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?

??

??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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5

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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

1000

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.

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 ~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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CLASS PARTICIPATION

xkcd.com Courtesy of xkcd.com. License CC BY-NC.

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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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