# Presentation: 004104

## betas, protons, alphas and other heavy charged particles as 16O, gamma and x-rays, and neutrons

to understand the physical basis for radiation dosimetry/radiation shielding, one must be able to comprehend the mechanisms by which radiations interact with matter including biological material

**to understand the physical basis for radiation dosimetry/radiation shielding, one must be able to comprehend the mechanisms by which radiations interact with matter including biological material**

**Interaction of Beta and Charged Particles with Matter**

## in any type of matter, radiation may interact with the nuclei or the electrons, in excitation or ionization of the absorber atoms

finally, the energy transferred either to tissue or to irradiation shield is dissipated as heat

Consider: What is the difference between excitation and ionization?

**finally, the energy transferred either to tissue or to irradiation shield is dissipated as heat**
**Consider: What is the difference between excitation and ionization?**

**Interaction of Beta and Charged **
**Particles with Matter**

## Heavy Charged Particles (HCP)

** ****Energy Loss Mechanisms**
**protons, alphas, ****12****C,  ****16****O, ****14****N; not electrons or positrons (β****-****, β****+****)**
**HCP traversing matter loses energy primarily through the ionization and excitation of atoms**
**except at low velocities, a HCP loses a negligible amount of energy in nuclear collisions**

## HCP exerts electromagnetic forces on atomic electrons and imparts energy to them

energy transferred can be sufficient to knock an electron out of an atom and ionize it

or it may leave the atom in an excited non-ionized state

since a HCP loses only a small fraction of its energy in a simple collision and almost in a straight path, it loses energy continuously in small amounts through multiple collisions leaving ionized and excited atoms

**energy transferred can be sufficient to knock an electron out of an atom and ionize it**
**or it may leave the atom in an excited non-ionized state**
**since a HCP loses only a small fraction of its energy in a simple collision and almost in a straight path, it loses energy continuously in small amounts through multiple collisions leaving ionized and excited atoms**

**Heavy Charged Particles (HCP)**

## Heavy Charged Particles (HCP)

**Maximum Energy Transfer in a Simple Collision**

**Heavy Charged Particles (HCP)**

## since momentum and energy are conserved:

**where E = MV****2****/2 is the initial kinetic energy of the heavy particle**

**Heavy Charged Particles (HCP)**

## when M = m, Qmax = E; so the incident particle can transfer all of its energy in a billiard ball type collision

calculate the maximum energy of a 10 MeV proton can lose on a single collision can be treated non-relativistically 

**calculate the maximum energy of a 10 MeV proton can lose on a single collision can be treated non-relativistically **

**since the mass of electron is « mass of the proton ******

**Heavy Charged Particles (HCP)**

## Heavy Charged Particles (HCP)

**for a relativistic expression:**

**Heavy Charged Particles (HCP)**

## Heavy Charged Particles (HCP)

**and**
**	****	****       ****β = v/c**
**c is the speed of light**
**	****            **
**Q****max**** = 21.9 keV**

**Heavy Charged Particles (HCP)**

## Maximum Possible Energy Transfer Qmaxin Proton Collision with Electron

## 3. Stopping Power
linear rate of energy loss to atomic electrons along the path of a HCP in a medium (MeV/cm) is the basic physical quantity that determines the dose that particle delivers in the medium
quantity -dE/dx is the stopping power of the medium for the particle

**linear rate of energy loss to atomic electrons along the path of a HCP in a medium (MeV/cm) is the basic physical quantity that determines the dose that particle delivers in the medium**
**quantity -dE/dx is the stopping power of the medium for the particle**

**Heavy Charged Particles (HCP)**

## where:
z  = atomic no. of HCP
e  = magnitude of electron charge
m = no. of electrons/unit volume in medium
c  = speed of light
β  = v/c = speed of particle relative to c
i  = mean excitation energy of medium

stopping power depends only on charge ze and velocity β of the particle 
mass of stopping power =
-dE/ρdx (stopping power/density)

**z  = atomic no. of HCP**
**e  = magnitude of electron charge**
**m = no. of electrons/unit volume in medium**
**c  = speed of light**
**β  = v/c = speed of particle relative to c**
**i  = mean excitation energy of medium**
**stopping power depends only on charge ze and velocity β of the particle **
**mass of stopping power =**
**-dE/ρdx (stopping power/density)**

**Heavy Charged Particles (HCP)**

## expresses the rate of energy loss of the charged particle per g/cm2

mass stopping power does not differ greatly for materials with similar atomic composition
eg 
for 10 MeV protons:
-dE/ρdx for H2O is 45.9 MeV cm2/g
              and for anthracine (C14H10) it is 
   44.2 MeV cm2/g

**mass stopping power does not differ greatly for materials with similar atomic composition**
_**eg**_** **
**for 10 MeV protons:**
***-dE/ρdx for H******2******O is 45.9 MeV cm******2******/g***
**              ****and for anthracine (C****14****H****10****) it is **
**   ****44.2 MeV cm****2****/g**

**Heavy Charged Particles (HCP)**

## Slide 14

## for 10 MeV protons and Pb (z = 82)
			-dE/ρdx = 17.5 MeV  cm2/g

in general heavy atoms are less efficient on a cm2/g basis for slowing down HCP

the reason being that many of their electrons are too tightly bound to the inner shells to absorb energy

**	****	****	****-dE/ρdx = 17.5 MeV  cm****2****/g**
**in general heavy atoms are less efficient on a cm****2****/g basis for slowing down HCP**
**the reason being that many of their electrons are too tightly bound to the inner shells to absorb energy**

**Heavy Charged Particles (HCP)**

## 4. Mean Excitation Energies
the following empirical formula can be used
		                      19.0 eV,   z = 1
I = 11.2 + 11.7z eV,   2 ≤ z ≤ 13
        52.8 + 8.71z eV,   z ≥ 13

for a compound or a mixture the stopping power is calculated by the separate contribution of the individual constituent elements

**the following empirical formula can be used**
**	****	****                      ****19.0 eV,   z = 1**
**I = 11.2 + 11.7z eV,   2 ≤ z ≤ 13**
**        ****52.8 + 8.71z eV,   z ≥ 13**
**for a compound or a mixture the stopping power is calculated by the separate contribution of the individual constituent elements**

**Heavy Charged Particles (HCP)**

## if there are nI atoms/cm2 of an element with atomic number zI and mean excitation energy iI   

**n is the total number of electrons/cm****2**** in the material**
**calculate mean excitation energy of H****2****o**
**	****	****	****	****I****n**** = 19.0 eV**
**	****	****	****I****0**** = 11.2 + 11.7 ******** 8 = 105 eV**
**electron densities n****i****z****i**** can be computed, however only rations n****i****z****i****/n are needed **

**Heavy Charged Particles (HCP)**

## H2O has 10 electrons, 2 to H and 8 to O  

**Heavy Charged Particles (HCP)**

## 5. Table for Computation of Stopping     Powers

to develop a numerical table to facilitate the computation of stopping power of HCP in any material

**to develop a numerical table to facilitate the computation of stopping power of HCP in any material**

**Heavy Charged Particles (HCP)**

## units of those e4n/mc

**replaced erg/cm to replace esu****2**
**converting  to MeV we get:**

**Heavy Charged Particles (HCP)**

## general formula of any HCP in any medium is:

**where**

**Heavy Charged Particles (HCP)**

## Data for Computation of Stopping Power for Heavy Charged Particles

## since for any given value any β, the KE of a particle is  proportional to its rest mass, the table can also be used for other HCP

ratio of KE of a deuteron and proton traveling at the same  speed is:

**ratio of KE of a deuteron and proton traveling at the same ******** speed is:**

- F(β) for 10  MeV is the same for a 20 MeV deuteron

**Data for Computation of Stopping **
**Power for Heavy Charged Particles**

## 6. Stopping Power of H2O for Protons
protons z = 1 and for water
      n = (10/18)  6.02  1023 = 3.34  1023 cm-3
      lnIeV = 4.312   

**protons z = 1 and for water**
**      ****n = (10/18) ******** 6.02 ******** 10****23**** = 3.34 ******** 10****23**** cm****-3**
**      ****lnI****eV**** = 4.312   ******

**at 1 MeV:**

**Data for Computation of Stopping **
**Power for Heavy Charged Particles**

## 7. Range

range of charged particle is distance it travels before coming to rest

reciprocal of the stopping power give the distance traveled per unit energy loss:

**range of charged particle is distance it travels before coming to rest**
**reciprocal of the stopping power give the distance traveled per unit energy loss:**

**Heavy Charged Particles (HCP)**

## where R(E) = range of the particle kinetic energy E

range is expressed in g/cm2

above equation can not be evaluated but range can be expressed as:

**range is expressed in g/cm****2**
**above equation can not be evaluated but range can be expressed as:**

**Heavy Charged Particles (HCP)**

## where:
		z - is the particle's charge
		g(β) - depends on the particle’s velocity

recall:

**	****	****z - is the particle's charge**
**	****	****g(β) - depends on the particle’s velocity**
**recall:**

**and M is the particle's rest mass  ******
**dE = Mg(β)dβ and g is another function of velocity**

**Heavy Charged Particles (HCP)**

## Heavy Charged Particles (HCP)

**where ƒ(β) depends only on velocity of HCP**
**since ƒ(β) is the same for two hcp with the same speed β, the ratio of their ranges is simply:**

## where:   
		m1 and m2 are the rest masses
		z1 and z2 are the charges

if particle number 2 is a proton then m1=z2=1, then the range r of the other particle (mass m1 = m proton mass and charge z1 = z2) is:

**	****	****m****1**** and m****2**** are the rest masses**
**	****	****z****1**** and z****2**** are the charges**
**if particle number 2 is a proton then m****1****=z****2****=1, then the range r of the other particle (mass m****1**** = m proton mass and charge z****1**** = z****2****) is:**

**where:**
**	****	****R****p****(β) is the proton range**

**Heavy Charged Particles (HCP)**

## Mass Stopping Power dE/ρdx andRange Rp for Protons in Water

**Mass Stopping Power dE/ρdx and****Range Rp for Protons in Water**

## problem: find the range of 80 MeV 3He2+ ion in soft tissue	

**range is 3/4 that of a proton with the speed and 80 MeV ****3****He****2+**** ion**
**	****	****	****speed e = mc****2****(γ-1) at - 80 MeV   ******
**	****	****	****  ****mc****2**** = 3 AMU= 3 ******** 931.48 =2794 MeV**

**Heavy Charged Particles (HCP)**

## where:
	  = 1.029
		β2 = 0.0550

value is between Rp = 0.623 and 0.864 g/cm2

by interpolation   β2    rp = 0.715 g/cm2

the range for 80 MeV 3He2+ is:
	3(0.715)/4 g/cm2 in soft tissue (assume unit density)

for a given proton energy the range in g/cm2 is > in Pb than H2o; which is consistent with the smaller mass stopping power

**	**** ******** ****= 1.029**
**	****	****β****2**** = 0.0550**
**value is between R****p**** = 0.623 and 0.864 g/cm****2**
**by interpolation  ******** β****2 ****   r****p**** = 0.715 g/cm****2**
**the range for 80 MeV ****3****He****2+**** is:**
**	****3(0.715)/4 g/cm****2**** in soft tissue (assume unit density)**
**for a given proton energy the range in g/cm****2**** is > in Pb than H****2****o; which is consistent with the smaller mass stopping power**

**Heavy Charged Particles (HCP)**

## Slide 33

## the range in cm for alpha particles in air is given by the approximate empirical relation 
		R = 0.56E  E<4
		R = 1.24E -2.62  4<E<8 where E is in MeV
radon daughter 214Po emits 7.69 MeV alpha particle.  What is the range of this particle in soft tissue?
recall:

**	****	****R = 0.56E  E<4**
**	****	****R = 1.24E -2.62  4<E<8 where E is in MeV**
**radon daughter ****214****Po emits 7.69 MeV alpha particle.  What is the range of this particle in soft tissue?**
**recall:**

**Heavy Charged Particles (HCP****)**

## ranges of both of these are the same for the same velocity

ratio of KE energies is:
			Eα/Ep = mα/mp = 4   
			Ep = Eα/4 = 7.69/4 = 1.92 MeV

the alpha particle range is equal to the range of 1.92 Mev proton

interpolation from mass stopping power table   
			Rp = Rα= 6.6  10-3 cm

**ratio of KE energies is:**
**	****	****	****E****α****/E****p**** = m****α****/m****p**** = 4   ******
**	****	****	****E****p**** = E****α****/4 = 7.69/4 = 1.92 MeV**
**the alpha particle range is equal to the range of 1.92 Mev proton**
**interpolation from mass stopping power table   ******
**	****	****	****R****p**** = R****α****= 6.6 ******** 10****-3**** cm**

**Heavy Charged Particles (HCP)**

## hence the 214Po alpha particle cannot penetrate the 7  10-3 cm minimum epidermal thickness from outside the body to reach the lung cells

however once inhaled the range of alpha particles is sufficient to reach cells in the bronchial epithelium

increase in lung cancer incidence among uranium miners has been linked to alpha particle doses from inhaled radon daughters

**however once inhaled the range of alpha particles is sufficient to reach cells in the bronchial epithelium**
**increase in lung cancer incidence among uranium miners has been linked to alpha particle doses from inhaled radon daughters**

**Heavy Charged Particles (HCP)**

## another way of estimating the range of alpha particles in any medium is:
		Rm mg/cm2 = 0.56 A1/3 R

where:
		A = atomic number of the medium
		R = range of the alpha particle in air

**	****	****R****m**** mg/cm****2**** = 0.56 A****1/3**** R**
**where:**
**	****	****A = atomic number of the medium**
**	****	****R = range of the alpha particle in air**

**Heavy Charged Particles (HCP****)**

## Slide 38

## what thickness of Al foil, density 2.7 g/cm3  is required to stop an alpha particle of  5.3 MeV 210Po
		 R = 1.24  5.3 - 2.62 = 3.95 cm
		Rm = 0.56  271/3  3.95 = 6.64 mg/cm2

for 27Al,  A = 27

let us introduce the concept of td (density thickness) where:
		td [g/cm2] = ρ [g/cm3]  tl [cm]
		ρ = density
		 tl = linear thickness

**	****	**** ****R = 1.24 ******** 5.3 - 2.62 = 3.95 cm**
**	****	****R****m**** = 0.56 ******** 27****1/3**** ******** 3.95 = 6.64 mg/cm****2**
**for ****27****Al,  A = 27**
**let us introduce the concept of t****d**** (density thickness) where:**
**	****	****t****d**** [g/cm****2****] = ρ [g/cm****3****] ******** t****l**** [cm]**
**	****	****ρ = density**
**	****	**** ****t****l**** = linear thickness**

**Heavy Charged Particles (HCP)**

## therefore 6.64 mg/cm2 is the density thickness, 2.7 g/cm3 is the density of aluminum   

**because effective atomic composition of tissue is not very much different from that of air we can have:**
**	****	****	****R****a**** ******** ρ****a**** = R****t**** ******** ρ****t**

**Heavy Charged Particles (HCP)**

## where:
	 Ra and Rt = ranges in air and tissue
	 ρa and ρt  = density of air and tissue 			       (1g/cm3)

what is the range of the 214Po 7.69 MeV alpha particle previously done?

**	**** ****R****a**** and R****t**** = ranges in air and tissue**
**	**** ****ρ****a**** and ρ****t****  = density of air and tissue ****	****	****	****       (1g/cm****3****)**
**what is the range of the ****214****Po 7.69 MeV alpha particle previously done?**

**as compared to 6.6 ******** 10****-3**** cm (35% higher)**

**Heavy Charged Particles (HCP)**

## 8. Slowing-down rate

one can calculate the rate at which a HCP slows down
rate of energy loss -dE/dt is expressed as (by the chain rule of differentiation):

**one can calculate the rate at which a HCP slows down**
**rate of energy loss -dE/dt is expressed as (by the chain rule of differentiation):**

**where****:**

**Heavy Charged Particles (HCP)**

## calculate the slowing down rate and estimate stopping time , for 0.5 MeV protons in water	

**Heavy Charged Particles (HCP)**

## stopping power ρ for protons in water

recall:

**recall:**

**Heavy Charged Particles (HCP)**

## to estimate the time it takes a proton of kinetic energy e to stop we take the ratio:

**Heavy Charged Particles (HCP****)**

## Calculated Slowing Down Rates -dE/dt and Estimated Stopping Time  for Protons in Water

## BETA PARTICLES (β+, β-)

**   ****1. Energy-loss Mechanisms**
**	**
**excitation and ionization- beta particles can also radiate energy by bremsstrahlung**
**2. Collision Stopping Power**
**	****different than for heavy charged particles because the beta particle can lose a large fraction of its energy in the first collision**
**also since β****-**** is identical to the atomic electrons and β****+****  is the anti-particle certain symmetry conditions are required**

## the collisional stopping power for β- and β+ is written:

**where:**

**	****     ******** ****=E/mc****2**** - is the KE of β****+**** or β****-**
**	****mc****2**** = electron rest energy**

**BETA PARTICLES (β****+****, β****-****)**

## as with HCP the symbols e, n, β2 are the same

**where:**

**BETA PARTICLES (β****+****, β****-****)**

## calculate the collisional stopping power of water for 1 MeV electrons

need  to compute β2,, F-(β) and g-(β)

for water

**need  to compute β****2****,********, F****-****(β) and g****-****(β)**
**for water**

**BETA PARTICLES (β****+****, β****-****)**

## in Iev = 4.31

using relativistic formula for e=1 MeV and mc2 = 0.511 MeV:

**using relativistic formula for e=1 MeV and mc****2**** = 0.511 MeV:**

**BETA PARTICLES (β****+****, β****-****)**

## finally

**BETA PARTICLES (β****+****, β****-****)**

## total stopping power for β+ and β- is the sum of the collisional and radiative contributions

**table in Turner exhibits these characteristics for 10 eV to 1000 MeV kinetic energy of beta particle**

**BETA PARTICLES (β****+****, β****-****)**

## BETA PARTICLES (β+, β-)

**BETA PARTICLES (β****+****, β****-****)**

##    3. Radiative Stopping Power

beta particles, because of their small mass can be accelerated by electromagnetic forces within an atom and hence emit radiation called Bremsstrahlung

Bremsstrahlung occurs where a beta particle is deflected in the electric field of a nucleus and to a lesser extent in the field of an atomic electron

at high beta particle energies, the radiation is emitted mostly in the forward direction

**beta particles, because of their small mass can be accelerated by electromagnetic forces within an atom and hence emit radiation called *****Bremsstrahlung***
**Bremsstrahlung occurs where a beta particle is deflected in the electric field of a nucleus and to a lesser extent in the field of an atomic electron**
**at high beta particle energies, the radiation is emitted mostly in the forward direction**

**BETA PARTICLES (β****+****, β****-****)**

## efficiency of Bremsstrahlung in elements of different atomic number Z varies nearly as Z2

for beta particles of a given energy bremsstrahlung losses are considerably greater in high-Z materials such as Pb than in low-Z materials such as water

collision loss rate is proportional to n and hence Z

radiative loss rate increases nearly linearly with beta particle energy where as collisional rate increases  only logarithmically

**for beta particles of a given energy bremsstrahlung losses are considerably greater in high-Z materials such as Pb than in low-Z materials such as water**
**collision loss rate is proportional to n and hence Z**
**radiative loss rate increases nearly linearly with beta particle energy where as collisional rate increases  only logarithmically**

**BETA PARTICLES (β****+****, β****-****)**

## at high energies Bremsstrahlung becomes the predominant mechanism of energy loss

the ratio of radiative and collisional stopping powers for an electron of total energy E (MeV) in an element number Z is:

**the ratio of radiative and collisional stopping powers for an electron of total energy E (MeV) in an element number Z is:**

**BETA PARTICLES (β****+****, β****-****)**

## for Pb (Z=82) we have: 

**when the total electron energy ******** 9.8 MeV (for KE = E-mc****2**** ******** 9.3 MeV)**
**for oxygen (Z = 8)**

**BETA PARTICLES (β****+****, β****-****)**

## when the total electron energy  100 MeV  KE have an order of magnitude difference to have the radiative and collisional stopping powers to be equal

at very high energies the dominance of the radiative over collisional energy results in electron-photon cascades which in turn produces Compton electrons and electron-positron pairs and more Bremsstrahlung 

**at very high energies the dominance of the radiative over collisional energy results in electron-photon cascades which in turn produces Compton electrons and electron-positron pairs and more Bremsstrahlung **

**BETA PARTICLES (β****+****, β****-****)**

## 4. Radiation Yield

an estimate of the radiation yield is very important in trying to deduce the potential Bremsstrahlung hazard of strong beta sources where:
Y = radiation yield
		Z = atomic number of absorber
E = critical KE energy of the beta 
	    particle

**an estimate of the radiation yield is very important in trying to deduce the potential Bremsstrahlung hazard of strong beta sources where:**
**Y = radiation yield**
**	****	****Z = atomic number of absorber**
**E = critical KE energy of the beta **
**	****    ****particle**

**BETA PARTICLES (β****+****, β****-****)**

## Bremsstrahlung

**BETA PARTICLES (β****+****, β****-****)**

## for aluminum:
	        ZE = 13  2 

**	****        ****ZE = 13 ******** 2 ******

**this represents 1.6% of the KE of the beta particle**

** ****problem: estimate the fraction of a 2 MeV **
**beta particle that is converted into Bremsstrahlung  when it is absorbed by aluminum and lead**

**BETA PARTICLES (β****+****, β****-****)**

## this represents 9% of the KE of the beta particle

hence it is prudent in shielding a source to stop the beta particles with a low z material and then attenuate the Bremsstrahlung photons with a high z material

**hence it is prudent in shielding a source to stop the beta particles with a low z material and then attenuate the Bremsstrahlung photons with a high z material**

** ****for Pb  ZE = 82 ******** 2 ******

**BETA PARTICLES (β****+****, β****-****)**

## BETA PARTICLES (β+, β-)

**BETA PARTICLES (β****+****, β****-****)**

## problem: 10 mCi 90Y source enclosed in a lead shield thick enough to stop all the beta particles where the maximum beta energy is 2.27 MeV and average beta energy is 0.76 MeV

estimate the rate at which energy is radiated as bremsstrahlung and estimate photon flux rate at 1 meter from the source

**estimate the rate at which energy is radiated as bremsstrahlung and estimate photon flux rate at 1 meter from the source**

**BETA PARTICLES (β****+****, β****-****)**

## total beta particle energy released for a 10 mCi source is:

(3.7  108/sec)(0.76 MeV) = 2.81  108 MeV/sec

fluence rate at 1 meter is calculated as when:
	   = flux 
	Eβ = average beta energy    

**(3.7 ******** 10****8****/sec)(0.76 MeV) = 2.81 ******** 10****8**** MeV/sec**
**fluence rate at 1 meter is calculated as when:**
**	********   ****= flux **
**	****E****β**** = average beta energy    ******

**BETA PARTICLES (β****+****,**** ****β****-****)**

## BETA PARTICLES (β+, β-)

## we divide by 2.27 MeV since it is assumed that all the beta particle energy is converted to 2.27 MeV photon

this is a conservative approach in assessing radiation hazards

another formula for estimating the yield is:
			Y = 3.5  10-4 ZE

**this is a conservative approach in assessing radiation hazards**
**another formula for estimating the yield is:**
**	****	****	****Y = 3.5 ******** 10****-4**** ZE**

**BETA PARTICLES (β****+****, β****-****)**

##   5. Range

the collisional mass stopping power for beta particles is smaller in high Z materials, such as Pb, than in water

the following empirical equation for electrons in low Z material relates the range R in g/cm2 to the kinetic energy E in MeV

**the collisional mass stopping power for beta particles is smaller in high Z materials, such as Pb, than in water**
**the following empirical equation for electrons in low Z material relates the range R in g/cm****2**** to the kinetic energy E in MeV**

**BETA PARTICLES (β+, β-)**

## for  0.01  E  2.5 MeV
			    R = 0.412 E1.27-0.095 lnE   or
			 lnE = 6.63 - 3.24 (3.29- lnR)1/2	

for  E > 2.5 MeV
			R = 0.530E -0.106   or
			E = 1.89R + 0.200

**	****	****	****    ****R = 0.412 E****1.27-0.095 lnE****   or**
**	****	****	**** ****lnE = 6.63 - 3.24 (3.29- lnR)****1/2****	**
**for  E > 2.5 MeV**
**	****	****	****R = 0.530E -0.106   or**
**	****	****	****E = 1.89R + 0.200**

**BETA PARTICLES (β****+****, β****-****)**

## Heavy Charged Particles (HCP)

**Heavy Charged Particles (HCP)**

## Heavy Charged Particles (HCP)

**Heavy Charged Particles (HCP)**

## problem: how much energy does a 2.2 MeV electron lose in passing through 5mm of lucite?
	(ρ = 1.19 g/cm2)

compare using both the equations and graph
	R = 0.412(2.2)1.27-0.00954 ln2.2
	    = 1.06 g/cm2

recall:

**	****(ρ = 1.19 g/cm****2****)**
**compare using both the equations and graph**
**	****R = 0.412(2.2)****1.27-0.00954**** ln2.2**
**	****    ****= 1.06 g/cm****2**
**recall:**

**BETA PARTICLES (β****+****, β****-****)**

## BETA PARTICLES (β+, β-)

**since the lucite is only 0.5 cm thick, the electron emerges with enough energy E******** to travel another (0.891 - 0.5) cm =.391 cm or  0.465 g/cm****2**

**BETA PARTICLES (β****+****, β****-****)**

## we then can use:
	ln E = 6.63 - 3.24 (3.29 - ln 0.465)1/2
                = 0.105
  	 E - 1.11 MeV

which all agrees with the graph

therefore the energy lost by the electron is:
	E - E = (2.20 - 1.1) MeV = 1.09 MeV

**	****ln E******** ****= 6.63 - 3.24 (3.29 - ln 0.465)****1/2**
**               **** ****= 0.105**
**  ********	**** ****E******** - 1.11 MeV**
**which all agrees with the graph**
**therefore the energy lost by the electron is:**
**	****E - E******** ****= (2.20 - 1.1) MeV = 1.09 MeV**

**BETA PARTICLES (β****+****, β****-****)**

## 
unlike alpha particles, beta particles have numerous radionuclides with ranges > the thickness of the epidermis

even a 70 keV electron can penetrate the 
    7 mg/cm2 of the epidermal layer

beta particles can be potentially damaging to both the skin and eyes

**unlike alpha particles, beta particles have numerous radionuclides with ranges > the thickness of the epidermis**
**even a 70 keV electron can penetrate the **
**    ****7 mg/cm****2**** of the epidermal layer**
**beta particles can be potentially damaging to both the skin and eyes**

**BETA PARTICLES (β****+****, β****-****)**

## problem: what must be the minimum thickness of a shield made of plexiglass and Al such that no beta particles from a 90Sr source pass through?

90Sr has a beta particle of 0.54 MeV but its daughter 90Y emits a beta particle whose max energy is 2.27 MeV

from the range graph 2.27 MeV beta particle 

**90****Sr has a beta particle of 0.54 MeV but its daughter ****90****Y emits a beta particle whose max energy is 2.27 MeV**
**from the range graph 2.27 MeV beta particle**** **

**	****is found to be 1.1 g/cm****2****   ******

**BETA PARTICLES (β****+****, β****-****)**

## since plexiglass may suffer radiation damage and crack if exposed to very intense radiation for a long time, aluminum is a better choice

using the same calculation for Al the thickness is found to be 0.41 cm

6. Slow Down Time
read Turner  - the calculations are similar to those done for heavy charged particle

**using the same calculation for Al the thickness is found to be 0.41 cm**
**6.** **Slow Down Time**
**read Turner  - the calculations are similar to those done for heavy charged particle**

**BETA PARTICLES (β****+****, β****-****)**

## 7. Single Collision Spectra in Water

interaction of low energy electrons with matter is fundamental to understanding the physical and biological effects of ionizing radiation

low energy electrons are responsible for producing initial alterations that lead to chemical changes in tissue and tissue-like materials such as water

interaction of an electron with kinetic energy e can be characterized by probability N(E,E)dE that it loses an amount of energy between E and E + dE

**interaction of low energy electrons with matter is fundamental to understanding the physical and biological effects of ionizing radiation**
**low energy electrons are responsible for producing initial alterations that lead to chemical changes in tissue and tissue-like materials such as water**
**interaction of an electron with kinetic energy e can be characterized by probability N(E,E********)dE that it loses an amount of energy between E******** ****and**** ****E******** + dE**

**BETA PARTICLES (β****+****, β****-****)**

## distribution N(E,E) is called a single collision spectrum of an electron energy of E

as a probability function it is normalized and has the dimensions of inverse energy

**as a probability function it is normalized and has the dimensions of inverse energy**

**calculated single collision spectra for electrons: 30, 50, 150 eV and 10 keV are shown in the following figure**

**BETA PARTICLES (β****+****, β****-****)**

## BETA PARTICLES (β+, β-)

**BETA PARTICLES (β****+****, β****-****)**

## for 10 keV, the average value of the single collision spectrum for energy losses between 45 - 50 eV is 0.1 eV-1

since the interval is 5 eV   
0.01 eV-1  eV = 0.05

this implies that a 10 keV electron in water has about a 5% probability of having an energy loss between 45 and 50 eV in its next collision

**since the interval is 5 eV   ******
**0.01 ****eV****-1**** ******** eV = 0.05**
**this implies that a 10 keV electron in water has about a 5% probability of having an energy loss between 45 and 50 eV in its next collision**

**BETA PARTICLES (β****+****, β****-****)**

## note that all the curves begin a 7.4 keV which is the minimum of energy needed for electronic excitation

at E = 30 eV, excitation is as probable as ionization with increasing energy ionization as more probable

**at E = 30 eV, excitation is as probable as ionization with increasing energy ionization as more probable**

**BETA PARTICLES (β****+****, β****-****)**

## BETA PARTICLES (β+, β-)

**BETA PARTICLES (β****+****, β****-****)**

## the collisional stopping power is related to the single collision spectrum n(E, E)

the average energy lost (E) by an electron of energy E in a single collision is  the weighted average over the energy-loss spectrum

**the average energy lost ************(E)**** by an electron of energy E in a single collision is  the weighted average over the energy-loss spectrum**

**BETA PARTICLES (β****+****, β****-****)**

## the stopping power at energy E is the product of (E) and the probability (E) per unit distance then an elastic collision occurs

**BETA PARTICLES (β****+****, β****-****)**

## 8. Electron Tracks in Water

Monte Carlo computer codes are used to simulate electron transport in water

each primary electron starts with 5 keV and each dot

represents the location at 10-11 sec of a chemical active species

**Monte Carlo computer codes are used to simulate electron transport in water**
**each primary electron starts with 5 keV and each dot**
**represents the location at 10****-11**** sec of a chemical active species**

**BETA PARTICLES (β****+****, β****-****)**

## Examples of Electron Tracks in Water

**Examples of Electron Tracks in Water**

## the Monte Carlo code randomly selects events from specified distributions of flight, distance energy loss and angle of scatter in order to calculate the fate of individual electrons

**BETA PARTICLES (β****+****, β****-****)**

## Phenomena Associated withCharged Particle Tracks

**1. Delta Rays**
**HCP or electrons passing through matter sometimes produce a secondary electron with enough energy to leave and create its own path**
**such an electron is called delta** **ray**

## 2. Restricted Stopping Power
stopping power gives the energy lost by a charged particle in a medium

this is not always equal to the energy absorbed in a target

this is particularly important for small targets such as DNA double helix whose diameter is 20 

restricted stopping power is given as:

**stopping power gives the energy lost by a charged particle in a medium**
**this is not always equal to the energy absorbed in a target**
**this is particularly important for small targets such as DNA double helix whose diameter is 20 **
**restricted stopping power is given as:**

**Phenomena Associated with****Charged Particle Tracks**

## it is defined as the linear rate of energy loss due only to the collisions in which the energy transfer does not exceed a specified value 

one integrates the weighted energy loss spectrum only up to 

**one integrates the weighted energy loss spectrum only up to ******

**Phenomena Associated with****Charged Particle Tracks**

## tables in Turner show the restricted mass stopping power for protons and restricted collisional mass stopping mass power for electrons

**Phenomena Associated with****Charged Particle Tracks**

## 3. Linear Energy Transfer (LET)

concept of LET introduced in the early 1950's to characterize the rate of energy transfer per unit distance along a charged particle track

distinction made between the energy transferred from a charged particle in a target and the energy actually absorbed

**concept of **_**LET**_** introduced in the early 1950's to characterize the rate of energy transfer per unit distance along a charged particle track**
**distinction made between the energy transferred from a charged particle in a target and the energy actually absorbed**

**LET has units of keV/micron**

**Phenomena Associated with****Charged Particle Tracks**

## 4. Specific Ionization

specific ionization is defined as the number of ion pairs that a particle produces per unit distance traveled

quantity expresses the density of ionization along a track

**specific ionization is defined as the number of ion pairs that a particle produces per unit distance traveled**
**quantity expresses the density of ionization along a track**

**Phenomena Associated with****Charged Particle Tracks**

## what is SI of 5 MeV alpha particle in air?

stopping power = 1.23 MeV/cm

an average of 36 eV needed to produce an ion pair   

**stopping power = 1.23 MeV/cm**
**an average of 36 eV needed to produce an ion pair   ******

**Phenomena Associated with****Charged Particle Tracks**

## in soft tissue:

**with  w = 25 eV to produce an ion pair**

**Phenomena Associated with****Charged Particle Tracks**

## 6. Energy Straggling
	read Turner

7. Range Straggling
	read Turner

8. Multiple Coulomb Scattering
	read Turner

**	****read Turner**
**7. Range Straggling**
**	****read Turner**
**8. Multiple Coulomb Scattering**
**	****read Turner**

**Phenomena Associated with****Charged Particle Tracks**