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  4kTRf

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  2Ief
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/ln (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