Why? The atomic nucleus. Radioactivity. Nuclear radiations. Length scale of the nature. The electrons and the nucleus

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1 The atomic ucleus. Radioactivity. Nuclear radiatios László Smeller Why? Medical alicatio of uclear radiatio: Nuclear imagig Radiotheray Legth scale of the ature m meter me -3 millimeter size of letters you ca read -6 micrometer size of a cell (e.g. erytrocyte) 7μm -9 aometer rotei - agstrom diameter of a atom, bod legth H atom agstrom (Å) icometer wavelegth of the X-ray femtometer size of the ucleus m The electros ad the ucleus -5 m Electros: => chemical roerties Nucleus: => radioactivity

Structure of the ucleus Stability of the ucleus Elemetary

mass uit Coulomb force: destabilizatio (electrostatic reulsio

acts oly o short rage (~fm) ideedet o the charge Quatized eergy

E A (mass umber) = umber of rotos umber of eutros Z (atomic

Tyical bidig eergy is i the MeV rage ev=,6-9 J Isotoes Table of

Variats of the same elemet the chemical roerties are idetical.

2 Structure of the ucleus Stability of the ucleus Elemetary charge=,6-9 C charge mass roto e atomic mass uit eutro atomic mass uit Coulomb force: destabilizatio (electrostatic reulsio betwee the rotos) Nuclear force: very strog attractive force acts oly o short rage (~fm) ideedet o the charge Quatized eergy levels for the ucleus. E A (mass umber) = umber of rotos umber of eutros Z (atomic umber) = umber of rotos 99 ucleo, 43 roto ad 56 eutro 99 Tc 43 Tyical bidig eergy is i the MeV rage ev=,6-9 J Isotoes Table of isotoes Number of rotos is the same Number of eutros is differet Variats of the same elemet the chemical roerties are idetical. Pl: 8 9 F F F Number of rotos ustable (radioactive) stable ustable (radioactive) isotoe <-> radioactive isotoe Number of eutros

for the heavy atoms β - decay : β - β - article = electro β β article = ositro Isomeric trasitio

3 Number of rotos Number of rotos Number of eutros Number of eutros Radioactive decays ad articles α -decay α - decay 4 α - article = He ucleus α - decay: a α article ( 4 He ucleus) will be emitted tyical for the heavy atoms β - decay : β - β - article = electro β β article = ositro Isomeric trasitio K-electro cature -ray characteristic x-ray hoto e.g. Lie sectrum E α ~MeV A Z A X Y 88 Ra 86 R 6 Z 4 4 α N α 4 α E α

4 eutro surlus ν β = β = e A Z β - decay X β ν remais i the ucleus β -ray A Z Y e.g. : cotious eergy sectrum β ν leave the ucleus e.g.: 9 F 3 5 P 59 6 Fe 3 53 I P 6S β N β E max E β ν roto surlus A Z e ν β - decay X A Z Y β ν remais i the ucleus β -ray e.g. : β ν leave the ucleus e.g.: 6 C 5 8O 8 9 F 5 6 Fe P 4Si β ν cotious eergy sectrum These isotoes must be roduced artificially (e.g. i cyclotro) Promt -radiatio Isomeric trasitio The daughter ucleus has a eergetically ufavoured arragemet of ucleos. The surlus eergy will be immediately (<s) emitted i form of the radiatio E α or β If the excited state of the daughter ucleus is metastable, the -radiatio will be emitted later. The aret ad daughter atoms ca be searated: the daughter atom emits oly -radiatio! => Isotoe diagostics (uclear imagig) E.g.: 99m Tc 99 β 99 4 Mo 43Tc m h 6 h Tc Atomic umber, mass umber are uchaged.

K-cature (iverse β-decay) v Some examles of the decay aths x-ray β ν Characteristics of radioactive decays i geeral activity half life time article eergy characterizes the source characterizes the

5 K-cature (iverse β-decay) v Some examles of the decay aths x-ray β ν Characteristics of radioactive decays i geeral activity half life time article eergy characterizes the source characterizes the seed of the decay* characterizes the radiatio* *deeds o the tye of the isotoe Λ = immeasurably small dn dt Activity (Λ) = ΔN Δt Activity= umber of decays i a uit time uit: becquerel Bq Bq= decay/sec level of atural activity N = Number of udecayed atoms t = time ΔN = Number of decays durig Δt time kbq, MBq, GBq, TBq i vivo diag. careful work with it! activity alied i radiotheray

ΔN = λnδt dn dt solutio: = λn Law of radioactive decay λ: decay costat

equatio N N: Number of udecayed uclei λt ( t) = N e Exoetial decrease

λ=, / S (decay robability) after sec: 9 (x,= decayed) after sec: 8

(decay robability) N(t) after s: 9 (x,= decayed) after s: 8 (9x,=9

N N o N o / N o /4 N o /8 N λt ( t) = Ne = N T / T / 3T / τ λ decay

6 ΔN = λnδt dn dt solutio: = λn Law of radioactive decay λ: decay costat (robability of the decay [/s]) /λ=τ average lifetime Differetial equatio N N: Number of udecayed uclei λt ( t) = N e Exoetial decrease umber of udecayed atoms at t= A examle At start: N = (umber of atoms λ=, / S (decay robability) after sec: 9 (x,= decayed) after sec: 8 (9x,=9 decayed) after 3 sec: 79 (8x,=8 decayed) after 4 sec: 656 (79x,=79 decayed). A examle Law of radioactive decay At start: N = (umber of atoms λ=, / S (decay robability) N(t) after s: 9 (x,= decayed) after s: 8 (9x,=9 decayed) after 3 s: 79 (8x,=8 decayed) after 4 s: 656 (79x,=79 decayed). Time [s] N o /e N N o N o / N o /4 N o /8 N λt ( t) = Ne = N T / T / 3T / τ λ decay costat (robability of the decay) T half life (T / ) τ average lifetime Theoretically ever decreases to zero! time λ = t T l = T,693 T

Λ o /e Decrease of the activity as a fuctio of time N Λ Λ o Λ o / Λ o /4 Λ o /8 dn dn Λ = = λn N( t) = Ne dt dt T /

time Durig about T the activity decreases to its / (e.

after sec: 9 (x,= decayed) after sec: 8 (9x,=9 decayed) after 3 sec: 79 (8x,=8 decayed) after 4 sec: 656 (79x,=79

Time [s] Few examles for half life 3 Th,4 y 38 U 4,5 9 y 4 K,3 9 y 4 C 5736 y 37 Cs 3 y 3 H,3 y Do t lear these

7 Λ o /e Decrease of the activity as a fuctio of time N Λ Λ o Λ o / Λ o /4 Λ o /8 dn dn Λ = = λn N( t) = Ne dt dt T / T / 3T / τ λt Λ=λN t λt T Λ( t) = Λe = Λ Λ decreases o the same mode as N! Theoretically ever decreases to zero! time Durig about T the activity decreases to its / (e.g GBq->MBq) Number of uclei decayed i each secods A examle At start: N = (umber of atoms λ=, / S (decay robability) after sec: 9 (x,= decayed) after sec: 8 (9x,=9 decayed) after 3 sec: 79 (8x,=8 decayed) after 4 sec: 656 (79x,=79 decayed). Time [s] Few examles for half life 3 Th,4 y 38 U 4,5 9 y 4 K,3 9 y 4 C 5736 y 37 Cs 3 y 3 H,3 y Do t lear these umbers! 6 Co 5,3 y 59 Fe,5 m 56 Cr m (8 d) 3 I 8 d 99m Tc 6 h 8 F mi C mi 5 O mi Th,8 ms Tyical eergy levels i the microworld Excitatio of the Electro trasitio Trasformatio outer electros betwee ier of the ucleus electros (decay) ev (aj) kev (fj) MeV (J) light X-ray Nuclear radiatio α, β,

8 α β β Absortio of the uclear radiatio (x-ray) articles with electric charge ucharged articles (hotos) ot a uclear radiatio, but its absortio is similar to that of the radiatio direct ioisatio differet tyes of iteractios with matter! idirect ioisatio Absortio of the charged articles Ioizig durig the ath => cotiuous decrease of the article eergy The eergy after a give ath legth decreases to the thermal value α effective rage β Effective rage β -radiatio α-article β -article aihilatio i air few cm ~ m i tissue,-, mm ~ cm β e N N effective rage effective rage see: Positro Emissio Tomograhy (PET) eetratio deth eetratio deth effective rage

9 Electro ad ositro articl atiarticle same mass, charge: same value, but differet sig aihilatio ad air roductio Eistei: mass-eergy ekvivalece e e- e E=mc m e c =5 kev,5 MeV Αbsortio of the -radiatio (ad x-ray) Absortio ricesses hae accidetally : Photoeffect, Comto-effect, Pair roductio, (elastic scatterig) Photoeffect Comto effect Comto-scatterig Pair roductio elastic scatterig

J J J /4 J Atteuatio of the radiatio ad x-ray D J = J e ever reaches zero!

few rules of thumb: x / =3,33 D x / = D J Itezitás: Egységyi felületre eső sugárzási teljesitméy

absorbig ceters, eergy of the radiatio) =μ(material,ρ,e hoto ) ρ μ m = μ ρ D δ = μ mass atteuatio

10 J J J /4 J Atteuatio of the radiatio ad x-ray D J = J e ever reaches zero! D μ x x J x o limited effective rage! few rules of thumb: x / =3,33 D x / = D J Itezitás: Egységyi felületre eső sugárzási teljesitméy J J J D x J = J e μ x μ: (liear) atteuatio coefficiet its uits are: /m, /cm μ(material, umber of absorbig ceters, eergy of the radiatio) =μ(material,ρ,e hoto ) ρ μ m = μ ρ D δ = μ mass atteuatio coefficiet eetratio deth Itesity decreases to the e-th art (c.a. 37%) mass atteuatio coeff. μ = m μ ρ Alicatios (atteuatio) lead glass μ m =τ m σ m κ m rotective aro τ m =cλ 3 Z 3

11 Alicatios: isotoes ad uclear radiatio Thak you for your attetio!

Why? The atomic nucleus. Radioactivity. Nuclear radiations. The electrons and the nucleus. Length scale of the nature

Why? The atomic nucleus. Radioactivity. Nuclear radiations. The electrons and the nucleus. Length scale of the nature The atomic ucleus. Radioactivity. Nuclear radiatios László Smeller Why? Medical alicatios of the uclear radiatio: - Nuclear imagig - Radiotheray Legth scale of the ature m meter me -3 millimeter size of