Spectroscopy Homework Problem Set #2c

1. What is the wavelength of the maxium emission for a blackbody radiator at 2800 K? At 3500 K? What type of source can operate at this temperature? If the bulb has a filliment that is 10 inches long with a radius of 0.05 mm, what is the total energy output?

2. Compare and contrast the following instrument components. (This means, discuss the advantages and disadvantages of each in YOUR own words. DO NOT explain how they work.):
   1. Hydrogen discharge and deuterium discharge lamps
   2. dispersive and diode array spectrometers
   3. photodiode and photomultiplier
   4. filter and monochrometer

3. Compounds A and B have the following molar absorbtivities. Graph the absorption spectrum for a solution that is :
   1. 6.78 x 10^-4M in A with a 1.00 cm cell.
   2. 5.43 x 10^-4M in B with a 1.00 cm cell.
   3. 6.78 x 10^-4M in A and 5.43 x 10^-4M in B and with a 1.00 cm cell.
   4. If a solution has an absorbance of 0.360 at 540 nm in a 1.00 cm cell, what is the concentration of B if the concentration of A is 5.00 x 10^-4M?

      Wavelength (nm)	A (M-1 cm-1)	B (M-1 cm-1)
      400	893	0
      420	940	0
      440	955	0
      460	936	24.6
      480	874	102
      500	795	185
      520	691	289
      540	574	428
      560	440	622
      580	297	980
      600	167	1178
      620	39.7	1692
      640	3.45	1742
      660	0	1806
      680	0	1809
      700	0	1757

4. A pH indicator has a different molar absorbtivity at 450 nm for the two different forms. When the pH is 1, a 8.00x10^-5M solution of the indicator has an absorbance of 0.758 in a 1.00 cm cell. When the pH is 13, this same solution has an absorbance of 0.076 in a 1.00 cm cell. if pK_a = 4.92 for this indicator, what is the absorbance when the pH is 4.92? Clearly state any simplifying assumptions that you make.

5. Phenanthrene is a highly fluorescent PAH (Polycyclic aromatic hydrocarbon) with an excitation maximum at 250 nm and an emission maximum at 370 nm. Results for a set of standards are given below.
   1. Construct a calibration curve for Phenanthrene
   2. Calculate the slope and intercept for the linear regression
   3. Calculate the standard deviation of the slope, the standard deviation of the intercept, and the standard deviation about the regression.
   4. Calculate the concentration of an unknown with a signal of 2.1562.
   5. Calculate the relative standard deviation for the concentration of the unknown.
   6. Calculate the relative standard deviation for the concentration of the unknown if it is the average of 4 measurements.

   Concentration	Intensity
   0.000	0.0558
   0.100	0.4755
   0.200	1.0089
   0.300	1.6262
   0.400	1.9294
   0.500	2.5002
   0.600	3.1108
   0.700	3.5893
   0.800	3.7099
   0.900	4.2843
   1.000	5.0206

Scott Van Bramer
Department of Chemistry
Widener University
Chester, PA 19013

© copyright 1996, S.E. Van Bramer
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Last Updated: Friday, January 09, 1998 11:15:31