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3-1
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
3-2
Signal to Noise• Value of the signal to
noise can vary Values less than 3
make it hard to detect signal
s
x
deviationdards
mean
N
S
tan
3-3
Sources of Noise
• Chemical Noise Uncontrollable variables affecting
chemistry of system under investigationChange in equilibria due to variations
* Temperature* Pressure* Sample variation* Humidity
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
3-5
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
fkTRvrms 4
fIeirms 2
3-6
Instrument Noise• Flicker Noise
Inverse of signal frequency Important below 100 HzDrift in instruments
• Environmental Noise Emanates from surroundings
Electromagnetic radiation
3-7
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
3-8
Hardware
• Difference and Instrumentation Amplifiers Subtraction of noise from a circuit
Controlled by a single resistorSecond stage subtracts noise
Used for low level signal• Analog filtering
Uses a filter circuit Restricts frequency
3-9
Hardware
• Modulation Changes low frequency signal to higher
frequencySignal amplified, filter with a high pass
filter, demodulation, low pass filter• Signal Chopping
Input signal converted to square wave by electronic or mechanical chopperSquare wave normalizes signal
3-10
Software Methods• Ensemble Average
Average of spectra Average can also
be sum of collected spectra
• Boxcar average Average of points
in a spectra
3-11
Software Methods
3-12
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
3-13
Chap. 6 Introduction to Spectrometric Methods
• Electromagnetic radiation
• Interaction with matter• Quantum mechanical
properties
• Electromagnetic radiation orthogonal in phase
oscillations
3-14
Wave Parameters
• Amplitude and wavelength
3-15
Electromagnetic Spectrum
3-16
Methods
3-17
X-ray Structure
• X-rays0.01 to 100 angtroms
12 keV to 1 MeVIonizing radiation
• RoentgenGas discharge tubeDetector with Ba/Pt CN
Scintillator
3-18
• 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.
3-19
3-20
Energy from X-ray
• From Cu13.6(29^2)=11.4 keV
Based on Bohr atom
Family of lines due to different levels
• Determination of elements
3-21
3-22
Mosley
• Measured 38 elementsMeasured emission
spectra and found pattern
Based on Z, not mass (Ar/K, Co/Ni, Te/I)
Place lanthanides on periodic table14 lanthanides
Up to U there are 92 elements
3-23
3-24
3-25
X-ray Structure
• Review of cathode ray tube and nomenclature
• Determination of elements from X-rays
• Coolidge1913
Vacuum tube
* Reduction of collision with gas
* Reduce glowHeating CathodeWater coolingShielding (Pb), Be windows
3-26
X ray linesLines with continuum
function of voltage
Mo BCC
from bremstrallung
3-27
Bremsstrahlung
E=qV=eV=E(photon)=12400/V Ang
Duane-hunt law
3-28
Use x-ray to examine crystals
• Model atoms as mirrorsUse classical optics
• Utilize interferenceConstructive and destructive
3-29
X-ray diffraction
• Emission spectrum from x-ray generatorComposite of 2
spectraCharacteristic
spectraContinuous
spectraCalculate lines by
Mosley’s Law
3-30
Braggs Law
Specifics conditions for interference
Set of reflections identifies structure
3-31
XRD
• Fixed wavelength, vary angle
• Powder specimen
• Grains act as single crystal
• Plot I vs angleAt Bragg angle produce
angle
3-32
Data analysis
Normalize data to 1st sin^2theta
Clear fractions
Speculate on hkl
Know wavelength from source, solve for a
3-33
Laue Technique
3-34
Spot pattern
• For symmetry2, 3, 4 fold symmetry
• May not work for thick specimenBackscatter and transmission
3-35
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
3-36
Atomic Spectra
• Quantum numbersn=1,2,3,4r=aon2/Z for gases with 1 electron
• EnergyE=-(mee4/8
2h2)Z2/n2
For ground state HE=2.18E-18 J/atom=k
* Can determine J/mole 1312 kJ/moleEnergy goes as –k/n2
* System converges to limit
3-37
Energy
• n=infinity, r=infinity , E=0, unbound e-
• Ionization energyk is ionization energy
• Velocityv=nh/2mer
• Ionization energyMinimum energy required to remove
electron from atom in gas phaseMultiple ionization energies
3-38
Balmer states
• Gas H in tubeFour lines in visible regionFit lines
• 1/=(1/22-1/n2)R, R=1.1E-7 m-1
1/(wavenumber)E=1/2mev2=eV (V=Volts)
At 1 V = 1.6E-19 J =eVK=13.6 eV
3-39
Matter energy interaction
• Eincident=1/2mv2=qV
• Escattered
E =Eincident-Escattered
E=kZ2(1/n2final-1/n2
in)=h=hc/
De-excitation of electron results in photon emissionCorresponds to line emission
3-40
Shell model and multielectrons
• Particle interactionParticle hits electron, electron has scatted kinetic
energyEinc=Ebinding+Eelectron scattered
* For ground state Ebinding is ionization energy
Einc= 0.5mv2
Etrans=-kZ2(1/n2)
For photon E=hc/
3-41
Rydberg)
n
1
n
1(
hc
k2o
2f
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
3-42
Bohr Atom
• Net force on the electron is zero0=Fdynamic+Fcoulombic
1/2mev2/r+q1q2/4r2
Force is 1/r2
Energy 1/r1/2mev2/r-Ze2/4r2
Z is charge on nucleus
• Quantize energy through angular momentummvr=nh/2n=1,2,3….
Can solve for r, E, v
FdrE
3-43
Bohr radius
• R=(h2/mee2)(n2/Z)
Radius is quantized and goes at n2
R=0.529 Å for Z=1, n=1Ao (Bohr radius)
3-44
Photoelectric effect