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Chapter 20: Q14P (page 525)
Calculate the power per unit area (the exitance, W/m2) radiating from a blackbody at 77 K (liquid nitrogen temperature) and at 298 K (room temperature).
The value of Planck distribution at 77k and 298k
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(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.
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
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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?
Explain how a laser generates light. List important properties of laser light.
The path length of a cell for infrared spectroscopy can be measured by counting interference fringes (ripples in the transmission spectrum). The following spectrum shows 30interference maxima between 1906andobtained by placing an empty KBrcell in a spectrophotometer.
The fringes arise because light reflected from the cell compartment interferes constructively or destructively with the unreflected beam.
If the reflected beam travels an extra distance, it will interfere constructively with the unreflected beam. If the reflection path length is , destructive interference occurs. Peaks therefore arise when and troughs occur when, where is an integer. If the medium between KBr theplates has refractive index n, the wavelength in the medium is l/n, so the equations become . The cell path length can be shown to be given by
where Nmaxima occur between wavelengthsand. Calculate the path length of the cell that gave the interference fringes shown earlier.
What are the advantages and disadvantages of decreasing monochromator slit width?
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