Chap. 5 (Signals and Noise), Chap. 6 (Spectroscopy
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Transcript Chap. 5 (Signals and Noise), Chap. 6 (Spectroscopy
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
Signal to Noise
• Value of the signal to
noise can vary
Values less than 3
make it hard to
detect signal
S
m ean
x
N s tandard deviation s
3-2
Sources of Noise
• Chemical Noise
Uncontrollable variables affecting
chemistry of system under investigation
Change in equilibria due to variations
* Temperature
* Pressure
* Sample variation
* Humidity
3-3
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
Instrument Noise
• Based on Boltzmann
vrms 4kTRf
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
irms 2Ief
3-5
Instrument Noise
• Flicker Noise
Inverse of signal frequency
Important below 100 Hz
Drift in instruments
• Environmental Noise
Emanates from surroundings
Electromagnetic radiation
3-6
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
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
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
Software Methods
• Ensemble Average
Average of spectra
Average can also
be sum of collected
spectra
• Boxcar average
Average of points
in a spectra
3-10
Software Methods
3-11
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
Chap. 6 Introduction to Spectrometric
Methods
• Electromagnetic
radiation
• Interaction with matter
• Quantum mechanical
properties
• Electromagnetic
radiation
orthogonal in phase
oscillations
3-13
Wave Parameters
• Amplitude and wavelength
3-14
Electromagnetic Spectrum
3-15
Methods
3-16
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
• 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 "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
3-19
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
3-20
3-21
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
3-23
3-24
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
X ray lines
Lines with continuum
function of voltage
Mo BCC
from bremstrallung
3-26
Bremsstrahlung
E=qV=eV=E(photon)=12400/V Ang
Duane-hunt law
3-27
Use x-ray to examine crystals
• Model atoms as mirrors
Use classical optics
• Utilize interference
Constructive and destructive
3-28
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
Braggs Law
Specifics conditions for interference
Set of reflections identifies structure
3-30
XRD
•
•
•
•
Fixed wavelength, vary angle
Powder specimen
Grains act as single crystal
Plot I vs angle
At Bragg angle produce
angle
3-31
Data analysis
Normalize data to 1st sin^2theta
Clear fractions
Speculate on hkl
Know wavelength from source, solve for a
3-32
Laue Technique
3-33
Spot pattern
• For symmetry
2, 3, 4 fold symmetry
• May not work for thick specimen
Backscatter and transmission
3-34
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
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
3-36
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
3-37
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/ln (wavenumber)
E=1/2mev2=eV (V=Volts)
At 1 V = 1.6E-19 J =eV
K=13.6 eV
3-38
Matter energy interaction
• Eincident=1/2mv2=qV
• Escattered
E =Eincident-Escattered
E=kZ2(1/n2final-1/n2in)=hn=hc/l
De-excitation of electron results in photon
emission
Corresponds to line emission
3-39
Shell model and multielectrons
• Particle interaction
Particle hits electron, electron has scatted
kinetic energy
Einc=Ebinding+Eelectron scattered
* For ground state Ebinding is ionization
energy
Einc= 0.5mv2
Etrans=-kZ2(1/n2)
For photon E=hc/l
3-40
Rydberg
k 1
1
n ( )
hc n f2 n o2
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
3-41
Bohr Atom
• Net force on the electron is zero
0=Fdynamic+Fcoulombic
1/2mev2/r+q1q2/4peor2
Force is 1/r2E Fdr
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
3-42
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)
3-43
Photoelectric effect
3-44