1. For each of the following properties that might be used to evaluate an instrument,
name and give the equation for at least one Figure of Merit used to evaluate that
property.
precision
Standard deviation
There are also others
bias
bias = ì-Xt, where ì is the population mean in a sample with a true mean
of Xt.
Sensitivity
Analytical Sensitivity(ã) = m/ss, where m is the slope and ss is the standard
deviation of the measurement.
Detection limit
Sm is the minimum analytical signal, Sbl(bar) is the average blank signal,
k is sone number of standard deviations, and sbl is the standard deviation
of the blank
Dynamic range
The low end of the dynamic range is set by the limit of quantitation (LOQ)
Which is generally taken as the average blank values + 10x the standard deviation of
the blank. The upper limit of the dynamic range is taken from the limit of linearity (LOL),
or the place where you calibration curve departs from a straight line
The ability to measure one compound in the presence of a second compound
that also gives a signal.
Signal = mA[A] + mb[B] + Sbl
Where ma and mb are the response slopes for a and b, and Sbl is our
blank value. The selectivity coefficient for A with respect to B is kB,A =
mB/mA.
2. Here are three equations that relate to some type of noise. Tell me the kind of noise
the equation describes, where it comes from, and what the equation says about how
you can minimize this kind of noise.
Shot Noise -Arises when electrons cross a junction. Can be
junctions between n and p material in a transistor, Electrons
jumping across a vacuum in a vacuum tube, solder joints in the circuit board, etc.
Arises because electrons are quanta of charge, and flow of charge across a junction is
therefor a multiple quanta event, and has to be dealt with using statistics. To reduce
this noise you must reduce the current in the circuit(I) or the frequency bandwidth of the
instrument (Äf)
Thermal Noise or Johnson Noise
Caused by thermal agitation of electrons and other charge carriers
in any part of the electronics (resistors, capacitors, Integrated
chips, transistors, wires, connections etc) and Random inhomogeneities of charge and
therefore voltage at readout. To reduce this noise you must lower the resistance of the
Circuit R or the T of the instrument (T) or the frequency bandwidth of the instrument Äf.
Noise %1/f Flicker noise or drift. Cause is not understood. To reduce this you
must increade the frequency of the signal.
3. In this class we are constantly changing between different measures of wavelength
or frequency. Perform the following conversions
280 nm (unit used in the UV) To ìm (unit used in the IR)
600 nm (unit used in Vis) to frequency in MHz (unit used in NMR)
c=ëí; 3x108m/s=600x10-9m @X; X=3x108m/s/600x10-9m = 5x1014 Hz
800 nm (unit used in near IR) to frequency in cm-1 (unit used in IR)
(Hint: cm-1 can be thought of as how many waves are in a cm)
1 cm = .01 m; .01/800x10-9m = 12500 waves/cm
4. Make a figure of what an emission spectrum from a material vs wavelength might
look like over a large range of wavelengths, and use this figure to illustrate the
difference between line spectra, a band spectra and a continuum. What causes these
three different kinds of emission from a material?
Figure like figure 6-15 from text. Line spectra are sharp lines, band are bands,
and the continuum is an overall raising of the baseline at lower wavelengths. Line
spectra are caused by electronic transitions in atoms, band spectra are caused many
closely spaced rotational and vibrations states that occur in small molecules or ions.
The continuum is a general emission of black body radiation that occurs in all material
dependent on their temperature.
5. What is stimulated emission and how does it relate to a laser?
Stimulated emission is the emission of radiation from a molecule or atom in an excited
state due to the passing of a photon that is at the same frequency (or energy) as the
excited atom or molecule. It is the SE in laSEr (light amplification by Stimulated
Emission of Radiation. It is the interaction that makes a laser work.
6. Describe four different types of photon transducers.
Photovoltaic of Barrier Layer cells
Cheap, Rugged, Not very sensitive, need lots of light
Vacuum Phototubes
Figure 7-27. Cathode and wire sealed in a vacuum. Photons hit
photoemissive cathode, electrons released, attracted to anode. + of
electrons proportional to amount of light.
Photomultiplier Tubes
Figure 7-29 Sort of similar to phototube but redesigned for extreme
sensitivity , so good at low light levels. Starts like phototube, with
photoemissive surface. Instead of electrons going directly to cathode,
goes toward a series of ‘dynodes’. As electrons hit dynode they release
additional electrons.
Silicon Diode Transducers
Essentially a transistor that passes more current when exposed to light
7. When you look at the sky in daylight light you see light that has been scattered two or
more times from gas molecules in the air. Rayleigh Scattering occurs when the
wavelength of the light is much larger than the molecule doing the scattering. Given
that the intensity of scattered light in Rayleigh Scattering is proportional to 1/ë4
A. Compare the intensity of scattered Blue light (ë= 400 nm) to scattered Red light
(ë=650 nm)
Say that light has intensity X
Scattered blue light (400 nm) = X/4004 = X/2.56x1010 = 3.9x10-11X
Scattered red light (650 nm) = X/6504 = X/1.78x1011 = 5.6x10-12X
So Blue light/Red light 3.9x10-11/5.6x10x10-12 = 6.9
So the scattered blue light is ~7 more intensity than the scattered red light,
so you see a blue sky.