March 7, 2001

Exam 2

Each question is worth 10 points

Hint: that's 5 minutes per question on average. Answers that take 10 minutes to write probably

have more detail than I'm seeking-- keep it focused. If your answer only takes one minute to write you are either very brilliant, you are short on details or you are missing the point of the question.

USe back of page or extra paper if you need more space.

• a. What is the molar extinction coefficient of the dye?
  • epsilon = -log10(0.442)/ (5.00 *0.0125)
• b. What concentration is needed to absorb 99.9% of the 546 nm light in a 1.0 mm layer?
  • conc = Abs/(path*eps) = -log10(0.001)/(0.1* epsilon, above)

• Lithium can be detected using the 670.8 nm emission line. This is a 2p --> 2s transition.
• The ionization potential of Li is 5.390 eV (1 eV = 1.6 x 10^-19 J)
• a. What fraction of the Li atoms in the flame are excited and thus able to emit?
• b. What fraction of the Li atoms are actually ionized,
• and what would be the expected signal loss due to ionization?
  • N(_j) / N(₀) = (P_j/P_o) exp (- E_j /k T)
  • k= 1.38 x 10^-23 J/K h= 6.62 x 10^-34 J sec c= 3.00 x 10⁸ m/sec
• part a --atoms
  • E*= (hc/lambda) = 6.62 x 10^-34 J sec * 3.00 x 10⁸ m/sec /670.8 x 10^-9 m
  • kT = 1.38 x 10^-23 J/K *(2400+273)
  • P3p/P3s = 3
  • N(3p)/N(0) = ______
• partb ions
  • E(ion) = 5.390 eV * 1.6 x 10-19 J/eV =
  • Presumably N*/N = 1/2 (two spin states for 2s electon, unique closed shell for Li+)
  • N(ion)/N(0) = ________
  • signal loss is basically fraction ionized (e.g., 10% ionized= 10% loss in signal)

• a) The excited state, Q*, has a lifetime of 0.72 nsec. and emits at 487 nm.
• b) Q* atoms are traveling with a mean velocity of 3.2 x 10⁴ m/sec
• c) Q* atoms collide with other species in the flame every 3.75 microseconds?
  • Dl/ l = v / c c= 3.00 X10⁸ m/sec
• part a-- delta-t x delta-nu = 1
  • delta nu = 1/0.72x 10^-9 = 1.4 x 10⁹ Hz
  • delta lambda = ______
    • lambda = c / freq
    • so d(lambda) = -(c/freq² ) d(freq)
    • d(lambda) = (lambda²/c) d(freq)= 487X10^-9)² * 1.4 x 10⁹/3.00 X10⁸
    • = 1.1 X10-12 m or 0.0011 nm
• part b-- doppler shift
  • delta-lambda/lambda = 3.2 x10⁴/ 3x 10⁸ = 0.0001
  • delta-lambda = 487 nm x 0.0001 = 0.05 nm
• part c (as in a but delta-t is 3.75 x 10^-6 sec)
  • could be 0.5-0.1 times that value if energy change averages every 2-10 collisions
  • will obviously be much less than in part a (i.e., negligible)
  • delta-nu= 0.3 x 10⁶ Hz
    • d(lambda) = (lambda²/c) d(freq)= (487X10^-9)² * 0.27 x 10⁶/3.00 X10⁸

• a. Briefly describe each type of lamp and the characteristic emission.
• b. Why is each lamp appropriate to its use, yet totally inappropriate for use in the other type of instrument.
• AA lamp involves an electrical discharge (plasma) in an inert gas. This sputters some cathode material so we get excited atoms, emitting. The result is a line spectrum (typically Neon and the selected metal atom.) Key point is that we get extremely narrow spectral liens that match the sample's absorption spectrum perfectly.
• The incandescent bulb gives us a continuum spectrum. We need that to find an absorption spectrum (we need to look at all wavelengths.) For spectrophotometry (molecular) we need to set wavelength to desired value so the lamp must supply light at all wavelengths. We use a monochromator to actually select the wavelength.
• If we swapped bulbs, the incandescent lamp would not have enough intensity for good AA measurements and we'd need a carefully tuned narrow band monochromator.

• refer to figure in text for the answer to this one
• certainly need to show lamp, monochromator, order-sorting filters, chopper and two paths, PMT.

• colorimeter
• photometer
• spectrometer
• spectrophotometer
• fluorimeter
• colorimeter -- can be visual comparison, white light or a filter
• photometer-- use a sensor and meter to measure light intensity, filter typically
• spectrometer-- measure light intensity at a specific wavelength (dispersive element required); would include array isntruments. Still has the idea of a meter that measures intensity
• spectrophotometer-- specifically measures absorbance at a specific wavelength
• fluorimeter-- measures light emitted by a sample when sample has absorbed light.

• ICP is Inductively Coupled Plasma-- plasma is a gas with significat ionization, rf power is supplied (coupled) from an external coil (iductive coupling.) Basically this is an extremely hot (active) gas; much hotter than flames.
• Hotter-- so much larger degree of excited states and more emission. Also, many elements are excited by ICP that fail to emit in typical flames. Also valid-- fewer interferences, wider conc range, and ability to do many elements simultaneously.
• Disadvantage-- realistically cost and complexity ($150,000 vs. $20,000) May also have higher degree of ionization than a flame.
• Nebulizer-- forms an aerosol from a solution, so small and uniform droplets of solution are supplied to the active region, evaporated and atomized.

• An L- xray occur when there is an electron vacancy in the L (n=2) shell and an electron from the n=3, 5, ... orbital jumps into the n=2 vacancy. The light emitted is the X ray and the orbital energy difference is the energy of the X-ray.
• Samples are excited with electron beams, radioactive isotopes or another X-ray beam of shorter wavelength.
• X-ray stops in the detector, producing a number of electrons and "holes". The electrons are collected and the current is measured. If each X-ray is separately detected we get pulses-- the amplitude of the pulse is proportional to the x-ray energy.
• XFS is typically nondestructive; AA and AES need to dissolve part of the sample. XFS is basically a surface analysis (especially when exciting source is an electron beam.)

• a. What is an internal standard?
• b. Briefly, how would you use an internal standard in such an analysis?
• c. Why is an internal standard more reliable or more convenient than simply measuring a series of standard solutions?
• d. Why are we more likely to use an internal standard in AES than in an AA analysis?
• An internal standard is another species (another element) added to the sample at a known level.
• We measure the relative signal for the IS and the element in question and compute sample concentration from the relative values. We need to base this on results from one or more samples in which both the sample species and the IS species are present at known concentrations.
• This typically corrects for instrument variation and many matrix effects of the sample. Sample and IS are subject to the same conditions.
• AA may be more difficult since we'd need to change lamps and wavelengths to measure the IS-- too many new variables. AES, especially ICP version, sees al elements (IS and sample) at the same time.

• a. Photomultiplier
• b. Diode Array (or a CCD array detector).
• A PMT uses the photoelecton effect
• light strikes a metal, frees an electron (photocathode)
• exiting electron sees a strong electical field (50-100 volts) and is accelerated to another metal suface (dynode)
• electron impact with dynode is energetic, kicks several electrons from the surface (amplification)
• typical tube has 6-12 such dynodes so tremendous amplification.
• micht note that the target area is moderately large (a few mm to a few cm) and the tube housing presvents another detector from being very close. Can only detect one signal at a time (one wavelength.)
• A array detector is a solid state light sensor (typically one electron per photon, no amplification)
• as an array, 100's-1000's of sensors, side by side, in area of 1-5 cm.
• typically charge, wait for light to cause charge to leak away, then measure. (Can improve sensitivity with longer integration periods.)
• typically measure light at all wavelengths similtanuously.

• a. What's the difference between spontaneous and stimulated emission?
• b. Briefly describe an Optical Cavity and its role in a laser design.
• c. What is a Population Inversion?
• d. Briefly describe one way of exciting the medium in a laser.
• e. Describe how one of these lasers achieves a population inversion (He-Ne, Dye, eximer laser)
• Spontanous emission-- intensity is proportional to species only; light emitted randomly in time and direction
• stimulated emission-- proportional also to the intensity of radiation (can build geometrically in intensity.) Radiation is similtaneous, in phase, in same direction.
• Optical cavly typically a pair of parallel mirrors with 99.999+% reflection. Allows field to build up after light passes through medium many times. Takes place of an extreelemly long laser tube.
• Population inversion occur when the higher energy state has a higher population than the lower energy state.
• Medium excited by
  • electrical discharge (in a gas)
  • optical pumping
  • chemical reaction
  • (solid state devices; electrical current)