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Atom, Nucleus, and Radiation

Atom, Nucleus, and Radiation. Electromagnetic Radiation Wave viewpoint. Changing B induces E Changing E induces B The inextricable exchange causes E and B fields to propagate outward at the speed of light c = 3 × 10 8 m/s in vacuum. (courtesy Dr. Naqvi).

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Atom, Nucleus, and Radiation

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  1. Atom, Nucleus, and Radiation March 11 2014

  2. Electromagnetic RadiationWave viewpoint • Changing B induces E • Changing E induces B • The inextricable exchange causes E and B fields to propagate outward at the speed of light • c = 3 × 108 m/s in vacuum (courtesy Dr. Naqvi)

  3. Electromagnetic Spectrum ~ eV range keV- MeV

  4. Electromagnetic RadiationQuantum viewpoint E =hn h= Planck’s constant = 6.63 × 10-34 J/Hz • A photon is a “packet” or “quantum” of EM radiation • The photon energy, hn, is proportional to the frequency, and hence inversely proportional to the wavelength, l • A photon has zero rest mass (m0c2=0), and can therefore travel, and hence according to relativity, can travel only at the speed of light, c (courtesy Dr. Naqvi)

  5. Plum Pudding Model • In mid-nineteenth century, optical spectroscopy • Balmer’s empirical formula Eq. (2.1) for visible spectra of H was derived theoretically by Bohr in 1913 • Eq. (2.1) was visible, and by replacing 22 by 12 or 32 (and 42, …) was ultraviolet or infrared, respectively • J. J. Thomson in 1897 • Charge-to-mass ratio of cathode rays (only ~1/1700 of H) • Atom ~ plum pudding model • Ionization by radiation

  6. Rutherford Nuclear Atom • In 1909, large-angle deflection of α-ptls (as probes) was evidence for the existence of a very small & massive nucleus of + charge • Planetary model with mostly empty space • Light e- move rapidly about the nucleus • Nuclear force vs. Atomic force • Saturate within ~ 10-15m vs. not saturate • i.e., a given nucleon interacts with only a few others vs. all pairs of charges interact with one another • Radius of nucleus ≈ 1.3·A1/3×10-15 m vs. Atomic size of all elements is more or less the same (~ 10-10 m)

  7. Bohr’s Theory of Hydrogen Atom • An accelerated charge emits EM radiation, but • Bohr’s theory • w/o radiating only in certain discrete orbits about the nucleus (2.3) • transition of e- from one orbit to another → emission or absorption of a photon of orbital energy lost or gained by e- (2.4) • Some definitions • Bohr radius • Fine-structure constant (1/137) • Ionization potential • Rydberg constant, RM & R∞

  8. Energy Levels of Hydrogen Atom Ionization Continuum 0 eV n = 4 n = 3 n = 2 Balmer Series (visible) Lyman Series (ultraviolet) -13.6 eV n = 1 The normal condition of the atom, or ground state, is the state with n = 1 The atom is in it’s lowest possible energy state and it’s most stable condition

  9. Problem with Bohr’s model & classical mechanics • Only correct for the energy levels of H & He+ • Semi-classical mechanics, i.e., mixing classical mechanic w/ quantizing certain variables + relativistic models • de Broglie’s wave/particle dualism • X-ray diffraction vs. Compton scattering • e- diffraction in Ni-crystal • Optical microscopy vs. electron microscopy (SEM, TEM)

  10. Quantum Mechanics • Heisenberg’s uncertainty principle (matrix mechanics) Δp·Δx ≥ħ & ΔE·Δt ≥ħ in 1925 • Uncertainties in momentum of e- in atomic orbit (10-10 m) and nucleus (10-15 m) vs. position: a few hundred MeV vs. a few eV • But, betas from nuclei ~ a few MeV → neutron in 1932 • Schroedinger’s wave mechanics, 2πr = nλ, n = 1, 2, 3 ... • Linear differential equ (2nd order in space & 1st order in time) > superposition > wave packets > ptl • Boundary condition > eigenvalue > discrete energy • Dirac’s 1st order in space & time for relativistic motion

  11. Atomic StructureBohr vs. Modern Quantum Models

  12. Application: x-ray tube - + Find the energy gained by an electron (in eV) when accelerated through a potential difference of 50 kV in an x-ray tube Anode Cathode 50 kV (x-ray tube picture Courtesy of Hyperphysics)

  13. Bremsstrahlung X-rays

  14. Characteristic X-rays

  15. Bremsstrahlung and Characteristic X-rays

  16. Assemblage of neutrons and protons clustered in a nucleus and surrounded by electrons whirling in a variety of orbits Atomic number, Z = No. of protons Mass number, A = No. of nucleons (protons, Z plus neutrons, N = A – Z) Nucleus ofAtom,

  17. Isotopes, Isomers, Isobars • Isotopes = elements having the same Z but different A, e.g., 131I, 125I, 127I • Isomers = identical elements, but different nuclear energy states, e.g., • Isobars = elements having the same A but different Z • Isotones = elements having the same N

  18. Nuclear Structure and Forces TUG-of-WAR between the ATTRACTIVE STRONG NUCLEAR FORCE and the REPULSIVE ELECTROMAGNETIC FORCE

  19. Binding Energy The nucleons (protons & neutrons) are bound together by a net force which NUCLEAR ATTRACTION forces exceed the ELECTROSTATIC (COULOMB) REPULSION forces. Associated with the net force is a POTENTIAL ENERGY of BINDING In order to separate the nucleus into its component nucleons, energy must be supplied from the outside Binding Energy (BE) = total mass of separate particles - mass of the atom

  20. Binding Energy

  21. Natural Radioactive Series

  22. Auger electron [1/3] • Physical phenomenon in which the transition of an e- in an atom filling in an inner-shell vacancy causes the emission of another e- • Releasing an energy equal to the difference in binding energies, EK–ELI. • As the alternative to photon emission, this energy can be transferred to an LIIIe-, ejecting it from the atom with a K.E. = EK– ELI – ELIII • Emission of an Auger e- increases the number of vacancies in the atomic shells by one unit Vacancy by P.E., internal conversion, PIXE, or orbital e- capture

  23. Auger electron [2/3] • Kfluorescence yield = No. of KX-ray photons emitted per vacancy in K shell • Auger cascades can occur in relatively heavy atoms, as inner-shell vacancies are successively filled by the Auger process, with simultaneous ejection of more loosely bound atomic e-’s • An original, singly charged ion with one inner-shell vacancy can thus be converted into a highly charged ion by an Auger cascade Auger e- Yield

  24. Auger electron [3/3] • 125I decays by electron capture. The ensuing cascade can release some 20 e-s, depositing a large amount of energy (~1 keV) within a few nanometers • A highly charged 125Te ion is left behind; DNA strand breaks, chromatidaberrations, mutations, bacteriophage inactivation, and cell killing

  25. Gamma Emission vs. Internal Conversion • Excited daughter nucleus decays to the stable nucleus via either g-emission or internal conversion • g-emission: • isomeric (Z & A unchanged) • discrete in g-spectrum • Internal Conversion (IC): • process in which the energy of an excited nuclear state is transferred to an atomic e-, most likely a K- or L-shell e- • Ee = E* -EB • atomic inner-shell vacancies and thus emits characteristic X-ray • isomeric (Z & A unchanged) • dominant in heavy nuclei with low-lying excited state (small E*)

  26. Gamma Emission vs. Internal Conversion Eavg of emitting beta = 1/3 Emax 10% IC A long-lived excited nuclear state is termed metastableand is designated by the symbol m: e.g.,

  27. Orbital Electron Capture • Inverse beta decay • too many protons and insufficient energy to emit a positron(>1.022MeV) • p+  +  e-  →  n0  +  νe • usually from the K or L electron shell (K-electron capture, also K-capture, or L-electron capture, L-capture) • QEC=∆P-∆D-EB • Characteristic X-rays & Auger e-

  28. N, No of unstable nuclei left at time, t A, Activity (Bq or Ci) at time, t Radioactive Decay • = decay constant [s-1] N0 = initial No of unstable nuclei

  29. Relation between half-life and decay constant HALF-LIFE (T) REPRESENTATION 2-t/T1/2 T1/2 is the time taken for 50% of the atoms to survive T1/2 = ln(2) / l = 0.693 / l DECAY CONSTANT () REPRESENTATION e-lt 1/l is the time taken for the fraction 1/e (37%) of the atoms to survive (i.e., mean-life time, t).

  30. Point Source in Vacuum (1/3)2 ∙ I0 = N/(32A )[photons/s/cm2] (1/22 ) ∙ I0 = N/(22A)[photons/s/cm2] (1/12 ) ∙ I0 = N/A [photons/s/cm2] N [photons/s]

  31. Photon Beam Attenuation N [atoms or electrons/cm3] Detector Source I(r) I + dI I0 [photons/cm2] 0 m= σ•N = linear attenuation coefficient [cm-1] Collimator Collimator r [cm] dr

  32. Photon Fluencein Matter • Point source in matter (collimated) • Point source in matter (Broad)

  33. Relation between half-value layer and attn coefficient HALF-VALUE LAYER (HVL) REPRESENTATION 2-x/HVL HVLis the thickness taken for 50% of the photons to survive HVL = ln(2) / m = 0.693 / m ATTENUATION COEFFICIENT (m) REPRESENTATION e-mx 1/m is the thickness taken for the fraction 1/e (37%) of the photons to survive (i.e., mean-free path, xm).

  34. Linear vs. Semi-log Plotting of e-µx or e-lt Mono-energetic photons, µ = constant and, thus HVL = constant Linear Semi-log

  35. Beam Hardening: Selective Absorption of Low-Energy Photons 100 1st HVL < 2nd HVL < 3rd HVL 1st HVL = 0.99mm 2nd HVL = 1.99 mm Transmittance (%) 3rd HVL = 2 mm Ē1st < Ē2nd <Ē3rd 10 0 1 2 3 4 5 6 Absorber Thickness (mm AL)

  36. Parallels between nuclear decay and photon attenuation

  37. Parallels of Exponential Behavior Note: (i) The exponent of exp, e.g. D/D0, µx, t, should be dimensionless

  38. e.g., λ, T1/2, μ, and HVL • Which of the following expressions is most appropriate? • A =A0·e-λ/t, I =I0·e-μ·x • A =A0·2-λ·t, I =I0·2-x/HVL • A =A0·e-t/T1/2, I =I0·2-μ·x • A =A0·e-ln2·t/T1/2, I =I0·2-ln2·x/HVL • A =A0·2-t/T1/2, I =I0·e-ln2·x/HVL

  39. e.g., Mass and Atomic No. An atom of Zn-65 has a mass number of 65. A. Number of protons in the zinc atom 1) 30 2) 35 3) 65 B. Number of neutrons in the zinc atom 1) 30 2) 35 3) 65 C. What is the mass number of a zinc isotope with 37 neutrons? 1) 37 2) 65 3) 67

  40. H.W. #1 • Calculate Q-value for 10B(n,α)7Li reaction • Calculate the atomic density of sodium, 0.97 g/cm3 • A sample contains 1.0 GBq of 90Sr and 0.62 GBq of 90Y. • What will be the total activity of the sample 10 days later? • What will be the total activity of the sample 29.12 years later? • A high-energy e- strikes a lead atom and eject one of K-e-’s from the atom. • What wavelength radiation is emitted when an outer e- drops into the vacancy? • What is the probability for Auger e- emitted? • Calculate the recoil energy of the technetium atom as a result of photon emission in the isomeric transition • Find the binding energy of the nuclide 24Na • Turner Chap. 2: 11, 12, 13, 14, 15, 18, 19, 36, 37, 43, 53, 56 • Turner Chap. 3: 3, 4, 8, 11, 17, 29

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