PSE ch 43 Nuclear Physics.pptx

Some Properties of Nuclei
• Atomic number Z: number of protons in nucleus
(sometimes called charge number)
• Neutron number N: number of neutrons in
nucleus
• Mass number A = Z + N: number of nucleons
(neutrons plus protons) in nucleus

Some Properties of Nuclei
X
A
Z  
56
26
mass number 56
Fe iron :
atomic number 26





26 protons and 56 – 26 = 30 neutrons
18 18
9 F F

12 13
6 6
11 14
6 6
C 98.9% C 1.1%
C and C:
produced in lab or by cosmic rays
 

Quick Quiz 43.1 Part I
The three nuclei 12C, 13N, and 14O have the same
number of what type of particle?
(a) protons
(b) neutrons
(c) nucleons

Quick Quiz 43.1 Part II
The three nuclei 12N, 13N, and 14N have the same
(a) protons
(b) neutrons
(c) nucleons

Quick Quiz 43.1 Part III
The three nuclei 14C, 14N, and 14O have the same
(a) protons
(b) neutrons
(c) nucleons

Charge and Mass
  
2
2 27 8
1.660 539 10 kg 2.997 92 10 m/s
= 931.494 MeV
R
E mc 
   

The Size and Structure of Nuclei
2 1 2
0
1
0 0 0
2
E
e
K U
q q
mv k
d
   
 
 
   
   
   
  
1 2
2 2
2
2
2
2 2
4
e e
e
e Ze
q q
d k k
mv mv
Ze
k
mv
 

15
1 fm 10 m



The Size and Structure of Nuclei
1/3 15
with 1.2 10 m 1.2 fm
r aA a 
   

Example 43.1:
The Volume and Density of a Nucleus
Consider a nucleus of mass number A, containing
protons and neutrons, each with mass approximately
equal to m.
(A) Find an approximate expression for the mass of the
nucleus.
nucleus
m Am


Example 43.1:
(B) Find an expression for the volume of this nucleus in
terms of A.
3 3
nucleus
4 4
3 3
V r a A
 
 

Example 43.1:
(C) Find a numerical value for the density of this
nucleus.
nucleus
3 3
4
nucleus 3 4
m Am m
V a A a

 

  
 
 
27
3
15
17 3
1.67 10 kg
4 1.2 10
2.3 10 kg/m




 


 

Example 43.1:
What if the Earth could be compressed until it had this
density? How large would it be?
24
7 3
17 3
5.97 10 kg
2.6 10 m
2.3 10 kg/m
E
M
V


   

 
1/3
7 3
1/3
3
2
3 2.6 10 m
4 3
3 4 4
1.8 10 m
V
V r r
r

 
 

 
 
   
 
   
 
 

Nuclear Binding Energy
   
X 931.494 MeV/u
A
b n Z
E ZM H Nm M
 
   
 

The Liquid-Drop Model
Four major effects influence binding energy of
nucleus in liquid-drop model:
1. Volume effect
2. Surface effect
3. Coulomb repulsion effect
2
/
e
k e r   1/3
3 1 /
C Z Z A
 
4. Symmetry effect
 
2
4 /
C N Z A
 

The Liquid-Drop Model
   
2
2/3
1 2 3 4
1/3
1
b
Z Z N Z
E C A C A C C
A
A
 
   
1
2
3
4
15.7 MeV
17.8 MeV
0.71 MeV
23.6 MeV
C
C
C
C




   
X 931.494 MeV/u
A
b n Z
E ZM H Nm M
 
   
 

Example 43.2: Applying the Semiempirical
Binding-Energy Formula
The nucleus 64Zn has a tabulated binding energy of
559.09 MeV. Use the semiempirical binding-energy
formula to generate a theoretical estimate of the
binding energy for this nucleus.
  
  
 
 
  
 
 
 
 
1
2/3
2/3
2
3 1/3 1/3
2 2
4
15.7 MeV 64 1005 MeV
C 17.8 MeV 64 285 MeV
1 30 29
0.71 MeV 154 MeV
64
34 30
C 23.6 MeV 5.90 MeV
64
C A
A
Z Z
C
A
N Z
A
 
 

 
 
  
1005 MeV 285 MeV 154 MeV 5.90 MeV 560 MeV
b
E     

The Shell Model
Magic numbers: Z or N = 2, 8, 20, 28, 50, 82

The Shell Model
Maria Goeppert-Mayer

Radioactivity
Photographic plate made by Henri Becquerel showing
effects of exposure to radioactivity

Radioactivity
Pierre and Marie Curie

Radioactivity
dN
N
dt

 
dN
dt
N

 
0
t
N N e 


0 0
t t
dN
R N N e R e
dt
 
   
   

Half-Life
1/2
0
0 0
2
T
t N
N N e N e 
 

  
The half-life of a
radioactive substance
is the time interval
during which half of
a given number of
radioactive nuclei
decay.
1/2
2 T
e
 1/2
ln 2 0.693
T
 
  
0
1
2
n
N N
 
  
 
10
1 Ci 3.7 10 decays/s
  1 Bq 1 decay/s


Quick Quiz 43.2
On your birthday, you measure the activity of a sample
of 210Bi, which has a half-life of 5.01 days. The activity
you measure is 1.000 Ci. What is the activity of this
sample on your next birthday?
(a) 1.000 Ci
(b)  0.2 Ci
(c)  0.01 Ci
(d)  1022 Ci

Example 43.3:
How Many Nuclei Are Left?
The isotope carbon-14, 6
14
C, is radioactive and has a
half-life of 5 730 years. If you start with a sample of
1 000 carbon-14 nuclei, how many nuclei will still be
undecayed in 25 000 years?
25000 yr
4.363
5730 yr
n  
4.363
0
1 1
1000 49
2 2
n
N N
   
  
   
   

Example 43.4:
The Activity of Carbon
At time t = 0, a radioactive sample contains 3.50 g of
pure 6
11
C , which has a half-life of 20.4 min.
(A) Determine the number N0 of nuclei in the sample at
t = 0.
6
7
3.50 10 g
3.18 10 mol
11.0 g/mol
n



  
  
7 23
0
17
3.18 10 mol 6.02 10 nuclei/mol
1.92 10 nuclei
N 
  
 

Example 43.4:
The Activity of Carbon
(B) What is the activity of the sample initially and after
8.00 h?
 
  
17
0 0 0
1/2
4 1 17 14
0.693 0.693 1 min
1.92 10
20.4 min 60 s
5.66 10 s 1.92 10 1.09 10 Bq
R N N
T

 
 
   
 
 
    
    
4 1 4
5.66 10 s 2.88 10 s
14
0
6
1.09 10 Bq
8.96 10 Bq
t
R R e e

 
  

  
 

Example 43.5:
A Radioactive Isotope of Iodine
A sample of the isotope 131
I, which has a half-life of
8.04 days, has an activity of 5.0 mCi at the time of
shipment. Upon receipt of the sample at a medical
laboratory, the activity is 2.1 mCi. How much time has
elapsed between the two measurements?
0 0
ln
t
R R
e t
R R


  
   
 
 
1/2
0 0
1
ln ln
ln 2
T
R R
t
R R

   
   
   
   
8.04 d 2.1 mCi
ln 10 d
0.693 5.0 mCi
t
 
 
 
 

Alpha Decay
4 4
2 2
X Y He
A A
Z Z


 
238 234 4
92 90 2
226 222 4
88 86 2
U Th He
Ra Rn He
 
 
0
R
E K
   
  2
X Y
R
Q E M M M c

    
 
X Y 931.494 MeV/u
Q M M M
   

Alpha Decay
ER
R
E K T
   

Quick Quiz 43.3
Which of the following is the correct daughter nucleus
associated with the alpha decay of 72
157
Hf?
(a) 72
153
Hf
(b) 70
153
Yb
(c) 70
157
Yb

Quick Quiz 43.3
associated with the alpha decay of 72
157
Hf?
(a) 72
153
Hf
(b) 𝟕𝟎
𝟏𝟓𝟑
𝐘𝐛
(c) 70
157
Yb

Example 43.6:
Mass Change in a Radioactive Decay
The 216Po nucleus is unstable and exhibits
radioactivity. It decays to 212Pb by emitting an alpha
particle. The relevant masses, in atomic mass units, are
mi = m(216Po) = 216.001 914 u and
mf = m(212Pb) + m(4He) = 211.991 898 u + 4.002 603 u.
(A) Find the mass change of the system in this decay.
 
29
211.991 898 u + 4.002 603 u 216.001 914 u
0.007413 u 1.23 10 kg
f i
m m m

  
 
    

Example 43.6:
Mass Change in a Radioactive Decay
(B) Find the Q value for this decay.
 
  
2
2
29 8
12
1.23 10 kg 3.00 10 m/s
1.11 10 J 6.92 MeV
R
Q E m c


    
    
  

Example 43.7:
The Energy Liberated When Radium Decays
The 226Ra nucleus undergoes alpha decay.
(A) Calculate the Q value for this process.
The masses are 226.025 408 u for 226Ra,
222.017 576 u for 222Rn, and 4.002 603 u
for 2
4
He.
 
 
 
X Y 931.494 MeV/u
= 226.025 408 u 222.017 576 u 4.002 603 u
931.494 MeV/u
0.005 229 u 931.494 MeV/u 4.87 MeV
Q M M M
   
 

  

Example 43.7:
The Energy Liberated When Radium Decays
(B) What is the kinetic energy of the alpha particle after
the decay?
Y Y
0 M v M v
 
 
2 2
Y Y
1 1
2 2
R
E K Q K Q M v M v
 
        
2
2 2
Y
Y Y
Y Y
Y Y
1 1 1
1
2 2 2
M v M
Q M v M M v
M M
M M M
K K Q
M M M
  
   

 

   
   
   
   
 
 

    
 

   
 
222
4.87 MeV 4.78 MeV
222 4
K
 
 
 

 

Beta Decay
 
 
1
1
X Y e incomplete expression
X Y e incomplete expression
A A
Z Z
A A
Z Z




 
 
 
 
14 14
6 7
12 12
7 6
C N e incomplete expression
N C e incomplete expression


 
 

Neutrino
Enrico Fermi Frederick Reines
Wolfgang Pauli

Neutrino
Properties of neutrinos:
• Zero electric charge
• Mass very small
• Spin ½
• Interacts weakly with matter

Beta-Decay Processes
1 1
14 14 12 12
6 7 7 6
X Y e + X Y e +
C N e + N C e +
A A A A
Z Z Z Z
 
 
 
 
 
   
   

Electron Capture
0
1 1
X + e Y
A A
Z Z 
 
 
7 0 7
4 1 3
Be + e Li 
  

Electron Capture
  2
X Y
Q M M c
 
  2
X Y 2 e
Q M M m c
  

Quick Quiz 43.4
associated with the beta decay of 72
184
Hf?
(a) 72
183
Hf
(b) 73
183
Yb
(c) 73
184
Ta

Quick Quiz 43.4
associated with the beta decay of 72
184
Hf?
(a) 72
183
Hf
(b) 73
183
Yb
(c) 𝟕𝟑
𝟏𝟖𝟒
𝐓𝐚

Carbon Dating
e+
Dead Sea Scroll
14C/12C = r0 = 1.3  1012

Conceptual Example 43.8:
The Age of Iceman
In 1991, German tourists discovered the well-preserved
remains of a man, now called “Ötzi the Iceman,” trapped
in a glacier in the Italian Alps. Radioactive dating with
14C revealed that this person was alive approximately
5 300 years ago. Why did scientists date a sample of Ötzi
using 14C rather than 11C, which is a beta emitter having
a half-life of 20.4 min?

Example 43.9:
Radioactive Dating
A piece of charcoal containing 25.0 g of carbon is found in some
ruins of an ancient city. The sample shows a 14C activity R of 250
decays/min. How long has the tree from which this charcoal came
been dead?
1/2
0 0
1
ln ln
ln 2
T
R R
t
R R

   
   
   
   
   
1/2
0 1/2 0 0
ln 2/ / ln 2
A A
RMT
R R
R T r m M N r mN
 
   
   
1 7
12 23 1
0
250 min 12.0 g/mol 5730 yr 3.156 10 s 1 min
0.667
1 yr 60 s
1.3 10 25.0 g 6.022 10 mol ln 2
R
R

 
 
  
 
  
   
 
  3
5730 yr
ln 0.667 3.4 10 yr
ln 2
t   

Gamma Decay
X* X
A A
Z Z 
 
12 12
5 6
12 12
6 6
B C* e
C* C



  
 

Nuclear Reactions
CERN LHC tunnel

Nuclear Reactions
a X Y b
    
X a, b Y
  2
a X Y b
Q M M M M c
   
 
4
7
Li p, He

1 7 4 4
1 3 2 2
H Li He He
  
1 19 16 4
1 9 8 2
H F O He
  
  
23 21
avg
3 3
1.38 10 J/K 300 K 6.21 10 J 0.04 eV
2 2
B
K k T  
     
1 1 1
0 n X X* X
A A A
X Z Z 
 
   

Nuclear Fission
Lise Meitner and Otto Hahn

Nuclear Fission
1 235 236
0 92 92
n U U* X Y neutrons
    
 
1 235 141 92 1
0 92 56 36 0
n U Ba Kr 3 n
   

Quick Quiz 43.5
When a nucleus undergoes fission, the two daughter
nuclei are generally radioactive. By which process are
they most likely to decay?
(a) alpha decay
(b) beta decay (e)
(c) beta decay (e+)

Quick Quiz 43.6
Which of the following are possible fission reactions?
   
   
   
1 235 140 94 1
0 92 54 38 0
1 235 132 101 1
0 92 50 42 0
1 239 137 97 1
0 94 53 41 0
a n U Xe Sr 2 n
b n U Sn Mo 3 n
c n Pu I Nb 3 n
   
   
   

Quick Quiz 43.6
Which of the following are possible fission reactions?
   
   
   
1 239 137 97 1
0 94 53 41 0
c n Pu I Nb 3 n
   
1 235 140 94 1
0 92 54 38 0
1 235 132 101 1
0 92 50 42 0
a n + U Xe + Sr + 2 n
b n + U Sn + Mo + 3 n
→
→

Example 43.10:
The Energy Released in the Fission of 235U
Calculate the energy released when 1.00 kg
of 235U fissions, taking the disintegration
energy per event to be Q = 208 MeV.
A A
m
N nN N
M
 
  
3
23 1
26
1.00 10 g
6.02 10 mol 208 MeV
235 g/mol
5.33 10 MeV
A
m
E NQ N Q
M

 

 
 
 
13
26 7
6
1.60 10 J 1 kWh
5.33 10 MeV 2.37 10 kWh
1 MeV 3.60 10 J
E

 
  
   
  

 
 

Nuclear Reactors
First nuclear reactor, University of Chicago

Safety and Waste Disposal
Chernobyl Reactor

Safety and Waste Disposal
Philippsburg Nuclear Power Plant, Germany

Nuclear Fusion
1 1 2
1 1 1
1 2 3
1 1 2
H H H e
H H He



   
  
1 3 4
1 2 2
3 3 4 1 1
2 2 2 1 1
H He He e
He He He H H


   
   

Quick Quiz 43.7
In the core of a star, hydrogen nuclei combine in fusion reactions.
Once the hydrogen has been exhausted, fusion of helium nuclei
can occur. If the star is sufficiently massive, fusion of heavier and
heavier nuclei can occur once the helium is used up. Consider a
fusion reaction involving two nuclei with the same value of A.
For this reaction to be exothermic, which of the following values
of A are impossible?
(a) 12
(b) 20
(c) 28
(d) 64

Terrestrial Fusion Reactions
2 2 3 1
1 1 2 0
2 2 3 1
1 1 1 1
2 3 4 1
1 1 2 0
H H He n 3.27 MeV
H H H H 4.03 MeV
H H He n 17.59 MeV
Q
Q
Q
   
   
   

Example 43.11:
The Fusion of Two Deuterons
For the nuclear force to overcome the repulsive
Coulomb force, the separation distance between two
deuterons must be approximately 1.0  1014 m.
(A) Calculate the height of the potential barrier due to
the repulsive force.
 
 
 
2
2 19
9 2 2
1 2
14
14
1.60 10 C
8.99 10 N m /C
1.0 10 m
2.3 10 J 0.14 MeV
E e e
e
q q
U k k
r r





    

  

Example 43.11:
(B) Estimate the temperature required for a deuteron to
overcome the potential barrier, assuming an energy of
3
2
kBT per deuteron (where kB is Boltzmann’s constant).
14
B
3
1.1 10 J
2
k T 
 
 
 
14
8
23
2 1.1 10 J
5.6 10 K
3 1.38 10 J/K
T



  


Example 43.11:
(C) Find the energy released in the deuterium–
deuterium reaction
3.016 049 u 1.007 825 u 4.023 874 u
 
4.028 204 u 4.023 874 u 0.004 33 u
0.004 33 u 931.494 MeV/u 4.03 MeV
 
  
1 2 3 1
1 1 1 1
H H H H
  

Example 43.11:
Suppose the tritium resulting from the reaction in part
(C) reacts with another deuterium in the reaction
2 3 4 1
1 1 2 0
H H He n
  
How much energy is released in the sequence of two
reactions?
 
3 2.014 102 u 6.042 306 u

4.002 603 u 1.007 825 u 1.008 665 6.019 093 u
  
Excess mass: 0.023 213 u

National Spherical Torus Experiment

Advantages and Problems of Fusion
Advantages:
1. Low cost and abundance of fuel (deuterium)
2. Impossibility of runaway accidents
3. Decreased radiation hazard
Disadvantages:
1. Scarcity of lithium
2. Limited supply of helium
3. Structural damage and induced radioactivity

Units of Radiation Doses
Roentgen (R): amount of ionizing radiation that
produces an electric charge of 3.33  1010 C in 1 cm3
of air under standard conditions
Rad: amount of radiation that increases the energy of 1
kg of absorbing material by 1  102 J

RBE and rem
Dose in rem  dose in rad  RBE

Uses of Radiation from the Nucleus:
Tracing

Materials Analysis
Data acquired through neutron activation
analysis: “gamma profile”
1 65 66 66
0 29 29 30
n Cu Cu Zn e 

    

Materials Analysis
Napoleon Bonaparte

Nuclear Magnetic Resonance and
Magnetic Resonance Imaging
 
1
I I 
27
5.05 10 J/T
2
n
p
e
m
 
  
proton 2.7928 n
 

neutron 1.9135 n
 
 

Nuclear Magnetic Resonance
 
μ B

PSE ch 43 Nuclear Physics.pptx

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