ANALYTICAL SPECTROSCOPY
Problem Set #2

Problems in Ingle and Crouch

• Chapter 3, # 3abcd. A monochromator has the following specifications: reciprocal linear dispersion, 2.5 nm/mm; focal length, 0.30 m; F-number, 6.0; grating size, 44.33 X 44.33 mm; groove density, 1200 gr/mm. Calculate the following at 400 nm assuming first order is used.
  • The angular and linear dispersion.
  • The projected limiting aperture diameter and projected limiting area.
  • The slit width needed to obtain a 5-nm geometric spectral bandpass.
  • The angle of incidence and angle of diffraction.
    
    
• Chapter 3, # 9. What performance characteristics of a monochromator are affected when only the grating groove density is changed?
  
  
• Chapter 3, # 15. A grating has a groove density of 1500 gr/mm. If the incident beam strikes the grating at an angle of 20.0^o;
  • What diffraction angles will the first order of 300, 400, 500, 600, and 700 nm appear>
  • What wavelength in the second order overlaps the 600 nm first-order beam?
  • What is the free spectral range for the first order at 600 nm?
    
    
• Chapter 3, # 19. Why are mirrors preferred over lenses for imaging in many spectroscopic instruments that must cover multiple wavelengths? If lenses must be used, how can their imaging properties be idealized at least for two wavelengths? What are the disadvantages of this approach?
  
  
• Chapter 3, # 22d. The monochromator in problem 21b (Czerny-Turner with a takeoff angle of 10.0^o and a 2000 gr/mm grating) has a focal length of 0.30 m. Describe in words why the radiant power throughput of a monochromator shows a different dependence on slit width for a continuum source than for a line source.
  
  
• Chapter 3, # 23. A Michelson interferometer has a mirror driven at 1.5 cm/s. What frequency would the interferogram show if the source radiation were at:
  • 400 nm;
  • 800 nm;
  • 10 µm?
    
    
• Chapter 3, # 24. What distance must the mirror be driven in a Michelson interferometer to separate:
  • infrared radiation at 10.15 and 10.18 µm;
  • visible radiation at 725 and 730 nm?
    
    
• Chapter 3, # 25. Characterize the shape of the slit function, and hence the shape of a scan of a line source, if the exit slit is twice as wide as the entrance slit, and vise versa.
  

Additional Problems

1. Calculate the distance separating the two very sensitive neutral resonance lines of Ni occurring at 310.188 nm and 310.155 nm on the focal plane of a 1-meter spectrograph with a 1180 g/mm grating used in the first order and having a fixed incident angle of 10^o.
   
   
2. Calculate the slit-width needed in order to just resolve the Ni doublet in problem #1.
   
   
3. Repeat the calculations requested in problem #1 for a 1-meter instrument with an 80 g/mm grating used in the 78th order and having a fixed incident angle of 75^o.
   
   
4. Aspirating a 100 ppm Ni solution into an ICP results in the generation of a cathode photocurrent of 3.0 x 10^-9 amps in a PMT detecting radiation from the 310.155 nm Ni resonance line. The PMT has 9 dynodes and a secondary electron coefficient (alpha) of 5.0 and an average cathode dark current of 1.0 x 10^-9 amps. Calculate the S/N if a 10,000-ohm load resistor is used to measure the anode current. Assume room temperature (20^oC) operation with a 10 MHz bandwidth.
   
   
5. Using the S/N calculated for a 100 ppm Ni solution in problem #4, calculate the detection limit for Ni at the 310.155 nm line using the above ICP source. (HINT: The detection limit is defined as the concentration of analyte needed to produce a S/N=3).
   
   
6. Calculate the detection limit for the system described in problem #4 if the 10,000-ohm load resistor is replaced with a 1,000,000-ohm resistor.
   
   
7. If a simple RC filter is added to the detector electronics of the system described in problem #4, the measurement bandwidth can be reduced to about 10 Hz. Calculate the detection limits obtainable with this new system.

---