sign in sign up
<<
Home , Internal conversion

Introduction to Structure of Matter

. Molecules: grouping of Structure of Matter . Atoms: Basic Nuclear Phenomenology Large sparse outer cloud: electron shells - chemistry Nuclear Stability and Decay Atomic MODEL

Ruth E. Schmitz, PhD - [email protected], 543-3316 Course Website with slides, practice questions/answers: } http://depts.washington.edu/uwmip/ Small dense core: nucleus - nuclear physics

Ruth E. Schmitz, May 25th , 2006 Ruth E. Schmitz, May 25th , 2006

Nuclear Model Basic Constituents of Matter

We can’t see the nucleus! » Constituents of the nucleus: - (charge +1) Treat as black box: typically probe it with particles and/or - (charge 0) » Held together by the strong gamma rays - see what comes out and build a model  Photons Gamma rays » Transmit the electromagnetic force » Massless » A Gamma-ray is a photon produced in a or decay p,n,d particles  Electrons, Positrons (Antielectrons) » Charge -1, +1 » Interact via the electromagnetic and weak forces but not the strong Heat, etc nuclear force » Nuclear β radiation consists of electrons (β-) or positrons (β+) Model: mathematical description that allows to  ν, ν (Neutrinos, Antineutrinos) » approx. massless calculate observed phenomena and to visualize » weak interaction only the underlying processes. Ruth E. Schmitz, May 25th , 2006 € Ruth E. Schmitz, May 25th , 2006

Classification of Atoms Examples of /Nucleus Classification

Atom = . Notation: Z electrons orbiting a nucleus Element (symbol X) with Z protons, N neutrons, A : with Z protons and N neutrons A A A ⇒ ZXN, often only ZX or X (equivalent to X-A) » Nucleus: A nucleons (A = N + Z) Example: Fluorine: symbol F, 9, – Z protons -- 10-13 cm, 1.7 x 10-24 g (938 MeV/c 2) with 18 nucleons (-- number?) – N neutrons -- 10-13 cm, 1.7 x 10-24 g (940 MeV/c 2) 18 18 18 ⇒ 9F9 , 9F , F , or F-18 Z = Atomic Number = Number of Protons N = Neutron Number . : A = N + Z = Mass Number Nuclear species of atoms uniquely identified by number of protons, » Atomic Size: 10-8-10-7 cm = 10-10-10-9 m number of neutrons, and energy content of the nucleus. » Nuclear Size: ~ 10-13 cm = 10-15 m = 1 fm (Fermi) Groups that share properties: » Atomic Mass: A atomic mass units (amu) - nuclides with the same (atomic) number, Z 1 amu ~ 1.66 x 10-24 g (~ 931.5 MeV/c2) ≡ 1/12 of the mass of C-12 - nuclides with the same neutron number, N Isobars - nuclides with the same mass number, A » Electron Mass: M = m = 9.1 x 10-28 g (0.511 MeV/c 2) e 0 Isomers - nuclides with the same A and Z, but different energy

Ruth E. Schmitz, May 25th , 2006 Ruth E. Schmitz, May 25th , 2006 Chart of the Nuclides Forces in the nucleus

 Analogous to the Periodic Table of the elements Coulomb force, Force on positively FC -> infinity as r -> 0 (repulsive)  Rows of constant Z (proton number): Isotopes (same chemical properties) charged particle Increases with more protons Example: C-12 and C-14: Z=6 FC  Columns of constant N: Isotones N 7 8 9 131 132 Example: 53I (N=78) and 54Xe (N=78) Z 15 16 17 0  Isobars lie on diagonals of O O O Distance from 8 center of nucleus constant mass number A 99 99 FNuc Example: Tc and Mo 7 14N 15N 16N Nuclear strong force,  Isomers are the same entry FNuc is short range (attractive) but VERY strong with different energy levels 6 13C 14C 15C Example: 99mTc and 99Tc Increases with more nucleons

Ruth E. Schmitz, May 25th , 2006 Ruth E. Schmitz, May 25th , 2006

Factors in Nuclear Stability Full Chart of the Nuclides

Line of N=Z  Nuclear stability represents a balance between: “Band of Stability” » Nuclear “strong force” (basically attractive) stable » Electrostatic interaction (Coulomb force) between protons (repulsive) » Pauli exclusion principle » Residual interactions (“pairing force”, etc.) Z  Stability strongly favors N approximately equal to (but slightly larger than) Z. This results in the “band of stability” in the Chart of the Nuclides. N

Ruth E. Schmitz, May 25th , 2006 Ruth E. Schmitz, May 25th , 2006

Phenomenology of Stability Nuclear Binding and Stability

 Protons and neutrons are more stable in a nucleus than free.  Stability strongly favors nuclides with even numbers of protons and/or neutrons The is the amount by which the nucleus’ energy (i.e. mass) is reduced w.r.t. the combined energy (i.e. mass) of » ~50% are Even-Even the nucleons. » ~25% are Odd-even  Example: N-14 atom - Measured mass of N-14 = 14.0037 » ~25% are Even-Odd mass of 7 protons = 7 * (1.00727 amu) = 7.05089 amu » Only 4 out of 266 stable nuclides are Odd-Odd! The heaviest stable Odd-Odd is 14N. mass of 7 neutrons = 7 * (1.00866 amu) = 7.06062 amu mass of 7 electrons = 7 * (0.00055 amu) = 0.00385 amu  “Magic Numbers” -- analogous to closed atomic shells mass of component particles of N-14 = 14.11536 amu » Result in many stable isotopes or isotones » Magic nuclei are particularly stable and more “inert” Binding energy is mass difference: Ebind = 0.11229 amu = 104.5 » Magic #’s: 2,8,20,28,50,82,126 MeV

Ruth E. Schmitz, May 25th , 2006 Ruth E. Schmitz, May 25th , 2006 Fundamental Concepts Raphex Questions

 Raphex 2003, G 16. In heavy nuclei such as 235U: 2  Total energy = E = mc A. There are more protons than neutrons. B. Protons and neutrons are equal in number. 2  Rest energy = Eo = moc C. There are more neutrons than protons. D. Cannot tell from information given. ⇒ C. With higher mass number, more neutrons needed to balance the attraction  2 Classic kinetic energy = 1/2(mv ) of all masses (nucleons) with the repulsion between positively charged protons.

 Classic momentum = P = mv  Raphex 2003, G12. A 10MeV _____ travels at the greatest speed in a vacuum. A. Alpha particle  Binding energy per = Eb (total Binding E)/A B. Neutron C. Proton D. Electron ⇒ D. 10MeV is the kinetic energy of the particle. The lightest one travels fastest. Ruth E. Schmitz, May 25th , 2006 Ruth E. Schmitz, May 25th , 2006

More Raphex Questions Nuclear Decay Occurs…

• Raphex 2001, G 15. The number of neutrons in a U-238 atom (Z=92) is: …when a nucleus is unstable A. 330 B. 238 C. 146  An unstable nucleus metamorphoses (“decays”) into a more D. 92 stable nucleus E. Cannot tell from information given. ⇒ C. Neutron Number N = A - Z = 146  Difference in energy levels ==> • Raphex 2000, G15. Elements which have the same Z but different A are called: mass and kinetic energy of the decay products A. Isotopes B. Isomers  Mass is converted into energy ==> radiation C. Isotones 2 D. Isobars E = mc ⇒ Isotopes have the same number of protons (atomic number, Z)

Ruth E. Schmitz, May 25th , 2006 Ruth E. Schmitz, May 25th , 2006

Nuclear (Radioactive) Decays

 Fission -- only very heavy (high Z) elements (U, Pu, etc.)  Spontaneous emission of an α particle (2p 2n = He-4 spontaneously fission. Nucleus splits into two smaller nuclei. nucleus)

 Alpha decay -- like very asymmetric fission, usually occurs in  Only occurs with heavy nuclides (A>150) heavy elements “above” the . Nucleus emits an  [often followed by gamma and characteristic x-ray emission] alpha particle: the same as a He nucleus, (2p 2n).  Emitted with discrete energy (nuclide-dependent, 2-10 MeV)  Not used in medical imaging  -- element X transforms into neighbor element X’. Nucleus converts a neutron to a proton or vice versa and emits a (electron): n -> p + e- + ν. - Can also occur as A A-4 4 +2 ZX → Z-2Y + 2He + transition energy

 Gamma decay -- “excited” nucleus reduces its excitation Example: 220 Rn 216 Po + 4 He+2 + 6.4 MeV transition energy energy without changing nuclear species (N, Z). Nucleus emits 86 → 84 2 a (electromagnetic quantum: the photon). - Can also occur as Internal Conversion Electron. Ruth E. Schmitz, May 25th , 2006 Ruth E. Schmitz, May 25th , 2006 Beta (β) Decay Beta (β) Decay - II

Basis: −  A free neutron decays:  Free neutron decay: n ⇒ p + e + ν neutron ==> proton + electron + antineutrino  - A A  Half-life (T1/2) = 10.5 minutes (for a free (unbound) neutron) Beta (β ) emission: Z X N ⇒ Z+1YN-1 _  The released energy is split between 3 decay products, so n ⇒ p + e +ν each has a spectrum of possible energies up to the max +  Positron (β+) emission: p ⇒ n + e + ν  This basic process (and its inverse) forms the basis of all β decay A A Electron - Neutron Z X N ⇒ Z-1YN +1 e Proton (beta, negatron)  Electron (e-) capture: p + e− ⇒ n + ν Orbital electron captured, characteristic x-ray emission follows Anti-neutrino ν Ruth E. Schmitz, May 25th , 2006 Ruth E. Schmitz, May 25th , 2006

Gamma Decay (Isomeric Transition) Decay in the Chart of the Nuclides

 Nucleus in excited state with lower-lying nuclear energy Nuclear Decay Modes Beta (β-) decay: levels open (usually formed as product daughter of other A A Z X N ⇒ Z+1YN-1 decay) Z+1- Z+1 Z+1 . Excited state marked by * (e.g. 99*Tc) βN-1 N N+1 Positron (β+) decay:  Gamma ray (high-energy photon) emitted during transition A A Z Z Z ⇒ to stable state Z X N Z-1YN+1 Z N-1 N N+1  Usually occurs instantaneously Alpha (α) decay:  Some excited states persist longer (10-12 sec - 600 years!) Z-1 Z-1 Z-1 A A-4 99m N-1 N N+1 ⇒ . Metastable or isomeric state (e.g. Tc, ) β+ Z XN Z-2YN-2  Can also emit internal conversion electron - all energy is Z-2 transferred to inner shell electron, which is ejected, αN-2 Gamma (γ) decay: characteristic x-rays follow to fill the opening A*(m) A Z XN ⇒ Z XN N Ruth E. Schmitz, May 25th , 2006 Ruth E. Schmitz, May 25th , 2006

Energy Level Diagram: Positron Level Diagram

18 99m 9F Nuclear Medicine Example: 43Tc

Mo99 Beta+ 97% Why the vertical line? 42 - decay: Mo99 -> Tc99m + e- EC 3% β 42 43 82%

P mass = 1.67252 x 10-27 kg 99m 18 N mass = 1.67482 x 10-27 kg Tc 0.143 O 43 Electron shell transition 8 -27 E mass = 0.0009 x 10 kg 0.141 Neutrino mass = 0 γ decay 141 keV γ T1/2 = 6 hours

So, part of Energy -> mass 0.0 Ground state

Ruth E. Schmitz, May 25th , 2006 Ruth E. Schmitz, May 25th , 2006 Decay Terms Decay Terms - II

 Activity, A  Half-life, T1/2 • Number of radioactive decays per unit time (t) - or » Time after which half of the initially present nuclei (N0) will have • Change in number of radioactive nuclei present: A = -dN/dt decayed • Depends on number of nuclei present. During decay of a fixed initial number » After n half-lives, N = N × (1/2)n nuclei will be left of nuclei, A will decrease. 0 • Measured in Becquerel (Bq): » Also characteristic of nuclide, constant in time 1 Bq = 1 disintegration per second (dps) » Related to decay constant, λ, by natural log of 2:

traditionally in Curies (Ci): λ = ln 2 / T1/2 = 0.693 / T1/2 1 Ci = 3.7 × 1010 Bq (1mCi = 37 MBq)

Radionuclide T1/2 λ  Decay Constant, λ Fluorine 18 110 min 0.0063 min-1 • Fraction of nuclei that will decay per unit time: λ = (−dN/dt) / N = A / N • Related to activity: A = λ N Examples: 99m 6.2 hr 0.1152 hr-1 • Constant in time, characteristic of each nuclide Iodine 123 13.3 hr 0.0522 hr-1 • Example: Tc-99m has = 0.1151 hr-1, i.e. 11.5% decay per hour λ Molybdenum 99 2.75 d 0.2522 d-1 Mo-99 has λ = 0.252 day-1, i.e. 25.2% decay per day Iodine 131 8.02 d 0.0864 d-1

Ruth E. Schmitz, May 25th , 2006 Ruth E. Schmitz, May 25th , 2006

Fundamental Decay Equation Raphex Questions

Raphex 2003 G 28. The following radioactive transformation  Nt/At: Number of nuclei / activity -λt -t log (2)/T represents ____ . Nt = N0 e = N0 e e 1/2 present after time t A A ZX → Z-1Y + γ + ν  τ: average lifetime A. Alpha -λt -t log (2)/T  λ: decay constant At = A0 e = A0 e e 1/2 B. Beta minus T : half-life 1/2 C. Beta plus D. Electron capture Example: Patient injected with 10 mCi F-18 FDG, scan started E. Isomeric transition 60 min later. How much activity is present in the scan? -λt -(60min*0.0063/min) ⇒ A(60min) = A0 × e = 10mCi × e Answer: D - As Z decreases by 1, it must be either beta plus or = 10 mCi × 0.685 = 6.85 mCi electron capture. However, no positron is created, so beta plus is ruled out. Nuclear decay is statistical process => can only predict averages!

Ruth E. Schmitz, May 25th , 2006 Ruth E. Schmitz, May 25th , 2006

More Raphex Questions Extra: Models of the Nucleus

Raphex 2002 G 23-30. Match the mode of decay to the description below:  Liquid Drop model A. Beta minus B. Beta plus Answers:  Shell model C. Alpha G 23: C  Optical model D. Isomeric G 24: A G 25: B  Collective model (includes ‘modern’ notions of G23. Ra-226 to Rn-222 G 27: D string vibration states, etc). G24. Z increases by 1 G 28: A G25. Z decreases by 1 G 29: D G27. A and Z remain constant G 30: B ⇒ The one of interest to Nuclear Medicine is the G28. Tritium (H-3) to Helium (He-3) Shell model G29. Tc-99m to Tc-99 ⇒ It need to explain nuclear stability and decay G30. Electron capture can be a competing mode of decay to this.

Ruth E. Schmitz, May 25th , 2006 Ruth E. Schmitz, May 25th , 2006 Shell model Consider 24Mg

 Similar to the electron shell model in atoms n -> p + e- + v => “Magic numbers” 24Na  Complicated by two kinds of nucleons (proton, neutron) Z=11 24Mg 4.12 Free 15N

1.36 Bound 24Mg Ground Z=12 Ground state state Energy Energy p n p n

Ruth E. Schmitz, May 25th , 2006 Ruth E. Schmitz, May 25th , 2006

Where does the energy go? 24Na to 24Mg

 When the nucleon changes levels (but not species), the  Decay occurs because there is a proton level open at a energy is usually emitted as a gamma ray (or internal lower energy than an occupied neutron level conversion electron).

24Na 24Na 2.76 MeV gamma ray 4.12

1.36 MeV gamma ray n -> p + e- + v 1.36 Beta decay 24Mg p n

Ruth E. Schmitz, May 25th , 2006 Ruth E. Schmitz, May 25th , 2006

18F to 18O

 Decay occurs because there is a neutron level open at a lower energy than an occupied proton level

Lets recap a few points p -> n + e+ + v

Positron decay

p n

Ruth E. Schmitz, May 25th , 2006 Ruth E. Schmitz, May 25th , 2006 Nuclear Decay Occurs... Nuclear Decay Characteristics

…when a nucleus is unstable (lower open energy  Type of decay (fission, alpha, beta, electron capture, etc.) levels)  Decay constant (transformation rate) -tλ  An unstable nucleus metamorphoses (“decays”) into a more » N = N0e Half-life, T1/2 = 0.693 / λ stable (more tightly bound) nucleus  Radiation type (β+, β-, α, fission fragments, etc.)  Emission energy -- if continuum, then express as  Difference in binding energy ==> maximum energy or mean (average) energy mass and kinetic energy of the decay products  Associated gamma (γ) or x rays

 Mass is converted into energy ==> radiation  “Daughter nucleus” » is it stable? E = mc2 » Produced in “ground state” or “excited state”? » With what probabilities (“branching ratios”)?

Ruth E. Schmitz, May 25th , 2006 Ruth E. Schmitz, May 25th , 2006

What’s next

Next week we will take a look at Radiation detection and measurements Dr. Lawrence MacDonald

Ruth E. Schmitz, May 25th , 2006