A Summary Of Health Physics

Jordan Daniel Ulmer Health Physics Cheat Sheet – SP2014 P a g e | 1

Time of print: 8:20 AM 5/8/2014

1. Classical Electromagnetism:

Gauss’ Law : ∮

Gravity is similar to field

Gauss’ Law : ∮ No magnetic monopoles

Faraday’s Law : ∮

Ampere’s Law : ∮

∫

2. Fundamental Forces of Nature:

Interaction Strong NuclearElectro-Weak

Gravitational Electromagnetic Weak Nuclear

Equation:𝐹

𝜕𝑈

𝜕𝑥

�� 𝑎𝑏 8𝜋𝐺

𝑐 �� 𝒂𝒃

Relative

Magnitude: − − 3 −

Acting on: Quarks Charged particles Quarks, leptons All particles

Action Descriptor:

Color Electric charge “Flavor” charge Mass

Exchange Particle:

Gluons (𝑔 ) (massless) Photon (𝛾 ) (massless) 𝑊+,𝑊−,𝑍 (massive) Graviton(𝐺 ) (massless)

Fundamental Theory:

(QCD) Quantum Chromodynamics(QED) Quantum

Electrodynamics(QFD) Quantum FlavorDynamics

General Relativity

Notes:Nuclear interactions govern the

shape of the periodic table.

Causes radioactive decay.

Nuclear Physics neglects gravitational effects

3. Newton’s Laws – Classical Mechanics: 1. Inertia: A body continues in motion unless acted upon by an outside force.

2. : The acceleration depends on the net external force.

3. Action Re-action: For every action there is an equal and opposite reaction.

Conservation Laws:

1. Conservation of momentum:

1.1. Collisions1 are the only way to transfer energy of an incoming radiation.

1.1.1. Fissions create fast moving neutrons

1.1.2. Moderators slow neutrons down.

1.1.3. Two body momentum exchange:

1 However particles do not have to “physically” touch.

https://sites.google.com/site/whoisjdu/



𝑝𝑐

𝑚𝑐

2. Conservation of Energy: ( ) ( )

2.1. Photons are massless momentum transfer particles and so

their energy is entirely due to their momentum. This is why

the travel at the speed of light.

2.2. Binomial expansion relativistic approximation of gamma:

2.2.1. √ ( ( ) )

3

2.2.2.

4. Quantum – Probabilistic Mechanics:

Quantum Polar Coordinants(QN):

1. Wave functions describe probabilities in regions of space2:

1.1. ( , , )

Quantum Numbers3 (QN):

2. Oscillations in the radial direction ( ) are described by:

2.1. – Principal QN:

2.2. , , , , , ,

3. Oscillations along the polar angle ( ) are described by:

3.1. – Azimuthal QN:

3.1.1. , , , ( )

4. Oscillations along the angle ( ) are described by:

4.1. – Magnetic QN:

4.1.1. | | , ( ) ( ),

5. Oscillations intrinsic to the particle are described by:

5.1. – Spin QN:

5.1.1. , , , ( )

5.2. – Spin QN:

5.2.1. | | , ( ) ( ),

5.2.2. For fermions(1/2 spin particles), −

6. Pauli Exclusion Principle:

2 CAUTION: Math uses ( , , ) for Spherical Polar Coordinates

3 (Nuclear Energy Levels for +and are described by “Magic numbers”)

𝑝 𝑖 𝑝 𝑖 𝑝 𝑓 𝑝 𝑓

𝑝 𝑚𝑣; 𝑝𝑟𝑒𝑙𝑎𝑡𝑖𝑣𝑖𝑠𝑡𝑖𝑐 𝛾𝑚𝑣

Figure 1: Physics Spherical Polar Coordinates




�� ⊥

𝒎𝒆

𝒒 𝒆

𝑴 𝒎𝒑 ≫ 𝒎𝒆

𝑸 𝒆

𝑭𝑬 𝒎 𝒗𝟐

𝑹𝒏

𝑃+

𝑹𝒏

𝑒−

6.1. No two electrons in an atom may share the same set of quantum numbers ( , , , )

7. Hund’s Rule – to obtain the lowest energy states:

7.1. Electrons spread out in space.

7.2. Electrons tend to orient in spin parallel directions.

Particle wave duality (Max Plank):

1. Massless particle(ie: photons) :

1.1.

2. Energy of an Orbital transition in Hydrogen Atom:

2.1. (

) ( ) (

)

2.2. ie: ( ) − ( ) −

2.2.1. ( ) (

)

Heisenberg Uncertainty principle:

1.

1.1. Nuclear interactions are at greater energies than chemical ones:

1.1.1. ( )

Angular Momentum:

1. Spin angular momentum:

1.1. Plank’s constant:

2. Electric Force:

3. Orbital Radius:

3.1. Bohr Radius:

4. Tangential velocity: ⊥

5. As the Electric Force increases the orbiting

particle’s distance from the center increases.

Hence higher orbitals have lower binding

energies.




5. Forms of Radiation:

Alpha Decay ( ):

1. Decay transformation – Two Daughter Particles:

1.1.

1.2.

1.2.1.

1.2.2.

1.3. Example ( ) :

1.3.1.

3

1.3.2. Conservation of Energy – Energy released:

1.3.2.1.

( ) ( )

1.3.2.2. ( ) (

) 8 8

1.3.3. Energy of Outgoing and – The two daughter particles have momentum in opposite

directions:

1.3.3.1.

(

)

((

) )

1.3.3.2.

8

1.3.3.3. 8 8

2. Rules of Thumb:

2.1. Alphas can be absorbed by a sheet of paper.

2.2. Larger mass than Betas and are monoenergetic.

2.3. Do not lose their energy until the end of their range.

2.4. Most harmful when an Alpha emitter is ingested.

3. Very “stable” due to the “Magic Number” of both +and −

3.1. May form in a nucleus and bounce around until it gains enough energy to escape or quantum

tunnels through the binding energy “barrier”.

Beta Decay ( − − ; + +):

1. Decay transformation – Three Daughter particles:

1.1. Neutron Rich Elements:

1.1.1. −

1.1.2.

1.2. Proton Rich Elements:

1.2.1. +

1.2.2.

2. Beta Attenuation:

2.1. ( ) −

( )

3. Rules of Thumb:




3.1. Energy Spectrum:

3.1.1. Large energy distributions.

3.1.2.

3

3.2. Conservation Constituents:

3.2.1. Neutrino conservation of energy and conservation of momentum.

3.3. Betas are easy to detect because of their charge.

Orbital Electron Capture: 4. Some wavefunctions have overlapping nucleus’s and −can be captured, most frequently from the

inner :

4.1. −

Internal Conversion: 5. Electrons absorb a gamma from a nucleus and is ejected from the atom.

Gamma Decay ( ):

1. Gammas are due to transitions of the nucleus from an excited state.

2. Gamma Attenuation:

2.1. Photons are not stopped but lose energy by changing their wavelength.

Bremmstrahlung – Breaking Radiation: 3. Causes gammas ( ):

3.1. Acceleration of a charge produces photons to transfer momentum. As the charge approaches

the speed of light, the Bremmstrahlung becomes more intense (ie: more photons are emitted).

3.2. See also Cherenkov radiation.

Neutron Decay ( ): 1. Neutron Attenuation:

1.1. Hydrogenous materials (Comparable masses to neutrons) best absorb the energy of incedent

neutrons.

2. Types of materials for “neutron mining”:

2.1. Fissile Isotopes:

2.1.1. Absorb thermal(slow enough to interact) neutrons and produces more neutrons and

byproducts.

2.1.2. Can create a sustained reaction for Nuclear Power.

2.2. Fertile Isotopes:

2.2.1. Isotopes that can be transformed into fissile elements.

2.3. Fissionable Isotopes:

2.3.1. Isotopes which can, at least , provide a temporary production of neutrons from an

incident neutron(fast or thermal).

3. Rules of Thumb:

3.1. Free neutrons decay (

)




3.2. Gammas are used to study neutron capture via neutron activation analysis, since neutrons are

neutral and do not interact electromagnetically.

Other Decays:

1. Multiple Alpha particles in a single decay.

2. Particles heavier than Alpha

6. Effect of different processes ( , , , ) radiation Vs. Energy:

Photoelectric Effect: 1. Energy of a photon is transferred to an electron causing it to be ejected from the atom.

1.1.

→ −

1.2. Similar to Internal Conversion

1.3. The Photoelectric effect is the dominating source for Low-Energy ( ) Gammas.

Compton Scattering Effect:

2. Where an incident gamma is absorbed and gives enough energy to an electron so that the electron

is ejected AND remaining energy is emitted as a new lower energy.

2.1.

→ −

2.2. The Compton Effect is the dominating source for Mid-Energy ( )

Gammas.

Pair Production:

3. The incident photon supplies enough energy to create and electron positron pair.

3.1. → − +

3.2. Effectively pair production is reversed Bremmstrahlung.

3.3. Pair production is the dominating source for High-Energy ( ( ) )

Gammas.

Photodisintegration:

4. Where incoming photons are absorbed by a nucleus which is then excited and subsequently decays

emitting a subatomic particle – a neutron proton or alpha particle is effectively knocked out of the

nucleus.

4.1. →

→ + −

4.2. Only present for very high energies..

Photofusion:

5. Only present for extremely high energies: solar fusion, supernovae….




7. Radioactive Decay and Equilibria Formulae:

1. Definitions:

1.1. ( )

1.2.

1.3. ( )

1.4.

2. Case ( )

Trivial Equilibrium ( ≫ ):

2.1. Assuming B decays MUCH faster than A thus A’s activity can be considered constant

2.1.1. If ( ≫ ) as (

)

;

2.1.2.

2.1.3. Activity Derivation:

2.1.3.1.

2.1.3.2. ∫

−

∫

2.1.3.3. ;

2.1.3.4.

( − )

−

Transient Equilibrium ( ):

2.2. Assuming ( and ( ) )

2.2.1. If B and A decay at a similar rates ( )

2.2.2. Then

− (

− − )

2.2.3. Activity Derivation:

2.2.3.1.

2.2.3.2.

2.2.3.3.

−

2.2.3.4.

( − )

2.2.3.5.

(

) ( − )

2.2.3.6. ∫

( − )

2.2.3.7.

−

( − )

2.2.3.8. if ( )

2.2.3.8.1.

−

2.2.3.9.

− (

( − ) )

2.2.3.10.

− (

− − )




2.2.3.11.

− (

− − )

2.2.3.12. if ( ≫ ) ;

2.2.3.12.1.

−

2.2.3.12.2.

−

2.2.4. Maximum Activity:

2.2.4.1.

( )

8. Radioactive Dose:

Definitions and Formulae:

1.

2. ( ⁄ )( )

( ) ( ) ( ) ( ) (

) (

) ( 3)

(

)

3. ( ⁄ )

4. ⁄ ( ) ⁄ ( ⁄ )

5. ( )

6. [

]

( )

(

3 ⁄

⁄

) [ ] (

) (

) [

](

) (

)

3 ⁄

⁄

7. [

]

( )

(

⁄

)

3

⁄

(

)

(

) [

]

8. [

]

( ) (

) (

) (

)

( )

Units: 1. Dose:

1.1. Physical quantity:

1.1.1. ⁄ ( )

( ⁄ )

1.2. Biological Effect:

1.2.1. ( ) ⁄

2. Exposure:

2.1. [ ( )] 88

2.2. [ ( )]

3. Quality Factor:

3.1. Signal processing concept equal to the center frequency divided by the bandwidth:

3.2.




Effectiveness of Radiation by Type

Form of radiation Energy Quality factor ( )

Gamma “Low” 1

Gamma “High” 10

Alpha ~ 20

Neutrons 10

9. Radiation and Biology:

Central Dogma of Biology:

{

{

The Cell Cycle:

Mitosis(“Mass production”): The cell splits once.

Meiosis(Reproductive): The cell splits four times.

(GAP-1)

•"Metabolic changes prepare cell for

devision"

S (Synthesis)

•"DNA synthesis replicates the genetic

material"

•Each chromosome consists of two sister

chromatids

(GAP-2)

•"Material is collected"

•Metabolic changes assemble cytoplasmic material needed for mitosis Cytokinesis.

Mitosis / Cytokinesis (M

Phase)

•"The actual splitting of the cell"

•Nuclear division and cell division

Cel

l Div

isio

n

Interphase: Chromozones become condensed and duplicate.

Polyphase: Chromosomes become "visable" & fiberous cnteriolies move to oposite sides of the cell.

Metaphase: Chromosomes "line up" to be "split apart".

Telophase: Membranes form & the cell begins to split in two.




Human Biological Systems:

Reproductive:

• "Sex organs:"

• Male:

• Testes

• Vas deferens

• Seminal vesicles

• Prostate

• Penis

• Female:

• Ovaries

• Fallopian tubes

• Uterus

• Vagina

• Mammary glands

Digestive:

• "Processes food with:"

• Salivary glands

• Esophagus

• Stomach

• Liver

• Gallbladder

• pancreas

• intestines

• rectum

• anus

Respiratory:

• "Breathing:"

• Pharynx

• Larynx

• Trachea

• Bronchi

• Lungs

• Diaphragm

Immune:

•"Systems that fight disease:"

•Leukocytes

•Eat bacteria and fungi

•Tonsils

•Adenoids

•Thymus

•Spleen

Musculoskeletal:

•"Movement and structure:"

•Muscles:

•Ligaments

•Tendons

•Skeleton:

•Bones

•Cartilage

Urinary:

•"Fluid and electrolyte balance and excretion:"

•Kidneys

•Ureters

•Bladder

•Urethra

Endocannabinoid:

•"Lipids and receptors that control:"

•Appetite

•Mood

•Motor learning

•Memory

•Synaptic plasticity

•"Speed of neural communication"

Endocrine:

•"Secretion of hormones made by:"

•Endocrine glands:

•Hypothalamus

•Pituitary gland

•Pineal body/gland

•Thyroid

•Parathyroids

•Adrenals

•Adrenal glands...

Lymphatic:

•"Systems that transfer of lymph(blood clotting fluid) through the body:"

•Lymph

•Nodes

•Source of lymph in lymphocytes

•Transfer vessels

Circulatory:

•"Pumps blood through the body with:"

•Heart

•Blood vessels

Vestibular:

•"Balance and orientation:"

•Inner ear:

•Cupula

•"Directional antenna"

•Otoliths

•"Accelerometer"




Effect of Radiation on Biological Systems:

Human Low-Dose Radiobiology Effect Process (Dr. Gary Yarrow):

Cellular lifetimes: Cellular Structure Lifetime

White Blood Cells 13 days

Red Blood Cells 120 days

Liver Cells 500 days

Nerve Cells 100 years (May develop but do not reproduce)

Prompt Effects: 1. Acute Damage: ” high dose in short period of time”

1.1. Kills cells:

1.1.1. (-): May kill too many cells for the body to “bounce back”

1.1.2. (+): Dead cells cannot create cancerous mutations

Prompt Effect of the Absorbed Radiation Dose Acute Dose (rem)

Blood count changes

Vomiting (threshold)

Energy Deposition in Tissues (Ea) Local Biochemical Change(s)

Genetic Aberrations

Delayed Physical Effects

Mutagenesis “Mutation” (Hereditary effects)

Carcinogenesis (Carcinogens cancer causing)

Teratogenesis “Embryonic Defects” (in utero effects)

Cellular Damages

Early physical effects-difficult/impossible To measure at low doses




Morality (threshold)

(Lethal Dose4 with minimal supportive medical care)

(Lethal Dose with supportive medical care) 8

mortality (Lethal Dose with best medical care) 8

Delayed Effects: 1. Chronic Damage: ” low dose over an extended period of time”

1.1. Effects not immediately seen.

Radiosensitivity of Biological Systems – Bergonie and Tribondeau “Law”:

4 Lethal Dose means , that there is an average mortality rate within of the dose reception.

Delayed Effects of Radiation

Cataracts Dose:

Target: Lense of Eye

Realization Timeline:

Cancer Dose/Risk Correspondence: risk of death from cancer , ,

Realization Timeline:

Radiation Induced Cancers: Leukemia, Multiple Myeloma, Brest Cancer, Lung Cancer, and Skin Cancer




10. Table of Contents:

1. Classical Electromagnetism: ................................................................................................ 1

2. Fundamental Forces of Nature: ........................................................................................... 1

3. Newton’s Laws – Classical Mechanics : ............................................................................... 1

4. Quantum – Probabilistic Mechanics: ................................................................................... 2

Quantum Polar Coordinants(QN): .............................................................................................. 2

Quantum Numbers (QN): ............................................................................................................ 2

Particle wave duality (Max Plank): .............................................................................................. 3

Heisenberg Uncertainty principle: .............................................................................................. 3

Angular Momentum: .................................................................................................................. 3

5. Forms of Radiation: .............................................................................................................. 4

Alpha Decay ( ): .......................................................................................................... 4

Beta Decay ( ; ): ............................................................................................ 4

Orbital Electron Capture: ...................................................................................................................... 5

Internal Conversion: .............................................................................................................................. 5

Gamma Decay ( ): ................................................................................................. 5

Bremmstrahlung – Breaking Radiation: ................................................................................................ 5

Neutron Decay ( ): .............................................................................................. 5

Most Sensitive

Least Sensitive




Other Decays: .............................................................................................................................. 6

Effect of ( , , , ) radiation Vs. Energy: ......................................................................... 6

Radioactive Decay and Equilibria Formulae: .................................................................................. 7

6. Radiation and Biology: ......................................................................................................... 8

Central dogma of biology: ........................................................................................................... 9

The Cell Cycle: ............................................................................................................................. 9

Human Biological Systems: ....................................................................................................... 10

Effect of Radiation on Biological Systems: ................................................................................ 11

Human Low-Dose Radiobiology Effect Process (Dr. Gary Yarrow): .................................................... 11

Cellular lifetimes: ................................................................................................................................ 11

Prompt Effects: ................................................................................................................................... 11

Delayed Effects: .................................................................................................................................. 12

Radiosensitivity of Biological Systems – Bergonie and Tribondeau “Law”: ........................................ 12

7. Table of Contents: .............................................................................................................. 13

A. Figures: ........................................................................................................................... 14

B. Tables: ............................................................................................................................ 14

A. Figures:

Figure 1: Physics Spherical Polar Coordinates 2

B. Tables:

No table of figures entries found.


A Summary Of Health Physics

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