Why? The atomic nucleus. Radioactivity. Nuclear radiations. The electrons and the nucleus. Length scale of the nature
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1 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 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
2 Structure of the ucleus Stability of the ucleus Elemetary charge=.6-9 C roto e charge mass 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 Variats of a elemet, where the - umber of rotos is the same - umber of eutros is differet the chemical roerties are idetical. E.g.: F F F Number of rotos ustable (radioactive) stable ustable (radioactive) isotoe <-> radioactive isotoe Number of eutros
3 Radioactive decays ad articles Number of rotos 4 α - decay α - article = He ucleus β - decay : β - β - article = electro β β article = ositro Isomeric trasitio -ray 2 K-electro cature characteristic x-ray hoto Number of eutros α - decay α - decay: a α article ( 4 He ucleus) will be emitted tyical for the heavy atoms e.g. Lie sectrum E α ~MeV A Z X Ra 86 R 226 A 4 Y 4 Z 2 2α N α 4 2 α E α 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.: 2 9 F 32 5 P Fe 3 53 I P 6S β N β E max E β ν
4 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 Fe P 4Si β ν cotious eergy sectrum These isotoes must be roduced artificially (e.g. i cyclotro) Promt -radiatio The daughter ucleus has a eergetically ufavoured arragemet of ucleos. The surlus eergy will ormally be emitted immediately (<s) i form of the radiatio Atomic umber, mass umber are uchaged. E α or β Isomeric trasitio 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) K-cature (iverse β-decay) v x-ray E.g.: 99m Tc 99 β Mo 43Tc m h 6 h Tc β ν
5 Some examles of the decay aths 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 = dn dt Activity (Λ) = ΔN Δt Activity= umber of decays i a uit time immeasurably small 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 (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=
6 A examle At start: N = (umber of atoms λ=. / S (decay robability) after sec: 9 (x.= decayed) after 2 sec: 8 (9x.=9 decayed) after 3 sec: 729 (8x.=8 decayed) after 4 sec: 656 (729x.=729 decayed). A examle At start: N = (umber of atoms λ=. / S (decay robability) N(t) after s: 9 (x,= decayed) after 2 s: 8 (9x,=9 decayed) after 3 s: 729 (8x,=8 decayed) after 4 s: 656 (729x,=729 decayed). Time [s] Law of radioactive decay Decrease of the activity as a fuctio of time N o /e N N o N o /2 N o /4 N λt ( t) = Ne = N2 λ decay costat (robability of the decay) T half life (T /2 ) τ average lifetime Theoretically ever decreases to zero! t T Λ o /e N Λ Λ o Λ o /2 Λ o /4 dn dn Λ = = λn N( t) = Ne dt dt λt Λ=λN t λt T Λ( t) = Λe = Λ 2 Λ decreases o the same mode as N! Theoretically ever decreases to zero! N o /8 T /2 2T /2 3T /2 τ time λ = l 2 = T,693 T Λ o /8 T /2 2T /2 3T /2 τ time Durig about T the activity decreases to its / (e.g GBq->MBq)
7 A examle Few examles for half life Number of uclei decayed i each secods At start: N = (umber of atoms λ=. / S (decay robability) after sec: 9 (x.= decayed) after 2 sec: 8 (9x.=9 decayed) after 3 sec: 729 (8x.=8 decayed) after 4 sec: 656 (729x.=729 decayed). Time [s] 232 Th.4 y 238 U y 4 K.3 9 y 4 C 5736 y 37 Cs 3 y 3 H 2.3 y Do t lear these umbers! 6 Co 5.3 y 59 Fe.5 m 56 Cr m (28 d) 3 I 8 d 99m Tc 6 h 8 F mi C 2 mi 5 O 2 mi 222 Th 2.8 ms Tyical eergy levels i the microworld Absortio of the uclear radiatio 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, α β β (x-ray) articles with electric charge ucharged articles (hotos) direct ioisatio differet tyes of iteractios with matter! idirect ioisatio ot a uclear radiatio, but its absortio is similar to that of the radiatio
8 Absortio of the charged articles Effective rage 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 i air α-article few cm i tissue,-, mm N α N β effective rage eetratio deth β -article ~ m ~ cm effective rage eetratio deth β -radiatio Electro ad ositro aihilatio see: Positro Emissio Tomograhy (PET) β e effective rage articl atiarticle same mass, charge: same value, but differet sig aihilatio ad air roductio Eistei: mass-eergy ekvivalece e E=mc 2 m e c 2 =5 kev.5 MeV
9 Αbsortio of the -radiatio (ad x-ray) Photoeffect Comto effect Comto-scatterig Absortio ricesses hae accidetally : Photoeffect, Comto-effect, Pair roductio, (elastic scatterig) Pair roductio elastic scatterig Atteuatio of the radiatio ad x-ray J J 2 J /4 J ever reaches zero! J J Itesity: Radiatio ower trasferred er uit area (W/m 2 ) J D = J e 2D μ x x x o fiite effective rage! few rules of thumb: x / =3,33 D x / = D
10 J J 2 J D 2D x J = J e μ x μ: (liear) atteuatio coefficiet its uits are: /m, /cm δ = μ eetratio deth Itesity decreases to the e-th art (c.a. 37%) mass atteuatio coeff. μ = m μ ρ μ m =τ m σ m κ m hoto lead μ(material, umber of absorbig ceters, eergy of the radiatio) =μ(material,ρ,e hoto ) ρ τ m =cλ 3 Z 3 water μ m = μ ρ mass atteuatio coefficiet hoto Alicatios (atteuatio) Alicatios: isotoes ad uclear radiatio lead glass rotective aro
Why? The atomic nucleus. Radioactivity. Nuclear radiations. Length scale of the nature. The electrons and the nucleus
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
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