phys 571 radiation physics - illinois institute of...

PHYS 571 Radiation Physics

Prof. Gocha Khelashvili

http://blackboard.iit.edu – login

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

Goals for Radiation Physics

Goals for Radiation Physics I

Goals for Radiation Physics I

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

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

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 :

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 :

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

Galilean Transformations

x x

x x Vty y dx dx Vdt dx dx V Vz z dt dt dt dtt t

υ υ

′ = − ′ ′= = − ′ ′→ → = = − = − ′ ′ ′= = ′ =

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• =

≈

≈

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•

= × ≈ × ≈

= × ≈ × ≈

Failure of Classical Concept of Velocity

Failure of Classical Concept of Velocity

Maxwell’s Equations

yElectricitforLawGaussqAdE enc '0

⇒=⋅∫ ε

∫ ⇒=⋅ MagnetismforLawGaussAdB '0

LawsFaradaydt

dsdE B '⇒Φ

−=⋅∫

LawMaxwellAmpereidt

dsdB encE −⇒+

Φ=⋅∫ 000 µεµ

Electromagnetic Waves

Give up the notion of electricity and magnetisn are the same in all inertial frames

OR

Give up Galilean addition rule for velocities

•

•

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

•

Hendrik Antoon Lorentz

Correspondence Principle

Does this mean that classical physics is all wrong?•

Classical Physics Laws

Relativistic Physics laws

cυ

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

− ′ = − ′ = − ′ = ′ = ≈ → → → ′ = ′ =≈

′ =− ′ =−

RELATIVISTIC COMBINATION OF VELOCITIES

2 2

0.80 ( 0.40 ) 0.911 1 (0.80 )( 0.40 ) /

xx

x

V c c cV c c c c

υυυ− − −′ = = =

− − −

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

=

•

Failure of Classical Theory of Particle Statistics

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

= − ×

Blackbody Radiation

4Stefan-Boltzmann Law R Tσ=

32.898 10 mK Wien's Displacement LawmTλ −= ×

Rayleigh-Jeans Equation

( ) ( )

( )

( )

4

4

14

148

8( )

R cU

R cu

n

kTu kTn

λ λ

πλλ

πλ λλ

=

=

=

= =

Rayleigh-Jeans Equation

4

8)(λπλ Tku =

∫∞

∞→0

)( λλ du

Planck’s Law

1)/exp(18)( 5 −

=kThc

hcuλλ

πλ

Photoelectric Effect

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 :

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)

Photoelectric Effect

max

Einstein's Explanation:

stop

stop

K eV

hV fe e

•

=

Φ = −

Photoelectric Effect

stophV fe e

Φ = −

Compton Effect

12

(1 cos )

2.426 10

c

c

hf hpc

h mmc

λλ λ φ

λ −

= =

∆ = −

= = ×

Atomic Spectra

Newton•

Fraunhofer 150 year later•

Atomic Spectra

nmn

nn 4

6.364 2

2

−=λ

Balmer Series

−= 22

111nm

Rmnλ

Rydberg – Ritz Formula

1710096776.1 −×= mRH

Rutherford’s Nuclear Model

J. J. Thompson’s Model of Atom

Rutherford’s Scattering Theory and the Atomic Nuclear - Experimental Setup

Force on a Point Charge due to Charged Sphere

Rutherford’s Scattering Theory and the Atomic Nuclear

Scattering Geometry

20

1( ) cot 2 4

kq Qb km V

α

α

θθπε

= =

Aiming Parameter and Scattering Cross Section

2( ) cot2

kq Qbm V

α

α

θθ =

Geiger and Marsden Results

ntbf 2π=

)2/(sin1

2 4

2

20

θ

=∆

k

sc

EkZe

rntAIN