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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 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鈥檚 constant, Cis the speed of light, and kis Boltzmann鈥檚 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
role="math" localid="1664862982839"
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?
Show that a grating with 103 grooves/cm provides a dispersion of 5.88 per mm of wavelength if n 5 1 and f 5 108 in Equation 20-4.
(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?
The variation of refractive index, n, with wavelength for fused silica is given by
where is expressed in .
(a) Make a graph of n versus with points at the following wavelengths: 0.2,0.4,0.6,0.8,1,2,3,4,5, and .
(b) The ability of a prism to spread apart (disperse) neighboring wavelengths increases as the slope increases. Is the dispersion of fused silica greater for blue light or red light?
Describe three general types of noise that have a different dependence on frequency. Give an example of the source of each kind of noise.
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