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
2
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
3
Correction of the book… REMEMBER!
Please ignore the c2. It is confusing
Book: Page 6
4
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
5
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
6
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:
7
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)
8
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
9
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
10
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
11
The error grows as v c
Reminder: simple error is
Accepted Value - Obtained Value100 % Error
Accepted Value
12
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
13
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
14
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
15
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
16
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?
Radiation Interaction with Matter
Ionizing Radiation
19
Photon Interactions
EnergyHighIntermediateLow
Pair Production
Compton Scattering
Photoelectric Effect
20
Pair Production
21
Compton Scattering
22
The Photoelectric Effect
23
Compton Scattering – The Experiment
E
E’
In 1922, Compton obtained this dataScattered X-Rays had an increase in wavelengthCan you explain why?
24
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’
25
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
