# Nuclear Physics Slides - Little Shop of Physics

```Nuclear Physics
• The forces holding
together the nucleus
are large. And so are the
energies involved.
natural process. Certain
nuclei fall apart and emit
dangerous but useful.
They can cause illness, but
they can cure or diagnose as
well.
• Lecture:
Monday, April 6: ! ! Nuclear Physics Basics
Wednesday, April 8: ! Nuclear Physics Applications
• Friday, April 10: ! ! Duck and Cover: Tales of the Atomic Age
• Monday, April 13: !! Applications to Bodies and the Biosphere
• Wednesday, April 15: !Exam #2 Review
• Friday, April 17: ! ! Exam #2
Exam:
• Exam #2 is on Friday, April 17.
• Practice Exam posted Monday, April 13.
• Practice in recitation on Tuesday, April 14.
• Practice in lecture on Wednesday, April 15.
•
•
•
This isn’t an x ray; it’s a bone scan. Radioactive
nuclei were used to show the presence of arthritis in
Remember: Particles have a wave nature.
Only certain wavelengths
meet the boundary
conditions, so only
certain energies are
allowed.
The Nucleus
Confining neutrons
and protons in the
“box” of the
nucleus means that
their allowed
energies are
enormous.
Changing Scale
The diameter of a typical atomic nucleus is about 10 fm.
(1 fm is 1x10-15 m.)
What are the “particle in a box” energy states for a
proton in a 1D box of this size?
2
1 ⎡ hn ⎤
h2 2
En =
=
n
8mL2
2m ⎢⎣ 2L ⎥⎦
n = 1, 2, 3, 4...
The Nucleus
Number of protons
determines the
element, number of
neutrons the
isotope.
Most elements have more
than one stable isotope.
We will never use
this number.
Never.
Notation
Mass number:
A=Z+N
238
92
U
Atomic number: Z
Z = # of protons
N = # of neutrons
112
50
Sn
114
50
Sn
115
50
Sn
116
50
Sn
117
50
Sn
118
50
Sn
119
50
Sn
120
50
Sn
122
50
Sn
124
50
Sn
Mass of an atom:
e.g. chlorine
1) Never acceptable:
Using atomic weights from
the periodic table.
2) Quick and dirty:
Use mass number:
35Cl: mass = 35 u
3) For energy calcs:
Use data from Appendix D:
35Cl: mass = 34.968853 u
11
3
Li
11
4
Be
Oxygen 18 variation from average (%)
Notation
How many neutrons are in each of the
following nuclei?
-3.0
11
5
B
11
6
C
A. 8
B. 7
C. 6
D. 5
Isotopes
More
18
8
O
Warmer
Less
18
8
O
Cooler
-3.5
-4.0
-4.5
-5.0
100000
50000
0
Years before present
Boron, atomic number Z=5, has two stable isotopes, with
atomic mass numbers A=10 and A=11. Boron’s chemical
atomic mass is 10.81. What are the approximate fractions
of the two stable boron isotopes found in nature?
! A.!! 92% 11B,! 8% 10B
! B.!! 80% 11B, ! 20% 10B
! C.!! 50% 11B, ! 50% 10B
! D.!! 20% 11B, ! 80% 10B
! E.! ! 8% 11B, !! 92% 10B
Holding it All Together
Helium nucleus
neutron
Strong force
proton
An especially
stable combo
n
n
n
p
p
p
Coulomb force
Stability
Too big; Coulomb
repulsion too
strongZ 5 83
Bismuth,
Just
right.
160
140
Stable isotope
Unstable isotope
Neutron number N
120
Too many
neutrons
100
80
N 5 Z line
60
16
O
40
Line of stability
12
C
Too few
neutrons
4
He
20
0
0
10
20
30
40
50
60
70
80
Proton number Z
Energy Levels in the Nucleus
Energy
(MeV)
0
Neutrons
n53
n52
n51
Protons
2
4
2
4
2
2
n53
n52
n51
250
For light nuclei, neutron and proton
energy levels are about the same.
90
100
Beta Decay
11
4
U (MeV)
Energy
(Mev)
Be
0
2
4
2
4
2
2
250
Neutrons
Protons
Beta Decay
11
5
U (MeV)
Energy
(Mev)
B
0
2
4
2
4
2
2
250
Neutrons
Protons
11
4
Be ⇒ 115 B + −10 e-
Alpha Decay
Parent nucleus
Nucleus too darn big.
And it does.
Wants to break apart.
Before:
A
XZ
After:
A24
YZ22
Daughter nucleus
238
92
U⇒
234
90
Alpha particle
Th + 24α
When atoms decay, they don’t disappear.
238
92
U⇒
234
90
Th + 24α
Gamma Decay
Excited
level
Gamma-ray
photon
Lower
level
99
Mo
Beta decay
e2
99
Tc *
Excited
state
Ground
state
Gamma decay
g
99
Tc
Determining the Daughter Nucleus
!
90Sr
→ ?X + e-
A.
B.
C.
D.
90Y
89Y
90Rb
89Rb
!
222Rn
A.
B.
C.
D.
→ ?X + α
220Po
218Po
220Ra
218Ra
Determining the Decay Mode
What is the decay mode of the following decays?
→ 137Ba + ?
A.!! alpha decay
B.!! beta-minus decay
C.!! beta-plus decay
D.!! gamma decay
137Cs
!
!
!
!
→ 226Ra + ?
A.!alpha decay
B.!beta-minus decay
C.!beta-plus decay
D.!gamma decay
230Th
!
!
!
!
12B
•
•
is an unstable isotope of boron (Z=5).
Sketch the energy level structure for the neutrons and
the protons in this nucleus.
What decay mode would you expect for this nucleus?
Energy
(MeV)
0
Neutrons
n53
n52
n51
Protons
2
4
2
4
2
2
n53
n52
n51
250
alpha least penetrating
gamma most penetrating
Operation of
Geiger counter
cancer treatment
is Part of
You Light
Up My
Half Life
⎡1⎤
N = N0 ⎢ ⎥
⎣2⎦
t t1/2
Chernobyl Cheese
The Chernobyl nuclear reactor accident in the Soviet Union
in 1986 released a large plume of radioactive isotopes into the
atmosphere. Of particular health concern was the short-lived
(half life: 8.0 days) isotope 131I, which, when ingested, is
concentrated in and damages the thyroid gland. This isotope
was deposited on plants that were eaten by cows, which then
gave milk with dangerous levels of 131I. This milk couldn’t be
used for drinking, but it could be used to make cheese, which
can be stored until radiation levels have decreased. How long
would a sample of cheese need to be stored until the number
of radioactive atoms decreased to 3% of the initial value?
⎡1⎤
N = N0 ⎢ ⎥
⎣2⎦
t t1/2
Activity is the rate of decay.
Decay:
⎡1⎤
N = N0 ⎢ ⎥
⎣2⎦
t t1/2
Activity:
0.693
t1/2
tt
⎡1⎤ 12
R = R0 ⎢ ⎥
⎣2⎦
R = rN =
Short half life means
high activity.
activity = decay rate = R =
238Pu, half
0.693N
t1/2
life 88 years
ray photon with energy 140 keV. What is the mass loss of the
nucleus,
u, upon decay,
emission of
thisactivity
gamma ray?decreases.
As
the in
atoms
the
27. || Cobalt has one stable isotope, 59Co. What are the likely decay
modes and daughter nuclei for (a) 56Co and (b) 62Co?
Decay:
28. || Manganese has one stable isotope, 55Mn. What are the likely
t t1/2
decay modes
nuclei for (a) 51 Mn and (b) 59Mn?
⎡ 1and
⎤ daughter
N = N0 ⎢ ⎥
⎣2⎦
Section 30.5 Nuclear Decay and Half-Lives
Activity:
29. | The
radioactive hydrogen isotope 3H is called tritium. It decays
by beta-minus0.693
decay with a half-life of 12.3 years.
= rNis=the daughter nucleus of tritium?
a. RWhat
t1/2
b. A watch uses the decay of tritium to energize its glowing
t t1 2
⎡ 1 ⎤ fraction
dial. What
of the tritium remains 20 years after the
R = R0 ⎢ ⎥
watch was
created?
2
⎣ ⎦
30. | The barium isotope 133Ba has a half-life of 10.5 years. A
sample begins with 1.0 * 1010 133Ba atoms. How many are left
after (a) 2 years, (b) 20 years, and (c) 200 years?
31. | The cadmium isotope 109Cd has a half-life of 462 days. A
sample begins with 1.0 * 1012 109Cd atoms. How many are left
after (a) 50 days, (b) 500 days, and (c) 5000 days?
32. || How many half-lives must elapse until (a) 90% and (b) 99%
Half
Life and Activity
of a radioactive sample of atoms has decayed?
235U and 238U.
two main
isotopes
33.There
|| The are
Chernobyl
reactor
accidentof
in uranium,
what is now
Ukraine was
the
worst
nuclear
disaster
of
all
time.
Fission
products
from
235
Two billion years ago, U comprised 3% of the uranium
in the earth’s crust. Now, it’s prevalence has dropped to
exposure to people in western Europe was due to the short-lived
0.7%
of the uranium in the earth’s crust.
(half-life 8.0 days) isotope 131I, which fell across the landscape
of thebyisotopes
has athat
longer
half life?
was ingested
grazing cows
concentrated
the isotope
•andWhich
in Iftheir
milk.
Farmers
couldn’t
sell
the
contaminated
238U, so
have a sample of 235U and a sample of milk,
each
•manyyou
opted to use the milk to make cheese, aging it until the
with the same mass (and therefore approximately the
radioactivity decayed to acceptable levels. How much time
same
number
atoms)
sample
have a131I
must
elapse
for the of
activity
of awhich
block of
cheese will
containing
activity?
to higher
drop to 1.0%
of its initial value?
34. |||| What is the age in years of a bone in which the 14C/12C ratio
t t* 10-13?
is measured to be
0.693N
⎡ 11.65
⎤ 1/2
85
R = used in bone
N 0 ⎢ ⎥ (half-life 65 days) isotope
35. || Sr N
is a=short-lived
2 ⎦ receives a dose of 85Sr witht1/2an activity
scans. A typical ⎣patient
of 0.10 mCi. If all of the 85Sr is retained by the body, what will
be its activity in the patient’s body after one year has passed?
36. || What is the half-life in days of a radioactive sample with
5.0 * 1015 atoms and an activity of 5.0 * 108 Bq?
37. ||| What is the activity, in Bq and Ci, of 1.0 g of 226Ra? Marie
Curie was the discoverer of radium; can you see where the unit
of activity named after her came from?
38. || Many medical PET scans use the isotope 18F, which has a half-life
of 1.8 h. A sample prepared at 10:00 a.m. has an0.693N
activity of 20 mCi.
activity = decay rate = R =
What is the activity at 1:00 p.m., when the patientt is injected?
1/2
39. ||| An investigator collects a sample of a radioactive isotope
Use the
form
mass:
with an activity
of “quick
370,000and
Bq. dirty”
48 hours
later,ofthe
activity is
120,000 Bq. What
is
the
half-life
of
the
sample?
m ( 226 Ra ) = 226 u = 3.75 × 10 −25 kg
m=
0.001 kg sample
= 2.67 × 10 21 atoms
3.75 × 10 −25 kg per atom
t1 2 ( 226 Ra ) = 1600 yr = 5.05 × 1010 s
R = 3.7 × 1010 Bq = 1.0 Ci
24/10/13 5:28 PM
A small sample
can give a big
count rate.
t tt t
⎡⎡11⎤⎤ 1/21/2
N
R == RN0 0⎢⎢ ⎥⎥
⎣⎣22⎦⎦
My watch has a tritium (t1/2 = 12 yr) dial. When I
purchased it in 2004, it had an activity of about 100 MBq.
What is the activity now?
A scrap of
parchment from
Scrolls was
found to have a
14C/12C ratio
that is 79.5% of
the modern
value.
Determine the
age of this
parchment.
⎡1⎤
N = N0 ⎢ ⎥
⎣2⎦
t t1/2
Relevant data from Appendix D:
t1/2 = 5730 yr
Special Relativity
Mass-energy conversion
The most famous equation in the world:
E = mc 2
1u
is equivalent to
931.49 MeV
Antimatter
A positron is
an anti-electron:
Same mass, but
positive charge
What, in MeV, is the minimum energy gamma ray
that can give rise to an electron-positron pair?
FIGURE 30.5 The binding energy of the
woofhydrogen
atoms
(taking
account
thebinding
atoms are
only
a few
eV, ofthe
energies of nuclei are tens or hundreds of
wo free neutrons as shown in FIGURE 30.5 . helium nucleus.
MeV,
that
mass equivalent is not negligible.
eater
thanenergies
that of thelarge
heliumenough
atom. The
dif-their
Electron
Separate atoms (taking account of the
wewas
break
a helium
atom into two hydrogen
Binding
Energy
om theSuppose
energy
that
put into
the system
into
can
useprotons
the conversion
of Equation
30.2 to and two freecomponents
two
and the
two electrons)
neutrons as shown in FIGURE 30.5 .
erence;
this energy
the binding components
energy B:
The mass
of theis separated
is greater than that of the helium atom. The dif-
Helium
∆m
ference=in28.30
mass
MeV/u)
MeV
= 0.03038 u arises from the energy that was put into the system
Proton
to
separate
the
tightly
bound
We can
use the conversion of Equation 30.2 to
y is computed
by energy:
considering
thenucleons.
mass Neutron
Binding
Helium
atom
hydrogen is
atoms,
findcomponents,
the energyZequivalent
of this
difference;
this22 energy
the binding energy B:
ated
hydrogen atoms
andmass
neutrons
28.30 MeV
Mass:
B = (0.03038 u)(931.49
MeV/u) =Mass:
28.30 MeV
4.00260 u
2 H atoms: 2.01566 u
Binding
* (931.49
MeV/u)energy
Generally,
the nuclear(30.4)
binding
+ 2 neutrons: 2.01732 u
energy is computed
by considering
the mass
4.03298 u
Total mass:
per nucleon:
components,
Z
hydrogen
atoms
and
ordifference
an atom of between the atom and its separatedDifference
in mass:
From
∆m = 0.03038 u
7.075 MeV
and
neutrons
N Nneutrons:
Appendix D
energy of iron
B = (ZmH + Nmn - matom) * (931.49 MeV/u)
(30.4)
Nuclear binding energy for an atom of
mass
m atomic
with Z protons and N neutrons
ss of Fe as 55.934940 u. Iron hasatom
o the nearest MeV?
56
FIGURE 30.5 The binding energy of the
helium nucleus.
Electron
Separate
into
components
Neutron Proton
Helium atom
Mass:
4.00260 u
2 hydrogen atoms,
2 neutrons
Mass:
2 H atoms: 2.01566 u
+ 2 neutrons: 2.01732 u
Total mass: 4.03298 u
Difference in mass:
∆m = 0.03038 u
arated into 26 hydrogen atoms and 30 neuts is more than that of the iron nucleus; the
ng Equation
30.4. The
of the hydroEXAMPLE
30.1masses
Finding
the
e 30.2. We find
is the nuclear
binding
Binding
Energy
65 u) What
- 55.934940
u)(931.49
MeV/u)
binding energy of iron
energy of 56Fe to the nearest MeV?
D gives the atomic mass of 56Fe as 55.934940 u. Iron has atomic
number
26,the
so anbinding
atom of 56
Fe couldper
be separated
atoms and 30 neuWhat
nucleonintoof2656hydrogen
Fe?
he nucleus
and is
its components
a energy
small
trons. The mass of the isseparated
components is more than that of the iron nucleus; the
must use several significant figures in our
us thethe
binding
half that of agives
proton—but
energy energy.
PREPARE
= 492.26
MeV ≃Appendix
492 MeV
.
A nuclear fusion weight-loss plan The
! 55.934 940
! Mass
of 56Fe:!
We solve
for the binding energy
Thethatmasses of the hydrosun’susing
energyEquation
comes from30.4.
reactions
1
! Mass
of theH:!
! 1.007
825
hydrogen
atoms to create a
gen
atom and
neutron
are given
incombine
Tablefour
30.2.
We find
atom of helium—a process called
! Mass of n:! ! ! 1.008 665single
nuclear fusion. Because energy is released,
SOLVE
B = (26(1.007825 u) + 30(1.008665 u) - 55.934940 u)(931.49 MeV/u)
ke a comparison with another energy value the mass of the helium atom is less than that
(0.52846tou)(931.49
= hydrogen
492.26 MeV
≃the
492
MeV
of the four
atoms. As
fusion
le iron nucleus is=equivalent
the energyMeV/u)
on molecules of ATP! The energy scale of reactions continue, the mass of the sun
decreases—by
130 trillion
tonsits
percomponents
year!
The difference
the nucleus
and
is a small
fromASSESS
that of chemical
processes.in mass between
That’s a lot of mass, but given the sun’s enorergy fraction
increases,ofsimply
because
there
are mous
the mass
of the
nucleus,
so we
must
use
several
significant
figures
in our
size, this change will amount to only a
ure for
comparing
mass
values.one
Thenucleus
mass difference
that of
ofthe
a proton—but
the energy
few hundredths ofhalf
a percent
sun’s mass
rgy per
nucleon. Iron,
with B=energy,
492 MeV
equivalent,
the binding
is enormous.
1u
is equivalent to
931.49 MeV
How much energy is 492 MeV? To make a comparison with another energy value
we have seen, the binding energy of a single iron nucleus is equivalent
to the energy
24/10/13 5:27 PM
released in the metabolism of nearly 2 billion molecules of ATP! The energy scale of
nuclear processes is clearly quite different from that of chemical processes.
As A increases, the nuclear binding energy increases, simply because there are
more nuclear bonds. A more useful measure for comparing one nucleus to another
is the quantity B/A, called the binding energy per nucleon. Iron, with B= 492 MeV
30.indd 979
Can get
energy by
fusion
Can get
energy by
fission
A nuclear fusion weight-loss plan The
sun’s energy comes from reactions that
combine four hydrogen atoms to create a
single atom of helium—a process called
nuclear fusion. Because energy is released,
the mass of the helium atom is less than that
of the four hydrogen atoms. As the fusion
reactions continue, the mass of the sun
decreases—by 130 trillion tons per year!
That’s a lot of mass, but given the sun’s enormous size, this change will amount to only a
few hundredths of a percent of the sun’s mass
24/10/13 5:27 PM
So where did the heavy elements come from...
65. ||| All the very heavy atoms found in the earth were created long
ago by nuclear fusion reactions in a supernova, an exploding
star. The debris spewed out by the supernova later coalesced to
form the sun and the planets of our solar system. Nuclear physics
suggests that the uranium isotopes 235U (t1/2 = 7.04 * 108 yr)
and 238U (t1/2 = 4.47 * 109 yr) should have been created in
roughly equal amounts. Today, 99.28% of uranium is 238U and
0.72% is 235U. How long ago did the supernova occur?
66. |||| About 12% of your body mass is carbon; some of this is
radioactive 14C, a beta-emitter. If you absorb 100% of the
49 keV energy of each 14C decay, what dose equivalent in Sv do
67. ||||| Ground beef may be irradiated with high-energy electrons
from a linear accelerator to kill pathogens. In a standard treatment, 1.0 kg of beef receives 4.5 kGy of radiation in 40 s.
a. How much energy is deposited in the beef?
b. What is the average rate (in W) of energy deposition?
c. Estimate the temperature increase of the beef due to this proFission
cedure. The specific heat of beef is approximately 3/4 of that
of water.
A nucleus
of 240Pu can be induced to fission into smaller
68.
||| A 70 kgWhat
humanare
body
140per
g ofnucleon
potassium.
fragments.
thetypically
bindingcontains
energies
of
Potassium
has
a
chemical
atomic
mass
of
39.1
u
and
has three
240Pu and the possible fission product 133Xe?
naturally occurring isotopes. One of those isotopes, 40K, is
Data
from Appendix
C: of 1.3 billion years and a natural
with a half-life
abundance ofAtomic
0.012%.mass
Each 40K decay deposits, on average,
Nucleus!!
1.0 MeV of energy into the body. What yearly dose in Gy does
240Pu:!! ! 240.053 808
the typical person receive from the decay of 40K in the body?
133
69. || Xe:!
A chest
uses 10906
keV photons. A 60 kg person receives
! !x ray
132.905
a
30
mrem
dose
from
1H:!! ! ! 1.007 825 one x ray that exposes 25% of the
patient’s body. How many x-ray photons are absorbed in the
n:!
! ! body?
! 1.008 665
patient’s
MCAT-Style Passage Problems
1u
is equivalent to
931.49 MeV
Plutonium-Powered Exploration
The Curiosity rover sent to explore the surface of Mars has an
electric
Fusion
238
Pu, a plutonium isotope that decays by alpha emission with a
3
Rounding
nucleus
a binding
energy of
half-life
of 88slightly,
years. the
At the
start ofHe
thehas
mission,
the generator
6
24
238
2.5 MeV
nucleon;
contained
9.6per
* 10
nuclei ofLi has
Pu. a binding energy of 5.0 MeV
70.
What is the daughter nucleus of the decay?
per| nucleon.
238
238
236
234
Amit beB.energetically
Pu
C. 238
Np
D.
Th 3HeE.nuclei
U
possible
for two
• A.Would
71. ||toWhat
the approximate
of theof
plutonium
source at
6Li?
fusewas
together
to formactivity
a nucleus
the start of the mission?
much energy would be released in the
• A.If so,
2 * how
1021 Bq
19
reaction?
B. 2 * 10 Bq
C.
2 *the
1017exact
Bq details of how the reaction would go.)
(Ignore
D. 2 * 1015 Bq
E. 2 * 1013 Bq
72. || The generator initially provided 125 W of power. If you
assume that the power of the generator is proportional to the
activity of the plutonium, by approximately what percent did
the power output decrease over the first two years of the rover’s
mission?
Carbon dating can be used to date skeletons, wood, paper, fur, food material, and
Up matter. It is quite accurate for ages to about 15,000
thing Warming
dated
992 Items
C H Aare
PTE
R 30 toNuclear
Physicsyears with a fair degree
eliability.
sotopes with longer half-lives are used to date geological samples.
PotassiumCarbon
dating can be used to date skeletons, wood, paper, fur, food mat
useful
for of organic matter. It is quite accurate for ages to abou
on dating, using 40K with a half-life of 1.25 billion years, is especially
ng rocks of volcanic origin.
years, about three half-lives. Items are dated to about 50,000 years with a fa
of reliability.
A
sample
of
1000
atoms
has
a
10
minute
half-life.
Isotopes
withand
longer half-lives are used to date geological samples. Po
rbon dating can be used to date skeletons, wood, paper, fur, food
material,
40
wing
oldelse
is the
sample
when
750
atoms
have
decayed?
argon
dating,
using
made of organic matter. It is quite accurate for ages to about 15,000 K with a half-life of 1.25 billion years, is especially u
OP TO THINK 30.6
dating
rocks
volcanic origin.
three half-lives.
Items
are dated to
50,000 years
a fair of
degree
A. 10 minutes
B. 15
minutes
20 minutes
D.with
30 minutes
iability.
otopes with longer half-lives are used to date geological samples.
STOP TOPotassiumTHINK 30.6
A sample of 1000 radioactive atoms has a 10 minute
40
How old isuseful
the sample
dating, using K with a half-life of 1.25 billion years, is especially
for when 750 atoms have decayed?
g rocks
of volcanic origin.
0.6
Medical
Applications
A. 10 minutes
B. 15 minutes
C. 20 minutes
D. 30 mi
of Nuclear Physics
A sample of 1000 radioactive atoms has a 10 minute half-life.
learisphysics
has brought
both
perilhave
and decayed?
old
the sample
when 750
atoms
P TO THINK 30.6
se tumors. At the same time, radiation can be used to diagnose and cure some
A. 10This
minutes
15 minutes
C. 20
minutes of nuclear
D. 30physics.
minutes
cers.
section is B.
a brief
survey of medical
applications
30.6 Medical Applications
of Nuclear Physics
diation Dose
Nuclear physics has brought both peril and promise to society. Radioact
lear radiation disrupts a cell’s machinery by altering and damaging biological molcause tumors. At the same time, radiation can be used to diagnose and cu
es, as we saw in Section 30.4. The biological effects of radiation depend on two
cancers. This section is a brief survey of medical applications of nuclear ph
ors. The first is the physical factor of how much energy is absorbed by the body. The
ond is the biological factor of how tissue reacts to different forms of radiation.
Dose
Suppose
a beta
travels
tissue,
losingtokinetic
energy
as it ionizes
ear physics
hasparticle
brought
both through
peril and
promise
society.
can
mstumors.
it passes.
The
energy
lost
by
the
beta
particle
is
a
good
measure
of
the
number
Nuclear
disrupts a cell’s machinery by altering and damaging biolog
At the same time, radiation can be used to diagnose and cure some
ons
produced
and
thus
the
amount
of
damage
done.
In
a
certain
volume
of
tissue,
we saw in Section 30.4. The biological effects of radiation depen
rs. This section is a brief survey of medical applications of ecules,
nuclearasphysics.
dose
e ionization means more damage. For this reason, we define the
factors.
The first
is the physical factor of how much energy is absorbed by the b
he energy from ionizing radiation absorbed by 1 kg of tissue. second
The SI unit
for
the
is the biological factor of how tissue reacts to different forms of radiati
Dose
abbreviated Gy. The Gy is defined as
eiation
is the gray,
Suppose a beta particle travels through tissue, losing kinetic energy as
cell’s
machinery
alteringenergy
and damaging
atomsbiological
it passes.molThe energy lost by the beta particle is a good measure of the
= 1.00
J/kg of by
absorbed
of doses:
s, as we Two
saw in different
Section 30.4.types
The biological
depend
on two
of ions
produced
and thus the amount of damage done. In a certain volume
of
depends
only
on the
energy
absorbed,
not
on the type
External
/factor
exposure
to
s.number
The first
the
physical
of how
much
energy
is absorbed
byionization
the
body. The
•isGy
more
means more damage. For this reason, we define the radiat
on
the
absorbing
Another
common
unit
for dose
d iswhat
the biological
factormaterial
how is.
tissue
reacts
to different
forms
/ofinhaled
or
ingested
isotopes
• Internal
as of
energy from ionizing radiation absorbed by 1 kg of tissue. The SI un
dppose
= 0.01
Gy.
a beta particle travels through tissue, losing kinetic dose
energy
as itgray,
ionizes
abbreviated Gy. The Gy is defined as
is the
A
1
Gy
dose
of
gamma
rays
and
a
1
Gy
dose
of
alpha
particles
have
different
s it passes. The energy lost by the beta particle is a good measure of the number
ogical consequences.
To account
for such differences,
the relative biological
Ionizing
the
s produced and thus
the amount
ofdamages
damage cells
done.ofIn
a certain volume of tissue, 1 Gy = 1.00 J/kg of absorbed energy
ctiveness (RBE) body,
is defined
as
the
biological
effect
of
a
it also damages bacteria and given dose relative to
ionization means morebut
damage.
For this reason, we defineThe
the number
Gy depends only on the energy absorbed, not on the type of
biological
effect
of
an
equal
dose of This
x rays.
Tablesource
30.3 lists
biological
other pathogens.
gamma
is the relative
Dose
&
Dose
Equivalent
energy
from
ionizing
absorbed
by
1
kg
of
tissue.
The
SI
unit
for
the
or ontowhat
absorbing
material is. Another common unit for dose is
usedforms
for sterilizing
medical
equipment.
ctiveness of different
Larger
values correspond
largerthe
bioDose:
Unit
is
the
gray:
gray,
abbreviated
Gy.
The
Gy
is
defined
as
is
the
The
blue
glow
is
due
to
the
ionization
of
1
=
0.01
Gy.
cal effects.
air around the source.
Gyand
dose
the of
product
of the
energy doseAin1 Gy
theof gamma rays and a 1 Gy dose of alpha particles have
1equivalent
Gy = 1.00isJ/kg
absorbed
energy
biological
consequences.
To account for such differences, the relative b
tive biological effectiveness. Dose equivalent is measured in sieverts, abbreviumber
of
Gy
depends
only
on
the
energy
absorbed,
not
on
the
type
of
effectiveness (RBE) is defined as the biological effect of a given dose re
equivalent: Unit is the sievert:
Sv. ToDose
be precise,
30.3
what the absorbing TABLE
material
is.Relative
Anotherbiological
common unit for
is theeffect
rad; of an equal dose of x rays. Table 30.3 lists the relative b
thedose
biological
dose equivalent
in Sv
= dose in Gy * RBE
effectiveness
effectiveness of different forms of radiation. Larger values correspond to la
= 0.01 Gy.
One
Svdose
produces
thetype
same
biological
regardless
of
the
type
logical
effects.
1 Gy
of gamma
rays and
a 1 Gy
doseRBE
ofdamage
alpha particles
have
different
Another common
unit
of
dose
equivalent
(also
called
biologically
dose equivalent is the product of the energy dose in Gy
The
gical
consequences.
To
account
for
such
differences,
the
relative
biological
X rays
1
1
rem
=
0.01
Sv.
ivalent
dose)
is
the
rem;
relative
tiveness (RBE) is defined as the biological effect of a given
dosebiological
relative toeffectiveness. Dose equivalent is measured in sieverts,
Gamma rays
1
ated
Sv.
To
be precise,
ological
effect
of
an
equal
dose
of
x
rays.
Table
30.3
lists
the
relative
NOTE ▶ In practice, the term “dose” is often used for both dose and dosebiological
equiva-
6 Medical Applications
of Nuclear Physics
Beta particles
1
iveness
values
to larger
bio- dose equivalent in Sv = dose in Gy * RBE
ent.
Use of
thedifferent
units as aforms
the unit is Larger
Sv or rem,
it is correspond
a dose equivalent;
if Gy
Protons
5
al
effects.
One
produces the same biological damage regardless of
Neutrons is the product 5–20
of the energy dose
in Sv
Gyofand
the
Another common unit of dose equivalent (also called bio
Alpha particles
20 measured inofsieverts,
abbrevive biological effectiveness.
Dose equivalent is
equivalent
dose)
is the rem; 1 rem = 0.01 Sv.
Sv. To be precise,
Typical Doses: External
Typical exposure
(mSv)
gible
een.
nize
y.
PET scan
7.0
Natural background
(1 year)
3.0
Mammogram
0.70
Chest x ray
0.30
e is no Transatlantic
airplane flight
0.050
cessary
natural Dental x ray
0.030
d from
ven the
though FIGURE 30.18 The use of gamma rays to
a tumor in the brain.
n. Doses:treat
Internal
al x ray (a)
t he or Food dose, per year
0.40 mSv
ammo(typical)
body.
), may Eating 40 tablespoons
0.10 mSv
of
peanut
butter
e. This
re.
Eating 1000 bananas
0.10 mSv
rapidly
a large
minimal
Smoking 1 pack per
30
(b) day
Gamma
from
for rays
a year
Collimator
external source
mSv
or that
mator is
Tumor
on Internal
the
mor are
Most of the internal radiation of the human body is
due to a single isotope, the beta emitter 40K, with half
urgical
life of 1.28×109 years. The body contains about 0.35%
f treat-
potassium by mass; of this potassium, about 0.012% is
40K. What is the total activity, in Bq, of a 70 kg human?
hin the
decay
n has a
The paths of the
allowed
gamma rays
40K: 40
Atomic mass of
intersect
atuthe tumor.
The collimator allows
-27 kg
1
u
=
1.66
x
10
gamma rays to penetrate
only along certain lines.
R=
0.693N
t1/2
In a previous example, we computed the activity of
the 40K in a typical person. Each 40K decay produces a
1.3 MeV beta particle. If 40% of the energy of these
decays is absorbed by the body, what dose, and what
dose equivalent, will a typical person (70 kg) receive in
one year?
1 MeV = 1.6 x 10-13 J
450
400
350
300
250
200
150
100
50
0
0
2000
4000
6000
8000
10000
12000
Radiation vs. Height on a Plane
A passenger on an airplane flying across the Atlantic will
from cosmic rays. How many hours of flying would it take
in one year for a person to double his or her yearly
radiation dose? Assume there are no other significant
80 hours / month
960 hours / year
Chain Reaction
1
0
n+ 235
92 U →
236
92
92
1
U → 141
56 Ba+ 36 Kr+3 0 n
Difficult Daughters
141
56
0 Ba → 141
t1 2 = 18.27 minutes
57 La+ -1 e
141
57
0 La → 141
t1 2 = 3.92 hours
58 Ce+ -1 e
141
58
0 Ce → 141
t1 2 = 32.5 days
59 Pr+ -1 e
141
59
Pr : stable
131
53
0 I → 131
54 Xe + -1 e t1 2 = 8.0 days
taken up by thyroid
137
55
0 Cs → 137
56 Ba* + -1 e t1 2 = 30.2 years
chemically similar to potassium
90
38
Sr →
90
39
Y + -10 e- t1 2 = 28.1 years
chemically similar to calcium
Transuranic elements
238
92
U + 01 n →
239
93
Np →
239
94
239
92
U→
Pu + -10 e-
239
93
Np + -10 e-
Fusion: More Energy Released.
H + H → He + n
2
2
3
1
1
1
2
0
The problem? Coulomb repulsion.
The solution?
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