Radiation PhysicsRadiation Physics

Ya-yun HsiaoYa-yun Hsiao

OutlineOutline

RadiodecayRadiodecay Interactions of radiations with matterInteractions of radiations with matter

ExampleExample

A 6.2 mg A 6.2 mg sample of 90Sr (half-life 29.12 sample of 90Sr (half-life 29.12 year) is in secular equilibrium with its dayear) is in secular equilibrium with its daughter 90Y (half-life 64.0h). (a) how manughter 90Y (half-life 64.0h). (a) how many Bq of 90Sr are present? (b) how many y Bq of 90Sr are present? (b) how many Bq of 90Y are present? (c) what is the maBq of 90Y are present? (c) what is the mass of 90Y present? (d) what will the activiss of 90Y present? (d) what will the activity of 90Y be after 100 years? ty of 90Y be after 100 years?

Secular equilibrium: λSrNSr=λYNY

YYYY

SrY

Sr

Y NNh

hN

T

TNNsr 8.3985

64

2436512.29

2/1

2/1

NSr +NY =NTOTAL= atoms

mol

atoms

mol

gg 1923

3

10148.410022.690

102.6

NY= atomsatoms 16

19

1004.18.3986

10148.4

NSr=1.04x1016 atoms /3985.8=4.147x 1019 atoms

A(t)= λN(t)

(a)(a)

(b)(b)

(c)(c)

(d)(d)

Bqsatomss

ASr1011019 1013.31013.310147.4

36002436512.29

2ln

Bqsatomss

AY1011016 1013.31013.31004.1

360064

2ln

mY= ggatoms

atomsM

Na

tN 623

16

1055.19010022.6

1004.1)(

BqeBqeAtAAy

ytSrSrY

9100

12.29

2ln

10 10897.21013.3)(

ExampleExample

Consider the following beta decay Consider the following beta decay chain with half-lives indicated,chain with half-lives indicated,

210Pb (22y)210Pb (22y) 210Bi (5d) 210Bi (5d) 210Po 210Po A sample contain 30 MBq of 210Pb A sample contain 30 MBq of 210Pb

and 15M Bq of 210Bi at t=0 (a) and 15M Bq of 210Bi at t=0 (a) calculate the activity of 210Bi at time calculate the activity of 210Bi at time =10d (b) If the sample were =10d (b) If the sample were originally pure 210Pb, how old would originally pure 210Pb, how old would it have been at t=0?it have been at t=0?

Interactions of photons Interactions of photons with matterwith matter

Photoelectric EffectPhotoelectric Effect Compton EffectCompton Effect Pair productionPair production

Photoelectric effectPhotoelectric effect

Most of this energy Most of this energy goes to an atomic goes to an atomic electron (with a small electron (with a small amount to the nucleus) amount to the nucleus) resulting in a free resulting in a free electron and an ionized electron and an ionized atom. atom.

The photoelectric effect The photoelectric effect may only occur if the may only occur if the incident photon has an incident photon has an energy higher than the energy higher than the binding energy of the binding energy of the atomic electron.atomic electron.

Top insert to illustrate the interaction of a photon with an atom Top insert to illustrate the interaction of a photon with an atom to eject an electron from the K shell to produce a to eject an electron from the K shell to produce a

photoelectron. When the hole in the K shell is filled, photoelectron. When the hole in the K shell is filled, characteristic radiation is emitted. Main graph – Photoelectric characteristic radiation is emitted. Main graph – Photoelectric attenuation coefficients for water and lead plotted on a log-log attenuation coefficients for water and lead plotted on a log-log

scale. scale.

Compton EffectCompton Effect An interaction An interaction

between a between a photonphoton and an and an atomic atomic electronelectron

An inelastic An inelastic process process

Some of the kinetic Some of the kinetic energy of the energy of the photon is required photon is required to overcome the to overcome the binding energy of binding energy of the atomic the atomic electron. electron.

Compton EffectCompton Effect

And the recoil electron energy is given byAnd the recoil electron energy is given by T = hν – hν' =T = hν – hν' =

High energy incident photons suffer a large High energy incident photons suffer a large energy change, but low energy incident energy change, but low energy incident photons do not. This is important in photons do not. This is important in radiotherapy since when the incident energy radiotherapy since when the incident energy of the photon is large most of the available of the photon is large most of the available energy goes into kinetic energy of the recoil energy goes into kinetic energy of the recoil electron, which goes on to deposit energy in electron, which goes on to deposit energy in tissue, and very little energy goes to the tissue, and very little energy goes to the scattered photon scattered photon

θCos(1α1

θCos(1ανh

Pair ProductionPair Production

Pair production is an interaction Pair production is an interaction between a between a photon photon and a nuleus in and a nuleus in which the photon is transformed into which the photon is transformed into an electron‑positron pair. In the an electron‑positron pair. In the center of mass syst~m, the energy center of mass syst~m, the energy threshold for this e‑p pair creation is threshold for this e‑p pair creation is 2moC2 = 1.022 MeV.2moC2 = 1.022 MeV.

Pair ProductionPair Production

Mass Attenuation Mass Attenuation CoefficientCoefficient

ρ

k

ρ

τ

ρ

σ

ρ

μ

Mass Energy Transfer Mass Energy Transfer CoefficientCoefficient

Mass Energy Transfer Mass Energy Transfer CoefficientCoefficient

Photons do not deposit energy in a Photons do not deposit energy in a material. It is the fast electrons that material. It is the fast electrons that they produce following interaction they produce following interaction that deposit energy. Over many that deposit energy. Over many interactions there will be an average interactions there will be an average energy transfer, , to the electron.energy transfer, , to the electron.

The mass The mass energy transfer coefficientenergy transfer coefficient is is tr/ρ tr/ρ

μ.hν

trEμ tr

Mass Energy Absorption Mass Energy Absorption CoefficientCoefficient

Letting g represent the average fraction of the initial kinetic energy transferred to electrons that is subsequently emitted as bremsstrahlung

Mass Energy Absorption Mass Energy Absorption CoefficientCoefficient