Signal to noise Source of noise Signal to noise enhancement

Transcription

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 3-1

2 Signal to Noise Value of the signal to noise can vary S N mean = s tan dard deviation = x s Values less than 3 make it hard to detect signal 3-2

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

4 Source of Noise Instrumental Noise Thermal noise Shot noise Flicker Environmental noise Thermal noise Thermal agitation of electrons in electronics Boltzmann s equation 3-4

5 Instrument Noise Based on Boltzmann R is resistance vrms = 4kTR f 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 i rms = 2Ie f 3-5

6 Flicker Noise Instrument Noise Inverse of signal frequency Important below 100 Hz Drift in instruments Environmental Noise Emanates from surroundings Electromagnetic radiation 3-6

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 3-7

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 3-8

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 3-9

10 Ensemble Average Average of spectra Average can also be sum of collected spectra Boxcar average Average of points in a spectra Software Methods 3-10

11 Software Methods 3-11

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 3-12

13 Chap. 6 Introduction to Spectrometric Methods Electromagnetic radiation Interaction with matter Quantum mechanical properties Electromagnetic radiation orthogonal in phase oscillations 3-13

14 Wave Parameters Amplitude and wavelength 3-14

15 Electromagnetic Spectrum 3-15

16 Methods 3-16

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 3-17

18 In November of 1895, Wilhelm Roentgen ( ) 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 "Xrays". 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. 3-18

19 3-19

20 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 3-20

21 3-21

22 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 3-22

23 3-23

24 3-24

25 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 3-25

26 X ray lines Lines with continuum Mo BCC function of voltage from bremstrallung 3-26

27 Bremsstrahlung E=qV=eV=E(photon)=12400/V Ang Duane-hunt law 3-27

28 Use x-ray to examine crystals Model atoms as mirrors Use classical optics Utilize interference Constructive and destructive 3-28

29 X-ray diffraction Emission spectrum from x-ray generator Composite of 2 spectra Characteristic spectra Continuous spectra Calculate lines by Mosley s Law 3-29

30 Braggs Law Specifics conditions for interference Set of reflections identifies structure 3-30

31 XRD Fixed wavelength, vary angle Powder specimen Grains act as single crystal Plot I vs angle At Bragg angle produce angle 3-31

32 Data analysis Normalize data to 1 st sin^2theta Clear fractions Speculate on hkl Know wavelength from source, solve for a 3-32

33 Laue Technique 3-33

34 Spot pattern For symmetry 2, 3, 4 fold symmetry May not work for thick specimen Backscatter and transmission 3-34

35 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 3-35

36 Atomic Spectra Quantum numbers n=1,2,3,4 r=a o n 2 /Z for gases with 1 electron Energy E=-(m e e 4 /8ε ο2 h 2 )Z 2 /n 2 For ground state H E=2.18E-18 J/atom=k * Can determine J/mole 1312 kj/mole Energy goes as k/n 2 * System converges to limit 3-36

37 Energy n=infinity, r=infinity, E=0, unbound e - Ionization energy k is ionization energy Velocity v=nh/2πm e r Ionization energy Minimum energy required to remove electron from atom in gas phase Multiple ionization energies 3-37

38 Balmer states Gas H in tube Four lines in visible region Fit lines 1/λ=(1/2 2-1/n 2 )R, R=1.1E-7 m -1 1/λ=ν (wavenumber) E=1/2m e v 2 =ev (V=Volts) At 1 V = 1.6E-19 J =ev K=13.6 ev 3-38

39 Matter energy interaction E incident =1/2mv 2 =qv E scattered E =E incident -E scattered E=kZ 2 (1/n 2 final -1/n2 in ) =hν=hc/λ De-excitation of electron results in photon emission Corresponds to line emission 3-39

40 Shell model and multielectrons Particle interaction Particle hits electron, electron has scatted kinetic energy E inc =E binding +E electron scattered * For ground state E binding is ionization energy E inc = 0.5mv 2 E trans= -kz 2 (1/n 2 ) For photon E=hc/λ 3-40

41 Rydberg ν = k 1 ( hc n k/hc=1.1e-7 m -1 = R (Rydberg constant) Visible light nm (1.8 to 3.1 ev) Quantum numbers n=1,2,3,4 l=0 to n-1 m l = +-l Spin=+-1/2 2 f n 1 2 o ) 3-41

42 Bohr Atom Net force on the electron is zero 0=F dynamic +F coulombic 1/2m e v 2 /r+q 1 q 2 /4πε ο r 2 Force is 1/r 2 Energy 1/r E 1/2m e v 2 /r-ze 2 /4πε ο r 2 Z is charge on nucleus Quantize energy through angular momentum mvr=nh/2π, n=1,2,3. Can solve for r, E, v = Fdr 3-42

43 Bohr radius R=(ε ο h 2 /πm e e 2 )(n 2 /Z) Radius is quantized and goes at n 2 R=0.529 Å for Z=1, n=1 A o (Bohr radius) 3-43

44 Photoelectric effect 3-44