Test 1 Flashcards
measurement
assigning a value to a physical quantity based on a standard
data domains
the ways that information can be encoded in an object or via a signal throughout the measurement process
error types
random, systemic (consistently lower or higher), human (bias)
what measurement represents precision
standard deviation, = random error
calibration sensitivity
slope of the detection line
analytical sensitivity
slope over standard deviation
ppm=
mg/L
ppb=
ug/L
flow of information in an instrument
stimulus (from device)> sample > response> transducer > some data domain> information processor> readout (usually a computer)
analog quantities are measured
by magnitude (electrical current, etc) over time
transducer
interconverts info from electrical to nonelectrical domains
input transducer
transducer that takes info from nonelectric to electric domains
detector
mechanical, electrical, or chemical detector to show change in temp, pressure, electricity, radiation, ion conc, *smoke detector
readout device
transducer that converts from electric to nonelectric domains
sensor
monitors a specific chemical species and changes reversibly in response to a change. has recognition>transducer>readout *glucose sensor
how to select instrumentation
consider required accuracy, amount of sample, concentration range, interference, physical and chemical properties, and number of samples to be processed
pop. mean and SD
u and sigma
sample mean and sd
x bar and s
normal distribution
1s: 68.3%, 2s: 95.45%, 3s: 99.73%
least square assumption
error in y > error in x
bias (gamma)
calculated as y= u - xbar (pop. - sample). = system error
accuracy calculation
comparing sample mean and pop. mean (bias calculation)
LOD equation
C = (3Sbl/m)
selectivity eq (general anal chem)
S = maCa + mbCb +……
selectivity coefficient (for interfering spp in sensors)
k(b,a) = mb/ma (closer to 0 is better)
dynamic range
which concs have reliable results, located btwn the LOQ and LOL
type 1 error
false positive
type 2 error
false negative
LOQ
limit of quantitation, above in measurements have 5% standard error
degree of freedom
n-2 because we need 2 of the points just to make a line
degree of freedom in sample mean
n-1 bc the mean occupies one number
Cdl
=3Sbl/m (the conc at the DL is 3 SD of the blank out)
standard deviation units
same as the mean
relative error
(Cmeasured - Creal)/Creal
thermal/Johnson noise
charge carriers in resistors, capacitators, (anything with resistance) cause random error corresponding to the bandwidth and temperature. - frequency independent
shot noise
quantized particles (whole numbers) cross a junction, cause random noise, frequency independent. can be dec with bandwidth change.
flicker noise
aka 1/f noise, inversely proportional to frequency
environmental noise
frequency dependent bc it is at specific frequencies, non-fundamental, things like EM waves from radio
S/N
signal to noise ratio is set equal to mean signal/standard deviation also = 1/RSD
non-random noise
systemic error in measurement equipment causes high or low interference
fundamental noise
noise due to uncertainty principle etc or factors of physical instrumentation
noise reducing hardware
grounding/shielding, difference/instrument amplifier, analog filter, modulation
noise reduction in measurement
take the same measurement many many times using S/N=sqrt(n)(Sx/Nx) for desired ratio
n in noise/signal
the number of measurements conducted
S/N at which signal is indiscernible
S/N =3
conjugate quantities
when one is measure precisely it is impossible to measure the other precisely ie. position and speed, creates fundamental noise
white noise
aka gaussian noise, any frequency independent noise (thermal, shot)
A/C frequency (in US)
60 Hz
chemical noise
variations in chemicals (ie batches of the same soln vary by 0.1%)
rising time
time interval it takes between 10% and 90% power of an electrical signal when activated
Poisson process
used to measure probability of something discrete (ie e- for shot noise) P= (lambda^k(e^-lambda))/k!
bandpass filter
filters out high and low ranges leaving some middle range of signal
high-pass filters
filter out long wavelengths
low-pass filters
filter out short wavelengths, often used for DC, thermal and shot noise
grounding and shielding
physically prevent electronic interference by surrounding with grounded conductive material which attracts signal to make it not be noise.
modulation
used for DC or low frequency signal, as 1/f noise is high, and then high pass filter can be used and it can be returned to og frequency with reduced noise. example: mechanic chopper
ensemble averaging
higher n to approach true value thru averaging
central limit theorem
more measurements approach normal distribution, with the center being the “true” value
adding values with associated noise
S(n) (+-) Nsqrt(n), and averaging this way shows how noise gets smaller
electric domain types
digital, analog, time
LOQ equation
C = (10Sbl/m)
quantitation
connecting concepts of measurement/calculation
difference/instrument amplifier
used instead of a normal amplifier when the signal is read so there is less noise. (difference cancels parts in common, instrument is second choice and reduces common noise with extra pieces). used for low signal in noisy environment
when the selectivity eq takes the form s = m(Ca + KCb …..) the term in parenthesis is..
the value measured by the instrument
Huygens
there are waves and wavelets - wave nature of light
energy of a photon =
hv, v = freq
Thomas Young
slit diffraction - it it diffracts it must be a wave (light)
wave number
number associated with a reciprocal wavelength in 1/cm
diffraction distance equation
wavelength = line segment BC*DE/(nOE), n = number of bands, where BC is distance between two entrance slits, OE is the horizontal distance between the slits and the far wall, and DE is the distance between the band and the part of the wall horizontal to the entrances.
transmission
speed of light changes based on medium
refractive index eq
engi = c/v (v is velocity). it is the ratio of the speed of light to the speed of light in the material ie how much slower it is
conserving energy in different media
c must change bc lambda = c/v and v cannot change
dispersion
variation in refraction index throughout a substance
dispersion of a substance eq
D = engi(lambda)
anomalous dispersion
sharp drop in dispersion graph due to shift in engi from absorption at a certain wavelength for the substance
speed and density
due to refraction, more dense objects dec. speed.
metamaterials
have negative ri (reflective index), the light direction flips
speed and refraction/reflection
reflection can have a negative speed, refraction cannot (they are vectors)
angle of incidence is equal to..
angle of reflection
reflection eq
Ir/Io = (eng2-eng1)^2/(eng2+eng1)^2, where Ir is intensity of reflected beam and Io is initial intensity
boundary
change between media (b to a = a to b)
black body
ideal physical object that is opaque, non-reflective, absorbs all EM waves
black body radiation
= thermal/cavity radiation. what surrounds a body (black body( at eq with its environment
photoelectric effect equation
E = hv = KE - work function
matter wave function
de Broglie, 1923, lambda = h/p (p is momentum)
hamiltonian and eigenvalues
measures of energy correspond to a hamiltonian operator and an eigenvalue
Compton scattering
inelastic scattering of light by a free moving charged particle like e-
Thomson scattering
Elastic scattering of light by a free moving charged particle like e-
inelastic scattering
energy of photons is changed
UV and visible light cause..
e- transitions/excitation, emission of light
infrared light causes..
atoms to vibrate
microwave radiation causes..
atoms to rotate
spectroscopy components in order
source of radiation, sample (in container), wavelength selector, radiation detector, photoelectric transducer, signal processor, signal readout
types of radiation sources
continuum, line, laser
continuum radiation source
changes in intensity slowly as a function of lambda
line radiation source
emits a limited number of lines or bands of radiation
laser radiation source
emits narrow, monochromatic, coherent, intense beam
source of noise in radiation for spectrometry
the fluctuation in radiation
narrow bandwidth is important bc
it gets you a linear relationship between concentration and signal
effective bandwidth
the width halfway up the peak
types of optical filters
long pass, short pass, bandpass, interference, absorption
long pass filter
transmission of >400 nm
short pass filter
transmission of <600 nm
bandpass filter
shows a large portion in the middle, around 100 nm range
interference filter
uses constructive interference, has dielectric layer and reflective part. wavelengths are usually UV to IR, eff bandwidths are 1.5% of the wavelength
absorption filter
absorb bandwidths maybe 30-250 nm
monochromators
can use grating or prism to direct a spec lambda out the exit
1 angstrom =
0.1 nm
Snell’s law
sin (angle of incidence)/sin(angle of refraction) = eng2/eng1 = v1/v2
refractive index
measure of how much a medium interferes with radiation
coherent radiation
sources have identical freq and phase relationships over time. necessary if you want to create a diffraction pattern
work function
constant that shows the min. electron binding energy in a substance
photoelectric effect
photoelectrons can be emitted from a substance when a specific wavelength of light / photons hit it
phosphorescence
light emitted by electrons going down in energy level but delayed after the initial energy input
resonance florescence
when emitted light has the same frequency as the beam used to excite the e-
stokes shift
shift down in energy between excitation beam and fluorescence due to the energy released by vibration of the e-
conserving energy in change of medium eq
speed = lambda1/freq1 = lambda2/freq2
does speed of light change
yes, it does, and wavelength does, so freq can stay constant
interference filter equation
lambda = 2t(eng)/n (n is order, t is thickness) OR 2dn (d = thickness, n = 1)
grating: angular dispersion eq
n/dcos(r) where r = reflection angle, d = distance of 1 slit, n = order of diffraction
grating: linear dispersion eq
focal length*(n/dcos(r)), where r = reflection angle, d = distance of 1 slit, n = order of diffraction
reciprocal linear dispersion eq
d/nf ..where d = distance of 1 slit, n = order of diffraction, f = focal length
resolving power of 2 freqs eqs
lamba hat = avg of 2 lambdas, over delta lambda = diff btwn the 2.
effective bandwidth eq
(lambda2-lambda1)/2 = half the distance
how to get slit width
lambda(eff)=w(D^-1) (effective bandwidth and reciprocal linear dispersion)
resolving power eq
R = nN where n is diffraction order, N is # of slits that have light on them
1 einstein
1 mol photons
bandwidth and slit width
bandwidth= the distance btwn lambdas that is the width of the beam, eff bandwidth is what actually comes out (1/2 distance), and that is the slit width. we want smaller signals so we want smaller bandwidth but this sacrifices time
data domain categories
physical/chemical, digital, analog, time
digital data domains
number, parallel, serial, count
analog data domains
current, voltage, charge
time data domains
phase, freq, pulse width(ie rising time)
focal length
how far light travels btwn diffraction and target
radiation detectors work by..
transforming radiation energy to electrical signal
information conducted in stages of spectrophotometry
intensity of beam, concentration of analyte, electrical charge, computation, then readout
prop of error for multiplication/ division
the square root of the sum of the % errors (both squared) = the % of the result - multiply by the result to get the actual error
radiation detector types
photon detectors or thermal detectors (only IR)
electric signal eq
S (signal) = kP + kd (kd = dark constant, k = calibration sensitivity, P= power of the radiation)
photomultiplier
photon detector where signal is amplified by a series of plates
signal processor in spectrophotometer
amplifies electrical signals from transducer, converts them from analog to digital
fiber optics
can be used to transmit electricity 100s of meters
prop of error adding and subtracting
square root of the sum of the squares of the errors
error in analytical processes
every stage has an associated error
