Chemistry 226

ANALYTICAL SPECTROSCOPY
Problem Set #1

January 21, 2003

Suggested Problems in Ingle and Crouch

Chapter 1, # 1. Express 4000 Å in nm, as a frequency, as a wavenumber (cm^-1), and as an energy in joules, ergs, and electron volts.
Chapter 1, # 7. A certain optical transition occurs in the visible region of the spectrum at 530 nm. Find the energy of the transition in J and in eV. What is the wavenumber of the transition?
Chapter 2, # 2. A point source emits 25.13 W. Express the intensity as a radiant intensity.
Chapter 2, # 4. A beam of 632.8-nm photons from a He-Ne laser strikes a detector area of 5.0 mm². The laser has a flux of 3.18 X 10¹⁵ photons/sec.
- What is the laser radiant power in watts?
- What is the laser irradiance at the detector? Give the answer in terms of watts and in terms of photons/sec.
Chapter 2, # 7. An extended source emits 2.00 W/cm²/sr/nm at 300 nm. Calculate the spectral radiant power impingent on a 1.00-cm² receptor that is 2.00 m away in W/nm and photons/sec/nm if a 1.00-mm-diameter aperture is placed at the source. What is the incident radiant power in watts over 10.0 nm centered at 300 nm if the source radiance is constant over this region?
Chapter 2, # 8. Consider a collection of atoms in thermal equilibrium at 3000^oC. What fraction of the atoms are in the first excited state if the energy difference between the ground and the first excited state corresponds to 400 nm? Assume the that the statistical weights of the ground and first excited states are the same and that higher excited states are not significantly populated.
Chapter 2, # 13. The 4p level of the Na atom is 3.75 eV above the 3s ground level. What wavelength of radiation (in nm) would be required to excite Na from the ground level to the 4p level? What frequency is required? What is the energy of this transition in joules?
Chapter 2, # 14. For the copper atom, there are resonance lines at 324.7 and 327.4 nm. What is the energy difference in eV between the two excited states involved in these two transitions?
Chapter 7, # 2. The total pressure of sodium (atoms plus ions) in a 2800-K flame is 1.0 X 10^-8 atm. The ionization energy of Na is 5.14 eV, and the equilibrium constant for ionization is K_i = 7.4 X 10^-8 atm. Find the fraction of Na present as nonionized atoms for the following conditions:
- All electrons in the flame arise from Na ionization.
- The partial pressure of electrons is buffered at 10^-7 by adding potassium.
Chapter 7, # 5. For the Ca 422.7-nm resonance line in a flame at 3000 K, calculate the Doppler half-width in nanometers.
Chapter 7, # 7. Oscillator strengths for absorption transitions are often tabulated as gf values, where g is the statistical weight of the lower level and f is the emission oscillator strength. For the Na ²S_1/2 --> ²P_3/2 transition at 5890 Å, gf = 1.3. Find the value of the Einstein transition probability (see Appendix F for the relationship between A and f), and the radiative lifetime of the upper level.
Chapter 7, # 10. The figure (shown in the text!) is a partial term diagram for Hg. Use the information in the diagram to answer the following questions:
- List the allowed transitions and justify according to the selection rules.
- If an external continuum source is used to observe the absorption of Hg atoms in a room-temperature vapor, list the transitions that will be seen if the selection rules are strictly obeyed.
Chapter 7, # 11. If the ³P_2,1,0 states of Hg are thermally populated in a flame at 2700 K, calculate the ratio of the populations of the ³P₂ and ³P₀ levels. The splitting is 6398 cm^-1.

Additional Problems

One of the strongest lines in the Ag(I) emission spectrum is the 3280.68 Å resonance line. Compute the excitation energy in eV for the upper level of the transition.
Compute the natural linewidth for the Ag(I) 3280.68 Å resonance line. For resonance transitions, (delta)E_res = h/(2(pi)t_q), where t_q is the average lifetime of excited state q. A_qp for this transition is 1.57 x 10⁸ sec^-1.
A radiation source at 5000K contains 1.0 x 10¹⁵ Ag atoms per cm³. Compute the concentration (atoms/cm³) of Ag atoms in the excited state responsible for the 3280.68 Å Ag(I) resonance line. The statistical weight of the excited state is 4.0, and the partition function at 5000K is equal to 20.0.
Compute the intensity of the Ag(I) 3280.68 Å line in erg/cm²-sec-sr emitted by the radiation source in problem #3 if the source thickness is 2.0 cm along the line of observation.
Compute the maximum and minimum excitation source temperatures allowed if the intensity of the 3280.68 Å line is to vary by no more than ~10% from the value computed in problem #4. Assume that the partition function is constant over the temperature interval.
Compute the number of 3280.68 Å photons passing through a 5 mm x 100 um aperture located 0.70 meters from the radiation source in problem #4.

Created and copyright by Joel M. Goldberg. Last updated: January 20, 2003

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