Chapter 6: #2, 3, 4, 5, 12
#2:
Calculate the frequency in Hertz, the energy in Joules, and the energy
in electron volts of an X-ray photon with a wavelength of 6.24 Å.
#3:
Calculate the frequency in Hertz, the wavenumber (in cm-1), the energy
in Joules, and the energy in KJ/mol associated with the 3.517-µm
vibrational absorption band of an aliphatic ketone.
#4: Calculate the wavelength and the energy in Joules associated with
an NMR signal at 368 MHz.
#5:
Calculate the velocity, frequency, and wavelength of the sodium D line
(589 nm) as light form this source passes through a species whose
refractive index, nD,
is 1.09.
#12:
Calculate the reflection loss when a beam of radiant energy passes
through an empty quartz cell, assuming the refractive index of quartz
is 1.55.
#13: Consider an infrared grating with 84.0 lines per millimeter and
15.0 mm of illuminated area. Calculate the first-order resolution (λ/Δλ) of this grating. How far apart (in cm-1) must the two lines centered at 1200 cm-1 be if they are to be resolved?
#18:
A monochromator has a focal length of 1.6 m and a collimating mirror
with a diameter of 3.5 cm. The dispersing device was a grating with
1500 lines/mm. For first-order diffraction:
a.) what is the resolving power of the monochromator if a
collimated beam illuminated 3.0 cm of the grating? b.) what are the first- and second-order reciprocal linear dispersions of the monochromator?
#22:
A Michelson interferometer had a mirror velocity of 2.75 cm/s.
What would be the frequency of the interferogram for (a) UV radiation
of 350 nm, (b) visible radiation of 575 nm, (c) infrared radiation of
5.5 µm, and (d) infrared radiation of 25 µm?
#23: What length of mirror drive in a Michelson interferometer is required to produce a resolution sufficient to separate (a) infrared peaks at 500.6 and 500.4 cm-1 ? (b) infrared peaks at 4002.1 and 4008.8 cm-1 ?
Chapter 16: #1, 2, 3, 7, 9, 14 #1: The IR spectrum of CO shows a vibrational absorption band centered at 2170 cm-1. (a) What is the force constant for the CO bond? (b) At what wavenumber would the corresponding peak for 14CO occur?
#2: Gaseous HCl exhibits IR absorption at 2890 cm-1 due to the hydrogen-chlorine stretching vibration. (a) Calcuate the force contstant for the bond. (b) Calculate the wavenumber (in cm-1) of the absorption band for 2HCl (i.e., DCl) assuming the force constant is the same as that calculated in part (a).
#3:
Calculate the absorption frequency corresponding to the -C-H stretching
vibration, treating the group as a simple diatomic C-H molecule with a
force constant of k = 5.0 x 102
N/m. Compare the calculated value with the range found in correlation
charts (such as the one shown in Figure 17-6). Repeat the calculation
for the deuterated bond.
#7: Indicate whether the following vibrations are active or inactive in the IR spectrum: (a) CH3-CH3 -> C-C stretching (b) CH3-CCl3 -> C-C stretching (c) SO2 -> Symmetric stretching (d) CH2=CH2 -> C-H stretching (see fig in question) (e) CH2=CH2 -> C-H stretching (see fig in question) (f) CH2=CH2 -> CH2 wag (g) CH2=CH2 -> CH2 twist
#9: What length of mirror drive in an FTIR spectrometer would be required to provide a resolution of (a) 0.050 cm-1, (b) 0.40 cm-1, and (c) 4.0 cm-1?
#14:
If a Michelson interferometer has a mirror velocity of 1.00 cm/s,
what will be the frequency at the transducer due to light leaving the
source at frequencies of (a) 4.8 x 1013 Hz, (b) 4.9 x 1013 Hz, and (c) 5.0 x 1013 Hz? What are the corresponding wavenumbers (in cm-1) of these frequencies?
Chapter 17: #9 #9: An empty cell showed 15 interference
fringes in the wavelength range of 6.0 to 12.2 µm. Calculate the
pathlength of the cell.
Additional
Problems
The
meter of an inexpensive spectrophotometer had a 5-inch scale scribed in
linear units from 0 to 100%T. The scale, which limited the precision of
the instrument, could be read to about ± 0.5 %T. Calculate the relative
precision of concentration determinations for an absorbance of: (a)
0.020, (b) 0.100, (c) 0.800, and (d) 2.000.
At 510 nm, the iron orthophenanthroline complex has a molar
absorptivity of 1.2 x 104. What is the
concentration of iron (in ppm) in a solution which gives an absorbance
of 0.002 in a 1.00-cm pathlength cell?
The
actual limit of detection in a spectrophotometric determination is
related to the UNCERTAINTY in the absorbance measurement. Specifically,
the detection limit is defined as the concentration of analyte which
produces a Signal-to-Noise ratio equal to 3. In the case of absorption
spectrophotometry, the "signal" is simply the absorbance and the
"noise" is the absolute uncertainty in the absorbance. If the
measurement described in question #2 was performed on an instrument
having a read-out uncertainty of ± 0.01 %-T, is the concentration of
iron determined in question #2 above or below the detection limit?
Calculate the actual detection limit.
Created and copyright by Joel M. Goldberg. Last
updated: February 5, 2012
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