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PHYS 571 Radiation Physics
Prof. Gocha Khelashvili
http://blackboard.iit.edu – login
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Textbooks:
1. “Radiation Physics for Medical Physicists”, E.B. Podgorsak, 2nd Edition, Springer, Electronic Book
2. “Atoms, Radiation, and Radiation Protection, James E. Turner 3rd Edition – Electronic Book
3. “Physics for Radiation Protection”, James E. Martin, 3rd Edition – ISBN: 978-3-527-41176-4
Homework Assignments – 30% of Grade Midterm and Final Exams – 35% each
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Goals for Radiation Physics
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Goals for Radiation Physics I
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Goals for Radiation Physics I
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Material Selection for PHYS571
• Failure of Classical Physics • Elements of Quantum Mechanics • Atomic Physics • Nuclear Physics • Radioactivity • Interaction of Heavy Charged Particles with Matter • Interactions of Light Charged Particles with Matter • Interaction of Photons (X-rays and Gamma rays) with Matter • Neutron Physics, Interaction with Matter
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Failure of Classical Physics • Review of Classical Physics • The Failure of Classical Concept of Space and Time • The Failure of the Classical Theory of Particle Statistics • Theory, Experiment, Law • Review of Electromagnetic Waves • Blackbody Radiation and Classical Physics • The Photoelectric Effect • The Compton Effect • Atomic Spectra • Rutherford’s Nuclear Model • Bohr’s Theory of Hydrogen Atom • X-Ray Spectra • Critique of Bohr’s Theory and the “Old” Quantum Mechanics
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Review of Classical Physics: Mechanics
2
2
or ( v)
v
net netd r dp dF ma m F mdt dt dt
p m
L r p
• →
= = = =
•
=
•
= ×
Equation of motion Newton's Second Law
Linear Momentum :
Angular Momentum :
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Review of Classical Physics: Mechanics 2
21 v2 2
Total energy of isolated system remains constant
Total linear mo
b
a
pK mm
U F dr
• = =
• = − ⋅
•
•
∫
Kinetic Energy :
Potential Energy :
Conservation of Energy :
Conservation of Linear Momentum :
mentun of isolated system remains constant
Total angular momentun of isolated system remains constant• Conservation of Angular Momentum :
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Newton's Laws are equaly valid - invariant in every inertial reference frame
Inertial frames are unaccelerated, but they differ in their uniform translational motion.
No mechanical experiment ca
•
•
• n detect a motion of inertial frame by itself.
Uniform translational motion of our inertial frame can only be detected only as motion of our reference frame with respect to another frame.
Is the r
•
• elativity of motion indicated by mechanical experiments applies to electric, magnetic, optical and other experiments?
Classical Principle of Relativity
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Galilean Transformations
x x
x x Vty y dx dx Vdt dx dx V Vz z dt dt dt dtt t
υ υ
′ = − ′ ′= = − ′ ′→ → = = − = − ′ ′ ′= = ′ =
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Failure of Classical Concept of Time
Average lifetime of -meson with v 0.913
63.7 ns in laboratory system
26.0 ns in pion system
L
c
T
Tπ
π• =
≈
≈
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Failure of Classical Concept of Space
( ) ( )
( ) ( )
Average distance travelled by -meson before decay:
Laboratory System v 0.913 63.7 ns 17.4 m
Pion System v 0.913 26.0 ns 7.11 m
L L
L L
D T c
D T c
π
π
π•
= × ≈ × ≈
= × ≈ × ≈
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Failure of Classical Concept of Velocity
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Failure of Classical Concept of Velocity
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Maxwell’s Equations
yElectricitforLawGaussqAdE enc '0
⇒=⋅∫ ε
∫ ⇒=⋅ MagnetismforLawGaussAdB '0
LawsFaradaydt
dsdE B '⇒Φ
−=⋅∫
LawMaxwellAmpereidt
dsdB encE −⇒+
Φ=⋅∫ 000 µεµ
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Electromagnetic Waves
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Give up the notion of electricity and magnetisn are the same in all inertial frames
OR
Give up Galilean addition rule for velocities
•
•
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Albert Einstein
Principle of Relativity Principle of Relativity - 1905,
Albert Einstein proposed that no experiment of any kind should detect an absolute motion of our reference frame - applies to all laws of physics
Founda
•
• tion of Special Theory of Relativity
At high speeds - near the speed of light - particles obey new, rela- tivistic laws which are very diffe- rent from Newton's Laws
•
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Hendrik Antoon Lorentz
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Correspondence Principle
Does this mean that classical physics is all wrong?•
Classical Physics Laws
Relativistic Physics laws
cυ
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Lorentz Transformations
2 2
2 2
2
2
2 2
1
0 if
0
1
x VtxV c x x Vt
y y y yV cV c
z z z zVx ct tt Vx ct
V c
− ′ = − ′ = − ′ = ′ = ≈ → → → ′ = ′ =≈
′ =− ′ =−
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RELATIVISTIC COMBINATION OF VELOCITIES
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2 2
0.80 ( 0.40 ) 0.911 1 (0.80 )( 0.40 ) /
xx
x
V c c cV c c c c
υυυ− − −′ = = =
− − −
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Failure of Classical Theory of Particle Statistics
int
Molar Heat Capacity: 1 (per degree of freedom)2
Monoatomic Gas: 3 2
Diatomic Gas (Rotating): 5 2
Diatomic Gas (Rotating + Vibrat
V
V
V
EC Rn T
C R
C R
•∆
= →∆
•
=
•
=
• ing): 7 2
Classical Theory: - independent of temperature and gas type
V
V
C R
C
=
•
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Failure of Classical Theory of Particle Statistics
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Classical Radiation Theory
22
3
2 | | - Nonrelativistic accelerated charge3
eP ac
=
( )2 2
6 23
2
2 - Relativistic accelerated charge3
1 v= and =c1-
ePcγ β β β
γ ββ
= − ×
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Blackbody Radiation
4Stefan-Boltzmann Law R Tσ=
32.898 10 mK Wien's Displacement LawmTλ −= ×
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Rayleigh-Jeans Equation
( ) ( )
( )
( )
4
4
14
148
8( )
R cU
R cu
n
kTu kTn
λ λ
πλλ
πλ λλ
=
=
=
= =
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Rayleigh-Jeans Equation
4
8)(λπλ Tku =
∫∞
∞→0
)( λλ du
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Planck’s Law
1)/exp(18)( 5 −
=kThc
hcuλλ
πλ
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Photoelectric Effect
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Photoelectric Effect
2
max
Light Intensity vs E.F. amplitude: Low intensity No Current Stopping Potential: Depends on light Intensity
e
stop
I EF eE F
K eV
•• → = < →• = →
Classical Physics :
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Photoelectric Effect
max
max
Low intensity Current No minimum intensity Stopping Potential: Independent of light intensity
Stopping Potential: Depends on light frequency (stop
stop
K eVK eV I
• → →• = →
• = → =
Experiment :
const)
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Photoelectric Effect
max
Einstein's Explanation:
stop
stop
K eV
hV fe e
•
=
Φ = −
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Photoelectric Effect
stophV fe e
Φ = −
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Compton Effect
12
(1 cos )
2.426 10
c
c
hf hpc
h mmc
λλ λ φ
λ −
= =
∆ = −
= = ×
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Atomic Spectra
Newton•
Fraunhofer 150 year later•
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Atomic Spectra
nmn
nn 4
6.364 2
2
−=λ
Balmer Series
−= 22
111nm
Rmnλ
Rydberg – Ritz Formula
1710096776.1 −×= mRH
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Rutherford’s Nuclear Model
J. J. Thompson’s Model of Atom
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Rutherford’s Scattering Theory and the Atomic Nuclear - Experimental Setup
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Force on a Point Charge due to Charged Sphere
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Rutherford’s Scattering Theory and the Atomic Nuclear
Scattering Geometry
20
1( ) cot 2 4
kq Qb km V
α
α
θθπε
= =
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Aiming Parameter and Scattering Cross Section
2( ) cot2
kq Qbm V
α
α
θθ =
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Geiger and Marsden Results
ntbf 2π=
)2/(sin1
2 4
2
20
θ
=∆
k
sc
EkZe
rntAIN