Full Test Bank X-Ray Related Techniques Ch10

Problem 10.1: The typical Jablonski diagram (i.e., Figure 8.3; also see the “Compare and Contrast—Optical Absorption versus Photoelectric Absorption”) shows electronic transitions for the valence shell of an atom or molecule. Using Figure 8.3 as a style guide, construct an energy diagram in the style of a Jablonski diagram for an XRF Kα emission. As you construct your Jablonski diagram, make sure you consider the differences in atomic versus molecular transitions.

Problem 10.2: Why is it quantum mechanically impossible to observe a characteristic Lβ emission for magnesium? A diagram similar to Figure 10.1 might be helpful in answering this question.

Problem 10.3: In the orbital diagrams depicted, an ejected electron “hole” is designated with a “⊕” and the arrow represents a higher n-value electron cascading into that hole. Label each transition (i.e., Kα, Lβ, and so on).

Problem 10.4: Compare and contrast photoelectric absorption of source radiation with molecular UV-vis and IR absorption of source radiation. In what ways are they similar? How are they different?

Problem 10.5: In what ways does the variable  in Equation 10.3 resemble the variable  in Equation 6.5? How is  different from ?

Problem 10.6: Use Equation 10.5 and Example 10.1 to determine the minimum wavelength, the maximum frequency and the energy in units of joules for the bremsstrahlung radiation generated by a X-ray tube with a voltage gradient of

(a) 25 kV (b) 50 kV (c) 100 kV

Problem 10.7: What voltage would you need to apply to the X-ray tube of an XRF spectrometer in order to induce a Kα emission from the following:

(a) Fe (d) Ru (g) Co

(b) Cu (e) Zn (h) Sn

(c) Ti (f) Ni (i) Ca

Problem 10.8: Given a crystal lattice distance of d = 2.35Å, use Bragg’s Law to calculate the (n = 1) angle required for the constructive interference of a  = 1.54 Å X-ray beam.

Problem 10.9: For an X-ray beam of 2.01 Å experiencing constructive interference incident on a crystal surface at an angle of 45 degrees, determine the crystal lattice distance “d,” assuming first-order (n = 1) Bragg diffraction.

Problem 10.10: It is customary to report XRF in units of eV. However, in Chapter 6, on UV-vis spectroscopy, we reported absorption wavelengths in units of nanometers. For comparative purposes, convert the range of 5 to 20 eV into units of nanometers. Compare the resolution of a typical XRF spectrometer to that of a UV-vis spectrometer in the context of the bandwidth of the X-ray and UV-vis regions of the electromagnetic spectrum.

Problem 10.11: In Problem 10.10, we converted the spectral resolution of WDXRF spectrometers from eV to nm. For comparative purposes, convert the spectral range of a typical EDXRF (100–300 eV) into nanometers.

Problem 10.12: Consider this scenario. You are writing a business plan in order to open a commercial laboratory that will conduct routine agricultural microanalysis of soil for the nutrients Ca, Mg, Cu, and Zn. You will need to be able to quantify these elements in the ppm range. The going rate for an analysis of this type in your area of the country is $60 per element per analysis. Your anticipated overhead will be $1500 per month, which does not include a loan payment plan for the instrument. Use the Internet to research commercially available XRF spectrometers and complete the business plan. Justify (in your business plan) your choice of XRF spectrometer and include in your final business plan the 5-year loan payments (5% APR) for your XRF. Do not forget to include your salary. How many analyses per week will you need to conduct in order for your business to succeed? Make sure you justify your choice of XRF spectrometer against the number of analyses per week you will be conducting.

Problem 10.14: Determine the Bragg angle () needed to obtain first-order (n = 1) constructive interference for an X-ray of wavelength 10 Å, given the interstitial distance (d) between lattice points in the diffraction crystal, for the following:

(a) 12 Å (c) 32 Å (e) 6.8 Å

(b) 7.5 nm (d) 6 × 10^-4 mm (f) 300 pm

Problem 10.15: Determine the Bragg angle () needed to obtain first-order (n = 1) constructive interference for a 200 eV X-ray, given the interstitial distance (d) between lattice points in the diffraction crystal for the following:

(a) 12 Å (c) 6 × 10^-4 mm (e) 6.8 Å

(b) 7.5 nm (d) 32 Å (f) 300 pm

Problem 10.16: Determine the Bragg angle () needed to obtain first-order (n = 1) constructive interference for an X-ray with a frequency of 3 × 10¹⁸ Hz, given the interstitial distance (d) between lattice points in the diffraction crystal for the following:

(a) 12 Å (c) 6.8 Å (e) 6 × 10^-4 mm

(b) 7.5 nm (d) 300 pm (f) 32 Å

Problem 10.17: Label each of the following Miller index points within the given crystal lattice. The origin is indicated by a black dot.

Problem 10.19: Sketch a unit cell similar to the one depicted in Figure 10.29 and shade and label the following planes:

(a) (010) (c) (100) (e) (001)

(b) (110) (d) (101) (f) (011)

EXERCISE 10.1: Define the following terms.

EXERCISE 10.2: Who is credited with the “birth” of XRF spectroscopy?

EXERCISE 10.3: Sketch a schematic of a Coolidge tube.

EXERCISE 10.4: The development of the Coolidge tube remedied two important technical difficulties of the early X-ray tubes. What were those technical difficulties?

EXERCISE 10.5: In this chapter, we described two different mechanisms for generating X-rays: the first was element specific characteristic emissions and the second was bremsstrahlung emissions. Describe the two mechanisms and point out how they differ.

EXERCISE 10.6: Using the graphic in Problem 10.3 as a guide, sketch an orbital diagram for each of the following transitions.

EXERCISE 10.7: Use Equation 10.4 to determine the minimum wavelength of the bremsstrahlung radiation generated by a Coolidge tube with a voltage gradient of:

(a) 35 keV (b) 65 keV (c) 150 keV

EXERCISE 10.8: Use Equation 10.5 and Example 10.1 to determine the minimum wavelength, the maximum frequency, and the energy in units of joules for the bremsstrahlung radiation generated by a X-ray tube with a voltage gradient of:

(a) 75 kV (b) 60 kV (c) 125 kV

EXERCISE 10.9: What voltage would you need to apply to the X-ray tube of an XRF spectrometer in order to induce a Kα emission from:

EXERCISE 10.10: What voltage would you need to apply to the X-ray tube of an XRF spectrometer in order to induce a Kα emission from:

EXERCISE 10.11: Why is it impractical to use refractive optics to focus X-rays?

EXERCISE 10.12: In your own words, explain the underlying principle of Wolter X-ray optics and capillary X-ray optics.

EXERCISE 10.13: Given a crystal lattice distance of d = 2.25 Å, use Bragg’s law to calculate the (n = 1) angle required for the constructive interference of the following X-ray beams:

(a)  = 8.44 Å (b)  = 7.24 Å (c)  = 2.04 Å

EXERCISE 10.15: Given an X-ray beam of 1.89 Å, incident on a crystal surface at an angle of 37 degrees, what crystal lattice distance “d” would you need to experience first-order (n = 1) Bragg diffraction?

EXERCISE 10.17: For the spectrometer shown in Figure 10.20, what is the minimum wavelength (min) generated by the source? Use the data in Table 10.1 to construct a list of elements that you could theoretically measure with the X-ray tube given in this instrument.

The spectrometer in Figure 10.20 uses a 50 kV x-ray tube. The Duane-Hunt law allows us to determine the minimum wavelength generated by this sourse.

EXERCISE 10.18: Describe the atomic principles of XPS. Include the following topics in your discussion.

(a) The atomic principles underlying the technique

(b) The basic measurement apparatus

(c) The significance of the kinetic energy of the photoejected electron and the equation that describes the electron’s energy

(d) The information that can be gained from an XPS measurement

EXERCISE 10.19: Describe the atomic principles of AS. Include the following topics in your discussion:

(a) The atomic principles underlying the technique

(b) The basic measurement apparatus

(c) The significance of the kinetic energy of the photoejected electron and the equation that describes the electron’s energy

(d) The information that can be gained from an XPS measurement

EXERCISE 10.20: How are XRF and XPS related?

EXERCISE 10.21: What is the measurand for each of the following? Be as specific as possible.

(a) XRF (b) XPS (b) AS

EXERCISE 10.22: Label each of the following Miller index points within the given crystal lattice. The origin is indicated by a black dot.

EXERCISE 10.25: Assume you are using a diamond single-crystal monochromator to select a bandwidth of X-rays from a source. The interstitial distance (d) between the planes in a diamond crystal is 3.567 Å.

1. At what angle would a (= 30 pm) incident angle X-ray beam need to be in order to experience first-order diffraction (see Equation 10.6).

(b) Determine the spectral resolution (i.e., bandwidth) of a monochromator made using this crystal if the exit slit is at a distance of 8 cm from the diamond crystal and has a width of 5 mm.