Lecture notes. Usually posted before the lecture. Kenneth S. Krane,. Introductory
Nuclear Physics, Wiley. David J. Griffiths. Introduction to Quantum Mechanics,.
22.02 INTRODUCTION TO
APPLIED NUCLEAR PHYSICS Spring 2012 Prof. Paola Cappellaro
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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?
© Wikimedia Foundation. License CC BY-SA. This content is excluded from our Creative Commons license. For more information, 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?
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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
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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. 17
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 9 8 7 6 5 4 3
A
0
50
100
150
(Mass number) 200
B(Z,A)/A ~ cst.(8 MeV) - corrections 18
250
(binding energy per nucleon)
B/A
B/A: JUMPS 9 8 7 6 5 4 3
A
0
50
100
150
200
(Mass number) 250
“Jumps” in Binding energy from experimental data 19
ATOMS PERIODIC PROPERTIES Ionization Energy (similar to B per nucleon)
Ê ‡
Ê ‡
kJ per Mole
2000
Ê ‡ Ê ‡
1500 Ê ‡
Ê ‡
Ê ‡
Ê ‡
Ê ‡ Ê ‡
Ê ‡ Ê ‡
1000
ʇ ‡ Ê
Ê ‡
Ê ‡
Ê ‡
Ê ‡
Ê ‡ Ê ‡
Ê ‡ Ê ‡
ʇ ‡ Ê
Ê ‡
Ê ‡
Ê ‡
Ê ‡
20
Ê ‡
ʇ ‡ Ê
Ê ‡
Ê ‡
Ê ‡
Ê Ê‡ ‡
Ê ‡
Ê ‡
Ê ‡
ʇ ‡ Ê Ê‡ Ê ‡
Ê ‡
Ê Ê‡ ‡
Ê ‡‡ Ê
Ê ‡
Ê Ê‡ ‡ ʇ Ê ‡ ʇ ‡ Ê
Ê ‡ Ê ‡ Ê ‡
Ê ‡ Ê ‡
Ê ‡ ʇ ʇ ‡ Ê
Ê ‡
Ê Ê‡ ‡
Ê ‡
Ê ‡
40
Ê ‡
Z 20
Ê Ê‡ ʇ ʇ ‡ ʇ ʇ ʇ
60
Ê ‡
Ê Ê‡ ʇ ‡
Ê Ê‡ ʇ ‡
Ê Ê‡ ʇ ʇ ‡ ʇ ‡ ʇ ʇ ʇ Ê
Ê ‡ Ê ‡
80
ʇ ‡ Ê Ê ‡
Ê ‡‡ Ê
100
ATOMIC PERIODIC TABLE
Periodic properties → atomic structure Ionization Energy (similar to B per nucleon) 21
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?
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WHAT ARE THE MAGIC NUMBERS? 2 8 20 28 50 82 126 And why are they called magic?
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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
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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
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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%
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CLASS PARTICIPATION
xkcd.com Courtesy of xkcd.com. License CC BY-NC.
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QUESTIONS?
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22.02 Introduction to Applied Nuclear Physics Spring 2012
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