22.02
INTRODUCTION TO
APPLIED NUCLEAR
PHYSICS
Spring 2012
Prof. Paola Cappellaro
1
GOALS OF 22.02
I NTRODUCTION TO A PPLIED N UCLEAR P HYSICS
Learn the basic principles of nuclear and
radiation science
After taking this class, you will able to
study (and understand) any application
of nuclear and radiation science
Keyword: WHY?
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YOUR GOALS?
What are your goals and INTERESTS?
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NUCLEAR PHYSICS
Describes nuclear properties and radiation:
structure and characteristics of nuclei
radiation sources and interaction with matter
To understand nuclear structure and radiation we study:
nuclei, nucleons and electrons
microscopic processes
To understand we need modern physics
Quantum mechanics
(Special Relativity)
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WHAT ARE THE MAGIC NUMBERS?
?
?4 ?
2 ?
65
?
10980
75
Image by MIT OpenCourseWare.
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WHAT ARE THE MAGIC NUMBERS?
A computer
program variable ?
Rock band?
Iphone App?
Games to win to clinch the season?
Number of jobs?
6
WHAT ARE THE MAGIC NUMBERS?
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see http://ocw.mit.edu/fairuse.
7
WHAT ARE THE MAGIC NUMBERS?
8
App screenshot © Design7; "The Magic Numbers" cover art © EMI; news article excerpt © The New York Times Company. All rights
reserved. This content is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/fairuse.
WHAT ARE THE MAGIC NUMBERS?
In nuclear physics?
2 8 20 28 50 82 126
And why are they magic?
You’ll find out at the end of this lecture
9
BINDING ENERGY
Mass-energy equivalence
E = mc2
Nuclei are composed of protons and neutrons,
held together by some energy
Z mproton + N mneutron 6= MNucleus
Difference in mass ➜ difference in energy
This explains why we get energy from nuclear fission,
from fusion, from radioactive decay products...
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NUCLEAR NOMENCLATURE
Atoms/nuclei are specified by # of
neutrons: N
protons: Z
[Z electron in neutral atoms]
Atoms of same element have same atomic number Z
Isotopes of the same element have same atomic number Z
but different number of neutrons N
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NUCLEAR NOMENCLATURE
Isotopes are denoted by
X
A
Z
X is the chemical symbol
A = Z + N is the mass
E.g.:
235U, 238U
92
number
[Z is redundant here]
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NUCLEAR NOMENCLATURE
NUCLIDE
atom/nucleus with a specific N and Z
ISOBAR
nuclides with same mass # A (≠Z,N)
ISOTONE
nuclides with same N, ≠Z
ISOMER
same nuclide (but different energy state)
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BINDING ENERGY
Mass-energy equivalence
E = mc2
Nuclei are held together by the binding energy
Z mproton + N mneutron 6= MNucleus
Difference in mass ➜ difference in energy
Why is there a mass difference?
14
BINDING ENERGY
Binding Energy = [Mass of its constituents-Nucleus Mass] x c2
⇥
B = Zmp + N mn
⇤
mN (A X) c2
In terms of measurable quantities:
B = Zmp + N mn
[mA ( X)
A
B is always negative
positive for stable nuclei
15
Zme ] c
2
SEMI-EMPIRICAL MASS FORMULA
M (Z, A) = Zm(1 H) + N mn
B(Z, A)/c2
From a simple model of the
nucleus, described as a
liquid drop
➜ formula for B(Z,A)
5 terms, plot B(Z,A) vs. A
Photo courtesy of cdw9 on Flickr. License CC BY-NC.
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SEMI-EMPIRICAL MASS FORMULA
M (Z, A) = Zm(1 H) + N mn
B(A, Z) = av A
Volume
as A
Surface
2/3
asym
(A
ac Z(Z
2Z)
A
symmetry
Photo courtesy of cdw9 on Flickr. License CC BY-NC.
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Coulomb
2
+
1)A
ap A
1/3
3/4
{
With binding energy given by:
B(Z, A)/c2
pairing
(binding energy per nucleon)
B/A
SEMF: Binding Energy per Nucleon
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5
4
3
A
0
50
100
150
(Mass number)
200
B(Z,A)/A ~ cst.(8 MeV) - corrections
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250
(binding energy per nucleon)
B/A
B/A: JUMPS
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5
4
3
A
0
50
100
150
200
(Mass number)
250
“Jumps” in Binding energy from experimental data
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ATOMS PERIODIC PROPERTIES
Ionization Energy (similar to B per nucleon)
Ê
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kJ per Mole
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1500
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Z
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ATOMIC PERIODIC TABLE
Periodic properties → atomic structure
Ionization Energy (similar to B per nucleon)
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CHART OF NUCLIDES
http://www.nndc.bnl.gov/chart/
“Periodic”, more complex properties → nuclear structure
© Brookhaven National Laboratory. All rights reserved. This content is excluded from
our Creative Commons license. For more information, see http://ocw.mit.edu/fairuse.
22
WHAT ARE THE MAGIC NUMBERS?
2 8 20 28 50 82 126
And why are they magic?
23
WHAT ARE THE MAGIC NUMBERS?
2 8 20 28 50 82 126
And why are they called magic?
24
WHAT ARE THE MAGIC NUMBERS?
2 8 20 28 50 82 126
And why are they called magic?
Maria Goeppert Mayer “discovered” them in ~1945
Observation of periodicity in binding energy
➜ shell model for nuclei
Eugene Wigner believed in liquid-drop model,
did not trust new theory
➜ called these numbers “magic”
Quantum mechanics only can explain them
As well as many other “misteries”,
e.g. randomness of radioactive decay
25
22.02 SPRING 2012
Class Logistics
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RECITATIONS
There will be weekly recitations
Recitations will review some topics from lecture and
mathematical background
27
TEXTBOOKS
Lecture notes
Usually posted before the lecture
Kenneth S. Krane,
Introductory Nuclear Physics, Wiley
David J. Griffiths
Introduction to Quantum Mechanics,
2nd edition Pearson Prentice Hall, 2005
28
P-SETS
The problem sets are an essential part of the course
Try solving the Pset on your own
Discuss with other students
Attend recitations
Ask TA and Professor
P-sets will be posted
9 P-sets, tentative schedule in Syllabus hand-out
P-set solutions will be posted
No p-sets will be accepted after the deadline
Worst P-set grade will be dropped
29
GRADING
Homework 25%
Worst P-set grade will be dropped
Mid-Term
30%
Week before Spring Break: Conflicts?
Final exam 40%
“Mostly” on second part of class
Class Participation 5%
30
CLASS PARTICIPATION
xkcd.com
Courtesy of xkcd.com. License CC BY-NC.
31
QUESTIONS?
32
MIT OpenCourseWare
http://ocw.mit.edu
22.02 Introduction to Applied Nuclear Physics
Spring 2012
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