing & Balancing Nuclear Equations
Problems 6 - 8 page 869
Problems 51 - 54, page 894
Half Life
Time for ½ of radioisotope
in sample to undergo
nuclear decay
Half life remains constant
In 7 half lives, <1% of
original radioactivity
remains
½½½½½½½
=1/27 = 1/128 = 0.8%
Decay of Strontium-90
Half Life
General expression for remaining material
after an integer number (n) of half-lives
have passed (page 871, text)
Remaining (N) = Initial Amount (N0) (1/2)n
If value of half life = T & elapsed time = t
(both quantities in same units of time)
Remaining (N) = Initial Amount (N0) (1/2)t/T
Expression works for non-integer t/T
t/T = 1.5, (1/2)1.5 = 0.354
Has form of exponential decay function
Exponential Decay
If value of half life = T & elapsed time = t
(both quantities in same units of time)
N = N0 (1/2)t/T
Expression works for non-integer t/T
Define decay parameter
 = T  ln(0.5) ln(0.5) = 0.693
Then equivalent expression to above is
N= N0 e-t/
More typical form for expressing decay
Half Lives of Radon (Rn)
Same element; isotopes have different half lives
(more stable as n/p ratio becomes closer to ideal)
Isotope
Rn-217
Rn-218
Rn-219
Rn-220
Rn-212
Rn-211
Rn-222
Half Life
0.6 milliseconds
35.0 milliseconds
3.96 seconds
55.6 seconds
24.0 minutes
14.6 hours
3.82 days
Half Life Reflects Stability
Isotope
Ra-216
C-15
Ra-224
I-125
C-14
U-238
Te-128
Half life
<0.2 nsec (shortest,
spin dependent)
2.4 sec
3.6 days
60 days
5730 years
4.5x109 years
7.7x1024 years (longest)
Practice
Radioactive Decay
Problems 16 – 17*, page 874
Problems 55 – 58*, page 895
Problems 4 - 6, page 991
* Problems 17, 57 & 58 require knowing
that:
if c = ab then log(c) = b log(a)
Radiochemical Dating
Nuclear decay rates not affected by
temperature, pressure, concentration,
catalyst
Can take advantage of constancy of half-life
to date objects
Carbon dating commonly used to measure
age of objects that were once living - based
on radioactive carbon-14
Other nuclei also useful for specialized
dating applications
Isotopes Useful in Radioactive Dating
t1/2
Isotope
(years)
Useful Range
(years)
Applications
H-3
12.3
1 to 100
Aged wines
Pb-210
22
1 to 75
Skeletal remains
C-14
5730
500 to 50,000
Organic material
K-40
1.3x109
U-238
4.5x109
Re-187 4.3x1010
104 to oldest Earth Earth & moon’s
samples
crust
107 to oldest Earth
Earth’s crust
samples
4x107 to oldest
Meteorites
samples in universe
Radiocarbon Dating
% C-14 (compared to
living organism)
Object’s Age (in years)
100%
90%
80%
60%
50%
40%
25%
10%
5%
1%
0
870
1850
4220
5730
7580
11,500
19,000
24,800
38,100
14C
Dating Overview
C-14 Formation Process
Cosmic ray protons blast nuclei in upper
atmosphere, producing large variety of
particles (including neutrons)
Top of Atmosphere
Cosmic ray
proton collides
with nucleus in
atmosphere
Neutron
C-14 Formation Process
These neutrons in
turn bombard
nitrogen (major
constituent of
atmosphere)
Absorption of neutron
by N-14 causes it to
emit a proton,
forming radioactive
isotope C-14
Carbon-14 Formation Rate
Fairly constant over time
C-14 dating calibrated against tree rings so
formation rate variations and other factors
that affect C-14 to C-12 ratio (other than C14 decay) have, in principle, been corrected
for
14C
14C
combines
with oxygen to
become C-14
labeled carbon
dioxide
14C
becomes part
of natural carbon
cycle - becomes
incorporated into
organisms
Dating
Living organism
continues to take in
14C while
simultaneously 14C
decays
When it dies 14C
continues to decay
without being
replenished
14C
dating measures
time of death
14C
Dating
Radiocarbon Dating Summary
Based on radioactive carbon-14
C-14 formed in upper atmosphere from
nitrogen at ~ constant rate
 percent of C-14 in atmosphere ~ fixed
Living organism exchanges CO2 with
atmosphere and ingests other carbon
compounds (e.g. carbohydrates)
Living organism has fixed % of C-14 in all
carbon containing molecules present
Radiocarbon Dating Summary
Living organism has fixed % of C-14 in all
carbon containing molecules present
Upon death of organism, supply of new C14 stops
C-14 already present decays
14 C  14 N + 0 b
½ life = 5730 yrs
6
7
-1
Amounts of stable C-12 & C-13 remain
unchanged
Measuring C-14 / (C-12 + C-13) in sample
and comparing to atmosphere gives age
Practice
Radiochemical Dating
Problem 18, page 874
Chapter 24 Nuclear Chemistry
24.1 Nuclear Radiation
24.2 Radioactive Decay (includes decay
rates & radiochemical dating)
24.3 Nuclear Reactions (Transmutation
Part only)
24.4 Applications & Effects of Nuclear
Reactions (except for radiation dose and
intensity/distance)
Section 24.3 Nuclear Reactions
Fission, the splitting of nuclei, and fusion, the
combining of nuclei, release tremendous
amounts of energy.
• Describe the transmutation process and its role in the
development of new isotopes and elements.
==========================================
Section 24.3 Nuclear Reactions
Key Concepts
• Induced transmutation is the bombardment of nuclei with
particles in order to create new elements.
• These particles can be other nuclei, neutrons or protons.
==========================================
Transmutation
All natural radioactive processes except
gamma emission involve transmutation –
conversion of atom of one element to an
atom of another element
Above is natural or spontaneous
transmutation
Can have induced transmutation by
bombarding nuclei with particles
All transuranium elements created this way
Transmutation
Particles used in bombardment include:
Neutrons
Protons
Charged nuclei of other elements
Transmutation reactions also can produce
neutrons and protons as products (not seen
in natural radiation processes)
Transmutation
First induced transformation by E.
Rutherford, 1919, using alpha particles
+
+
Transmutation
What element is produced?
?
22 Ne + 244 Am  266
10
95
105Db
(Dubnium)
Transuranium Elements
All elements following uranium on
periodic table (AN>92)
All are synthetic elements – produced
in lab by induced transmutation
First discovered in 1940, neptunium
(Np) and plutonium (Pu) produced by
bombarding U-238 with neutrons
238 U
92
+ 10n  23992U  23993Np + 0-1b
239 Np  239 Pu + 0 b
93
94
-1
Transmutation
If particle used to bombard nucleus has +
charge (common), need high-velocity (high
energy) to overcome charge repulsion with
positively charged nucleus
High energy created in particle accelerators
Success in producing a somewhat stable
new nucleus depends on obtaining
favorable neutron to proton ratio
Practice
Induced Transmutation
Problems 19 - 21, page 876
Problems 59, 69 - 71, page 895
Chapter 24 Nuclear Chemistry
24.1 Nuclear Radiation
24.2 Radioactive Decay (includes
decay rates & radiochemical dating)
24.3 Nuclear Reactions
(Transmutation
Part only)
24.4 Applications & Effects of
Nuclear Reactions (except for
radiation dose and intensity/distance)
Section 24.4 Applications and Effects of Nuclear
Reactions
Nuclear reactions have many useful
applications, but they also have harmful
biological effects.
• Name and describe several methods used to detect and
measure radiation.
• Name and describe several non-medical applications of
radiation
• Describe and explain several ways that radiation is used to
diagnose and to treat disease.
• Describe some of the damaging effects of radiation on
biological systems and how it can be used as an advantage in
the treatment of disease.
Section 24.4 Applications and Effects of Nuclear
Reactions
Key Concepts
• Different types of counters are used to detect and measure
radiation.
• Radiotracers are used to diagnose disease and to analyze
chemical reactions.
Detecting Radiation
Effect of radiation on photographic film
similar to effect of light
Film used to provide quantitative measure
of radioactivity
Common implementation is film badge
Detecting Radiation
Geiger Counter
Ionizing radiation – energetic enough to
ionize matter with which it collides
Geiger counter responsive to ionizing
radiation
Detecting Radiation
Scintillation Counter
Detects bright flashes of light with
photodetector when ionizing radiation
excites electrons of certain types of atoms
Detecting Radiation
Luminous dials information I
Luminous dials information II
Scintillation counter uses phosphor-coated
surface to detect radiation
Scintillations = bright flashes of light
Number & brightness of scintillations can be
detected & recorded by a variety of sensors
sensitive to light
Nonmedical Uses of Isotopes
Smoke detectors
Am-241 produces a radiation to ionize air
Smoke blocks ionized air, breaks circuit
Insect control - sterilize males
Food preservation
Smoke Detector
http://www.howstuffworks.com/inside-smoke.htm
Ionization
Chamber
with
radioactive
Am-241
source
Electronic
Horn
Agricultural Application
Solution of phosphate, with radioactive P-32,
injected into root system of plant
P-32 behaves identically to P31 (common, non-radioactive
form of element) and is used by
plant in same way
Geiger counter detects
movement of P-32; information
used to understand detailed
mechanism of how plants
utilize P to grow and reproduce
Radiation - Medical Applications
Tracers
Imaging (use radiation to detect
features inside the body)
Therapy (radiation put into body to kill
targeted cells)
Medical Radiotracers
Radioactive isotopes of an element have
same chemical properties as nonradioactive isotopes
Certain organs absorb most or all of a
particular element
Isotopes also can be bound in chemical
structure that targets particular organs
Tracers used to track distribution &
breakdown of substance in body
Some Medical Radiotracers
Nuclide
Iodine-131
Iron-59
Molybdenum-99
Phosphorus-32
Strontium-87
Technetium-99
Half-life
8.1 days
45.1 days
67 hours
14.3 days
2.8 hours
6 hours
Organ/System
thyroid
red blood cells
metabolism
eyes, liver
bones
heart, bones, liver,
lungs
Radioactivity must be able to leave body
and be detected – gamma is preferred,
alpha totally useless
Bone Scans
Positron Emission Tomography
Cyclotron generated positron (01b) emitting
isotopes with short half lives: C-11 (~20 min), N13 (~10 min), O-15 (~2 min), and F-18 (~110 min)
18 F
9
 01b + 188O
0 e = 2 g
b
+
1
-1
0
(positron emission)
(matter/anti-matter annihilation)
Isotopes incorporated into compounds normally
used by body such as glucose, water or ammonia
Injected into body - trace where they are
distributed (radiotracers)
Positron Emission Tomography
FDG taken up by highglucose-using cells
such as brain, kidney,
and cancer cells
Oncology scans using
FDG make up over
90% of all PET scans in
current practice
Positron
+
(b )
Decay
Nucleus
Neutrons
18F-FDG
+
+
+
Protons
Electrons
Positron Annihilation
Annihilation of positron
(antimatter) when it
encounters an electron
(matter) gives
• 2 x g rays (180 degrees
apart)
• Line of response
Scanner: photon counter
• Counts gamma-ray
pairs vs. single gammas
• Time window ~ 1 ns
511 keV
e+
e511 keV
PET Imaging Overview
Synthesize
radiotracer
Inject radiotracer
Measure gammaray emissions
from isotope
(~20-60 min)
Reconstruct
images of
radiotracer
distribution
Positron Emission Tomography
Scintillator
(detects
pair of
light
bursts
from
passage
of
x g
photons)
Positron-electron annihilation to
produce opposite g photons
Coincidence
Processing Unit
Image Reconstruction
Radiotherapy
Cancer treatment - cancer cells more
sensitive to radiation than healthy cells –
can be destroyed by radiation treatment
Options include:
• place radioisotope directly at site of
cancer
• use radiation from outside body
• use radioisotopes that naturally
concentrate in one area of body
Gamma Knife System
One advanced application of g rays:
successful treatment of brain tumors
Delivers precise beams of radiation to
diseased brain tissue or tumor from large
number of directions - 201 beams of
radiation intersect on targeted area of
abnormal or cancerous tissue within brain
Very precise: damages and destroys
unhealthy tissue while sparing adjacent
normal, healthy brain tissue
Gamma Knife Treatment
201 small cobalt sources
(gamma) arrayed in hemisphere
within thickly shielded structure
Energy focused into
overlapping beams by
collimators
Beams focused on target
through metal helmet, in which
patient’s head is placed by
using fixation of head frame
attached to head
Gamma radiation at focal point
of collimators extremely intense
Gamma Knife Treatment
Gamma Ray Treatment
Practice
Radiation detection and uses
Problems 28, 29, 31, page 890
Problems 73, 75, page 895

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