ne 105 - introduction to nuclear engineering spring 2011 classroom session 4 - fundamental concepts...
TRANSCRIPT
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NE 105 - Introduction to Nuclear EngineeringSpring 2011
Classroom Session 4 - Fundamental Concepts End
Nuclear Energetics Intro
•Classic and Relativistic Calculations•Photon Interactions with Matter•Nuclear Energetics
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Electron Volt
Work done by one electron accelerated through a potential difference of one volt
1 eV = 1.60217646x10-19 J
Example:What is the speed (m/s) of a 12 eV 134Xe
ion?(from the chart of the nuclides: 134Xe Weights = 133.905394
AMU)Use classic concept of KE for nowamu in table 1.5Joule = Energy, Work = Force (N) x d =kg m2/s2
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Correction of the book… REMEMBER!
Please ignore the c2. It is confusing
Book: Page 6
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4156.4 m/s ~9,300 m.p.hi.e. even very low energy ions are moving pretty fast
Please remember this is ONLY for classical calculations.At energies close to “c”, need to use relativistic calculations
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What is the speed of a 100.00 MeV proton:
102
,540
m/s
5,4
67 g
/s
1.3
8e8
m/s
138
40 m
/s
3e8
m/s
20% 20% 20%20%20%1. 102,540 m/s2. 5,467 g/s3. 1.38e8 m/s4. 13840 m/s5. 3e8 m/s
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100MeV proton = 0.46 c :close to the speed of light.
i.e. classic equations do NOT hold
i.e. 0.46 is likely wrong
What is the speed of a 100.00 MeV proton:
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Newton Laws
For over 200 years, Newton’s laws worked Accurately described many physical
behaviors Unifying the earth and the skies
Previously: Sub-lunar sphere: impure and imperfect Skies: perfect and immutable (circle,
ether)
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Special Theory of Relativity - Effects
“Mass Increase” with increasing velocity
Increase quantified by Lorentz factor ():
m(v) m0
1 v 2 c 2
2 2 1
v<<<c 1 classic limit1 always
v~c 0 effect is max
v c
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Length and time are also modified relative to an object’s speed
For example: To find speed…
L(v) L0 1 v 2 c 2
22
0
1)(
cv
tvt
Special Theory of Relativity - Effects
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What is the kinetic energy of a 100.00 MeV proton?
Hint: Relativistic speeds, i.e. use this equation:
Special Theory of Relativity - Effects
2 20E mc m c KE
m(v) m0
1 v 2 c 2
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The error grows as v c
Reminder: simple error is
Accepted Value - Obtained Value100 % Error
Accepted Value
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Remember
Relativistic calculation required when:
kinetic energy ~ rest energy
What is the rest mass of an electron? What is the rest mass of a p+ or n0? What is the rest mass of heavy ions?
(Table 1.5 book)
Use:eVkeVMeV
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What is the kinetic energy of a 1 MeV electron? Rest mass of the electron, me=0.511MeV
0.5
11 M
eV
0.4
89 M
eV
0.9
99 M
eV
1 M
eV
0 M
eV
20% 20% 20%20%20%
1. 0.511 MeV2. 0.489 MeV3. 0.999 MeV4. 1 MeV5. 0 MeV
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What is the speed of a 1 MeV electron? Rest mass of the electron, me=0.511MeV
0.58c 0.81c
0.86c 0.94c
0.993c
20% 20% 20%20%20%
1. 0.58c2. 0.81c3. 0.86c4. 0.94c5. 0.993c
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Solution:2 2
0
22 0
2
0.511 1 1.511
m cand solving for v, from relativistic equation mc = :
0.5111 0.94
1.511
mc m c KE MeV MeV MeV
v c c
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Special Theory of Relativity - Effects
In Nuclear Engineering we rarely work with neutrons of more than 10MeV.
We stick to classic calculations for KE of p, n, , ions, and fission fragments
Homework 2.3. What is the error in computing speed of a 10 MeV neutron classically instead of relativistically?
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Radiation Interaction with Matter
Ionizing Radiation
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Photon Interactions
EnergyHighIntermediateLow
Pair Production
Compton Scattering
Photoelectric Effect
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Pair Production
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Compton Scattering
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The Photoelectric Effect
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Compton Scattering – The Experiment
E
E’
In 1922, Compton obtained this dataScattered X-Rays had an increase in wavelengthCan you explain why?
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Compton Scattering – Light has p!
If light is a wave, then radiation scattered by an electron should have no change in wavelengthIn 1922, Compton demonstrated that that x-rays scattered from electrons had a decrease in wavelength.
This is only possible if light is treated as a particle with linear momentum equal to p=h/
)cos1(' secm
h
Why the equation written for the photon angle?
1 1 1(1 cos )
' seE E m c
EE’
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Follow equations
But pay attention to unitsFor wavelength please use nm
6.63 -34
e
h e J
m c
. s
9.11e-31 kg 3e8 m / s
1 kg
2m
1 J 2. s
1 9
1
e nm
m [ ] nm