atom, nucleus, and radiation

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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). - PowerPoint PPT Presentation

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Atom

Atom, Nucleus, and RadiationLec 2 of Intro Rad SciMarch 11 2014Electromagnetic 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) 2Electromagnetic Spectrum

keV- MeV~ eV range3Electromagnetic RadiationQuantum viewpoint 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

E = hnh = Plancks constant = 6.63 10-34 J/Hz(courtesy Dr. Naqvi) 4Plum Pudding ModelIn mid-nineteenth century, optical spectroscopyBalmers 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, respectivelyJ. J. Thomson in 1897Charge-to-mass ratio of cathode rays (only ~1/1700 of H)Atom ~ plum pudding modelIonization by radiationRutherford Nuclear AtomIn 1909, large-angle deflection of -ptls (as probes) was evidence for the existence of a very small & massive nucleus of + chargePlanetary model with mostly empty spaceLight e- move rapidly about the nucleusNuclear force vs. Atomic forceSaturate within ~ 10-15 m vs. not saturate i.e., a given nucleon interacts with only a few others vs. all pairs of charges interact with one anotherRadius of nucleus 1.3A1/3 10-15 m vs. Atomic size of all elements is more or less the same (~ 10-10 m)6Bohrs Theory of Hydrogen AtomAn accelerated charge emits EM radiation, butBohrs theoryw/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 definitionsBohr radiusFine-structure constant (1/137)Ionization potentialRydberg constant, RM & REnergy Levels of Hydrogen AtomIonization Continuumn = 1n = 2n = 3n = 4-13.6 eV0 eVLyman Series (ultraviolet)Balmer Series (visible)The normal condition of the atom, or ground state, is the state with n = 1 The atom is in its lowest possible energy state and its most stable condition8Problem with Bohrs model & classical mechanicsOnly correct for the energy levels of H & He+Semi-classical mechanics, i.e., mixing classical mechanic w/ quantizing certain variables + relativistic modelsde Broglies wave/particle dualismX-ray diffraction vs. Compton scatteringe- diffraction in Ni-crystalOptical microscopy vs. electron microscopy (SEM, TEM)9Quantum MechanicsHeisenbergs uncertainty principle (matrix mechanics) px & Et in 1925Uncertainties 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 1932Schroedingers wave mechanics, 2r = n, n = 1, 2, 3 ... Linear differential equ (2nd order in space & 1st order in time) > superposition > wave packets > ptlBoundary condition > eigenvalue > discrete energyDiracs 1st order in space & time for relativistic motionAtomic StructureBohr vs. Modern Quantum Models

Find the energy gained by an electron (in eV) when accelerated through a potential difference of 50 kV in an x-ray tube

-+Application: x-ray tube50 kV(x-ray tube pictureCourtesy ofHyperphysics)CathodeAnode

Bremsstrahlung X-raysCharacteristic X-rays

Bremsstrahlung and Characteristic X-rays

Nucleus of Atom,

Assemblage of neutrons and protons clustered in a nucleus and surrounded by electrons whirling in a variety of orbitsAtomic number, Z = No. of protonsMass number, A = No. of nucleons (protons, Z plus neutrons, N = A Z)

Isotopes, Isomers, IsobarsIsotopes = elements having the same Z but different A, e.g., 131I, 125I, 127IIsomers = identical elements, but different nuclear energy states, e.g.,

Isobars = elements having the same A but different ZIsotones = elements having the same N

Nuclear Structure and ForcesTUG-of-WAR between theATTRACTIVE STRONG NUCLEAR FORCEand theREPULSIVE ELECTROMAGNETIC FORCE

Binding EnergyThe 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 atom19Binding Energy

Natural Radioactive Series

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, EKELI. As the alternative to photon emission, this energy can be transferred to an LIII e-, ejecting it from the atom with a K.E. = EK ELI ELIIIEmission of an Auger e- increases the number of vacancies in the atomic shells by one unit

Vacancy byP.E., internal conversion,PIXE, or orbital e- captureAuger electron [2/3]K fluorescence yield = No. of K X-ray photons emitted per vacancy in K shellAuger 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-sAn original, singly charged ion with one inner-shell vacancy can thus be converted into a highly charged ion by an Auger cascade

Auger e- YieldAuger 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, chromatid aberrations, mutations, bacteriophage inactivation, and cell killing

Gamma Emission vs. Internal ConversionExcited daughter nucleus decays to the stable nucleus via either g-emission or internal conversiong-emission: isomeric (Z & A unchanged) discrete in g-spectrumInternal 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* -EBatomic inner-shell vacancies and thus emits characteristic X-rayisomeric (Z & A unchanged)dominant in heavy nuclei with low-lying excited state (small E*)

Gamma Emission vs. Internal Conversion

10% ICEavg of emitting beta = 1/3 EmaxA long-lived excited nuclear state is termed metastable and is designated by the symbol m:e.g.,

28

Orbital Electron CaptureInverse beta decaytoo many protons and insufficient energy to emit a positron(>1.022MeV)p+ + e- n0 + eusually from the K or L electron shell (K-electron capture, also K-capture, or L-electron capture, L-capture)QEC=P-D-EBCharacteristic X-rays & Auger e-

Radioactive Decay

N, No of unstable nuclei left at time, t

A, Activity (Bq or Ci) at time, t

= decay constant [s-1]N0 = initial No of unstable nuclei Relation between half-life and decay constant2-t/T1/2 e-lt HALF-LIFE (T) REPRESENTATIONDECAY CONSTANT () REPRESENTATIONT1/2 is the time taken for 50% of the atoms to survive1/l is the time taken for the fraction 1/e (37%) of the atoms to survive (i.e., mean-life time, t). T1/2 = ln(2) / l = 0.693 / lPoint Source in Vacuum

N [photons/s](1/12 ) I0 = N/A [photons/s/cm2](1/3)2 I0 = N/(32A )[photons/s/cm2](1/22 ) I0 = N/(22A) [photons/s/cm2]

32Photon Beam Attenuation

m = N = linear attenuation coefficient [cm-1] Sourcer [cm]drI(r)I + dII0 [photons/cm2]N [atoms or electrons/cm3]CollimatorCollimatorDetector0Photon Fluence in MatterPoint source in matter (collimated)

Point source in matter (Broad)

Relation between half-value layer and attn coefficient2-x/HVL e-mx HALF-VALUE LAYER (HVL) REPRESENTATIONATTENUATION COEFFICIENT (m) REPRESENTATIONHVL is the thickness taken for 50% of the photons to survive1/m is the thickness taken for the fraction 1/e (37%) of the photons to survive (i.e., mean-free path, xm). HVL = ln(2) / m = 0.693 / mLinear vs. Semi-log Plotting of e-x or e-lt

Mono-energetic photons, = constant and, thus HVL = constantLinearSemi-log36Beam Hardening: Selective Absorption of Low-Energy Photons 101000123456Absorber Thickness (mm AL)Transmittance (%)1st HVL = 0.99mm2nd HVL = 1.99 mm3rd HVL = 2 mm1st HVL < 2nd HVL < 3rd HVL1st < 2nd

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