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Chap. 5 (Signals and Noise), Chap. 6 (Spectroscopy introduction)

Chap. 5 (Signals and Noise), Chap. 6 (Spectroscopy introduction). Signal to noise Source of noise Signal to noise enhancement Signal has the information of the analyte Noise is the extraneous information in the information due to electronics, spurious response, and random events

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Chap. 5 (Signals and Noise), Chap. 6 (Spectroscopy introduction)

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  1. Chap. 5 (Signals and Noise), Chap. 6 (Spectroscopy introduction) • Signal to noise • Source of noise • Signal to noise enhancement • Signal has the information of the analyte • Noise is the extraneous information in the information due to electronics, spurious response, and random events • Signal to noise ratio • Noise is generally constant and independent of the signal • The impact of noise is greatest on the lowest signal • The ratio of signal to noise is useful in evaluating data

  2. Signal to Noise • Value of the signal to noise can vary • Values less than 3 make it hard to detect signal

  3. Sources of Noise • Chemical Noise • Uncontrollable variables affecting chemistry of system under investigation • Change in equilibria due to variations • Temperature • Pressure • Sample variation • Humidity

  4. Source of Noise • Instrumental Noise • Thermal noise • Shot noise • Flicker • Environmental noise • Thermal noise • Thermal agitation of electrons in electronics • Boltzmann’s equation

  5. Instrument Noise • Based on Boltzmann • R is resistance • k is Boltzmann’s constant • 1.38E-23 J/K • T in K • f is frequency bandwith (1/3*risetime) • Relates to response time in instrument • Shot Noise • Electrons crossing a junction • pn junction, anode and cathode • Random events • e = 1.6e-19 C

  6. Instrument Noise • Flicker Noise • Inverse of signal frequency • Important below 100 Hz • Drift in instruments • Environmental Noise • Emanates from surroundings • Electromagnetic radiation

  7. Signal to Noise Enhancement • Hardware and software methods • Hardware is based on instrument design • Filters, choppers, shields, detectors, modulators • Software allows data manipulation • Grounding and Shielding • Absorb electromagnetic radiation • Prevent transmission to the equipment • Protect circuit with conduction material and ground • Important for amplification

  8. Hardware • Difference and Instrumentation Amplifiers • Subtraction of noise from a circuit • Controlled by a single resistor • Second stage subtracts noise • Used for low level signal • Analog filtering • Uses a filter circuit • Restricts frequency

  9. Hardware • Modulation • Changes low frequency signal to higher frequency • Signal amplified, filter with a high pass filter, demodulation, low pass filter • Signal Chopping • Input signal converted to square wave by electronic or mechanical chopper • Square wave normalizes signal

  10. Software Methods • Ensemble Average • Average of spectra • Average can also be sum of collected spectra • Boxcar average • Average of points in a spectra

  11. Software Methods

  12. Digital Filtering • Numerical methods • Fourier transform • Time collected data converted to frequency • NMR, IR • Least squares smoothing • Similar to boxcar • Uses polynomial for fit • Correlation

  13. Chap. 6 Introduction to Spectrometric Methods • Electromagnetic radiation • Interaction with matter • Quantum mechanical properties • Electromagnetic radiation • orthogonal in phase oscillations

  14. Wave Parameters • Amplitude and wavelength

  15. Electromagnetic Spectrum

  16. Methods

  17. X-ray Structure • X-rays • 0.01 to 100 angtroms • 12 keV to 1 MeV • Ionizing radiation • Roentgen • Gas discharge tube • Detector with Ba/Pt CN • Scintillator

  18. In November of 1895, Wilhelm Roentgen (1845 - 1923) was working in his laboratory using a Crookes tube (known in German as either a Hittorf valve or a Hittorf-Crookes tube) when he noticed that a sample of barium platinocyanide, which accidentally lay on the table, gave off a fluorescent glow. As the Crookes tube was covered at the time, Roentgen was puzzled as to the mechanism whereby the platinum compound was being stimulated to glow. After carrying out a series of exceptionally careful experiments, Roentgen realized that the Crookes tube was emitting a new kind of radiation which he described as "X-rays". In investigating the penetrating ability of these rays, Roentgen placed a photographic plate behind his wife's hand and recorded the first x-ray photo. In this figure, below, notice his wife's wedding rings that stand out as dark rings.

  19. Energy from X-ray • From Cu • 13.6(29^2)=11.4 keV • Based on Bohr atom • Family of lines due to different levels • Determination of elements

  20. Mosley • Measured 38 elements • Measured emission spectra and found pattern • Based on Z, not mass (Ar/K, Co/Ni, Te/I) • Place lanthanides on periodic table • 14 lanthanides • Up to U there are 92 elements

  21. X-ray Structure • Review of cathode ray tube and nomenclature • Determination of elements from X-rays • Coolidge • 1913 • Vacuum tube • Reduction of collision with gas • Reduce glow • Heating Cathode • Water cooling • Shielding (Pb), Be windows

  22. X ray lines Lines with continuum function of voltage Mo BCC from bremstrallung

  23. Bremsstrahlung E=qV=eV=E(photon)=12400/V Ang Duane-hunt law

  24. Use x-ray to examine crystals • Model atoms as mirrors • Use classical optics • Utilize interference • Constructive and destructive

  25. X-ray diffraction • Emission spectrum from x-ray generator • Composite of 2 spectra • Characteristic spectra • Continuous spectra • Calculate lines by Mosley’s Law

  26. Braggs Law Specifics conditions for interference Set of reflections identifies structure

  27. XRD • Fixed wavelength, vary angle • Powder specimen • Grains act as single crystal • Plot I vs angle • At Bragg angle produce angle

  28. Data analysis Normalize data to 1st sin^2theta Clear fractions Speculate on hkl Know wavelength from source, solve for a

  29. Laue Technique

  30. Spot pattern • For symmetry • 2, 3, 4 fold symmetry • May not work for thick specimen • Backscatter and transmission

  31. Transmission of radiation • Polarization • Directional filtering of light • Light will be scattered by larger molecules • Radiation transfer to molecules • Absorption spectroscopy • Material consideration • Glass, quartz, plastic

  32. Atomic Spectra • Quantum numbers • n=1,2,3,4 • r=aon2/Z for gases with 1 electron • Energy • E=-(mee4/8eo2h2)Z2/n2 • For ground state H • E=2.18E-18 J/atom=k • Can determine J/mole 1312 kJ/mole • Energy goes as –k/n2 • System converges to limit

  33. Energy • n=infinity, r=infinity , E=0, unbound e- • Ionization energy • k is ionization energy • Velocity • v=nh/2pmer • Ionization energy • Minimum energy required to remove electron from atom in gas phase • Multiple ionization energies

  34. Balmer states • Gas H in tube • Four lines in visible region • Fit lines • 1/l=(1/22-1/n2)R, R=1.1E-7 m-1 • 1/l=n (wavenumber) • E=1/2mev2=eV (V=Volts) • At 1 V = 1.6E-19 J =eV • K=13.6 eV

  35. Matter energy interaction • Eincident=1/2mv2=qV • Escattered • DE =Eincident-Escattered • DE=kZ2(1/n2final-1/n2in)=hn=hc/l • De-excitation of electron results in photon emission • Corresponds to line emission

  36. Shell model and multielectrons • Particle interaction • Particle hits electron, electron has scatted kinetic energy • Einc=Ebinding+Eelectron scattered • For ground state Ebindingis ionization energy • Einc= 0.5mv2 • DEtrans=-kZ2D(1/n2) • For photon E=hc/l

  37. Rydberg k/hc=1.1e-7 m-1 = R (Rydberg constant) Visible light 400-700 nm (1.8 to 3.1 eV) Quantum numbers n=1,2,3,4 l=0 to n-1 ml= +-l Spin=+-1/2

  38. Bohr Atom • Net force on the electron is zero • 0=Fdynamic+Fcoulombic • 1/2mev2/r+q1q2/4peor2 • Force is 1/r2 • Energy 1/r • 1/2mev2/r-Ze2/4peor2 • Z is charge on nucleus • Quantize energy through angular momentum • mvr=nh/2p, n=1,2,3…. • Can solve for r, E, v

  39. Bohr radius • R=(eoh2/pmee2)(n2/Z) • Radius is quantized and goes at n2 • R=0.529 Å for Z=1, n=1 • Ao (Bohr radius)

  40. Photoelectric effect

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