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Introduction to Applied Nuclear Physics
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22.02 INTRODUCTION TO
APPLIED NUCLEAR PHYSICS
Spring 2012
Prof. Paola Cappellaro
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GOALS OF 22.02 INTRODUCTION TO APPLIED NUCLEAR PHYSICS
Learn the basic principles of nuclear andradiation science
After taking this class, you will able tostudy (and understand) any applicationof 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?
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109
42?
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??65
8075
Image by MIT OpenCourseWare.
WHAT ARE THE MAGIC NUMBERS?
A computer program variable ? Rock band?
Iphone App? Games to win to clinch the season?
Number of jobs?
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WHAT ARE THE MAGIC NUMBERS?
© Wikimedia Foundation. License CC BY-SA. This content is excluded from ourCreative Commons license. For more information, see http://ocw.mit.edu/fairuse.7
WHAT ARE THE MAGIC NUMBERS?
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.
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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
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BINDING ENERGY
Mass-energy equivalence
2E = mcNuclei are composed of protons and neutrons,held together by some energy
= MZ mproton + N m
neutron 6 Nucleus 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: Nprotons: 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
XZA
X is the chemical symbol
A = Z + N is the mass number
E.g.: 235U, 238U [Z is redundant here] 92
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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
2 E = mc
Nuclei are held together by the binding energy
= MZ mproton + N m
neutron 6 Nucleus
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
� mN (AX)⇤ c2B =
⇥Zmp + Nmn
In terms of measurable quantities:
2B = �Zmp + Nmn � [mA(AX) � Zme] c
B is always negative for stable nuclei positive
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SEMI-EMPIRICAL MASS FORMULA
M(Z, A) = Zm(1H) + Nmn � B(Z, A)/c2
From a simple model of thenucleus, 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(1H) + Nmn �B(Z, A)/c2
With binding energy given by:Surface Coulomb
B(A, Z) = avA � asA2/3 � acZ(Z � 1)A�1/3
Volume (A� 2Z)2�a + �apA�3/4
symA {
symmetry pairing
17Photo courtesy of cdw9 on Flickr. License CC BY-NC.
SEMF: Binding Energy per Nucleon
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A (Mass number)
B/A
(bin
ding
ene
rgy
per n
ucle
on)
0 50 100 150 200 250
B(Z,A)/A ~ cst.(8 MeV) - corrections
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B/A: JUMPS B
/A
(bin
ding
ene
rgy
per n
ucle
on) 9
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3 A (Mass number)
0 50 100 150 200 250
“Jumps” in Binding energy from experimental data
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ATOMS PERIODIC PROPERTIES kJ
per
Mol
e
2000
1500
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Z
Ionization Energy (similar to B per nucleon)
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ATOMIC PERIODIC TABLE
Periodic properties → atomic structure
Ionization Energy (similar to B per nucleon) 21
CHART OF NUCLIDES
“Periodic”, more complex properties → nuclear structure
http://www.nndc.bnl.gov/chart/
© Brookhaven National Laboratory. All rights reserved. This content is excluded from our Creative Commons license. For more information, see http://ocw.mit.edu/fairuse.
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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 ~1945Observation 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
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22.02 SPRING 2012
Class Logistics
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RECITATIONS
There will be weekly recitations
Recitations will review some topics from lecture andmathematical 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
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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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QUESTIONS?
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MIT OpenCourseWarehttp://ocw.mit.edu
22.02 Introduction to Applied Nuclear PhysicsSpring 2012
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