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Chapter 20: Q5P (page 525)
What is the role of a filter in a grating monochromator?
The role of a filter in a grating monochromator is to eliminate different wavelengths at the same angle as the desired wavelengths.
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The photograph of upconversion in Color Plate 21shows total internal reflection of the blue ray inside the cuvet. The angle of incidence of the blue ray on the wall of the cuvet is. We estimate that the refractive index of the organic solvent is 1.50and the refractive index of the fused-silicacuvet is 1.46. Calculate the critical angle for total internal reflection at the solvent/ silica interface and at the silica/air interface. From your calculation, which interface is responsible for total internal reflection in the photo?
Light passes from benzene (medium1)to water (medium 2) in Figure 20at (a)or (b). Find the anglein each case.
The exitance (power per unit area per unit wavelength) from a blackbody (Box 20-1) is given by the Planck distribution: where is wavelength, Tis temperature K), his Planck’s constant, Cis the speed of light, and kis Boltzmann’s constant. The area under each curve between two wavelengths in the blackbody graph in Box 20-1is equal to the power per unit areaemitted between those two wavelengths. We find the area by integrating the Planck function between wavelengthsand
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For a narrow wavelength range, the value of is nearly constant and the power emitted is simply the product .
(a) Evaluate and at
(b) Calculate the power emitted per square meter atin the intervalby evaluating the product
(c) Repeat part (b) for the interval
(d) The quantityis the relative exitance at the two wavelengths. Compare the relative exitance at these two wave-lengths atwith the relative exitance at 100K. What does your answer mean?
(a) In the cavity ring-down measurement at the opening of this chapter, absorbance is given by whereis the length of the triangular path in the cavity, Cis the speed of light, Tis the ring-down lifetime with sample in the cavity, and is the ring-down lifetime with no sample in the cavity. Ring-down lifetime is obtained by fitting the observed ring-down signal intensityto an exponential decay of the form , whereis the initial intensity and t is time. A measurement ofis made at a wavelength absorbed by the molecule. The ring-down lifetime for 21.0-cm-1 along empty cavity is andfor a cavity containing.role="math" localid="1664865078479" Find the absorbance ofat this wavelength.
(b) The ring-down spectrum below arises from and from of methane in outdoor air at 0.13. The spectrum arises from individual rotational transitions of the ground vibrational state to a second excited C-H)vibrational state of the molecule. (i) Explain what quantity is plotted on the ordinate ( Y-axis). (ii) The peak foris at. What is the wavelength of this peak in? What is the name of the spectral region where this peak is found?
(a) What resolution is required for a diffraction grating to resolve wavelengths of 512.23 and 512.26 nm? (b) With a resolution of 104, how close in nm is the closest line to 512.23 nm that can barely be resolved? (c) Calculate the fourth-order resolution of a grating that is 8.00 cm long and is ruled at 185 lines/mm. (d) Find the angular dispersion () between light rays with wavelengths of 512.23 and 512.26 nm for first-order diffraction (n 5 1) and thirtieth-order diffraction from a grating with 250 lines/mm and f 5 3.08.
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