CHEM-5181 – Fall 2009
Univ. of Colorado-Boulder
Homework Assignment #5
Assigned 23-Sept / Due 6-Oct
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Please make an effort to produce a clean solution. Use a big “font” and plenty of space for
your diagrams and arguments.
Please briefly explain your answers, and solution procedures. We grade as much on the
thinking process as on the final result.
The current homework will always be posted on the course page in Word to save you the
typing, should you decide to type your homework.
Problem 5.1- Ion Optics Simulations in Igor
The figure below is a schematic of an electron ionization source and its extraction optics. (FYI: this is
the ion source used in the Aerosol Mass Spectrometer used by the Jimenez Lab). Ions are created
inside the box to the left, as electrons are emitted from the filament (small circle below the “cathode”
voltage) they ionize some of the neutral molecules inside the box.
Using the values of voltages from the table below, (5.1.1) write an Igor program that calculates the
position, velocity, and acceleration vs. time, and plot the velocity and acceleration vs. position curves
for (a) an H2O+ ion and (b) a Hg+ ion as they are extracted by the ion optics and they enter the
quadrupole mass analyzer (labeled as “rod system”). (5.1.2) Then program a realistic animation of the
motion of the two ions simultaneously. Turn in the Igor code and a writeup by email to
chem5181@gmail.com.
Assume that the entire box interior is sitting at the V1 (“ion reference”) voltage and that ions are
formed on the central axis of the ion source. Measure the distances from the graph (please use mm and
not inches) and assume that the graph is drawn on a 1:1 scale. Note that most of the voltages are
defined relative to the “ion reference” voltage.
Note: Disregard superscripts on the voltages.
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Problem 5.2 – Ion Optics Simulations
Now we will deal with the more complex case of two-dimensional ion trajectories. Rather than
programming it in Igor, this time you will use the ion optics simulation program from
http://www.vias.org/simulations/simusoft_ionoptics.html , with 1 tick of beam width and 1 tick of
beam angle, create (a) an ion reflector and (b) an optic that can turn the ions 90 degrees up, with as
little ion dispersion as you can get (at the point in which the ions leave the box). Do those designs
work for ion beams with 4/0 and 0/4 ticks ? (you don’t need to optimize the designs to work for every
case, it only needs to work for the 1/1 case and then you can report whether it works or not for the
other cases and why). Pls submit the screen shots (Alt + PrintScreen in Windows) as the solution,
along with any comments on tricks, problems etc.
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Problem 5.3- Order of Magnitude Calculations for an Electron Ionization Source
Note: these calculations are approximate by nature, so don’t try to get many significant figures. Make
the simplifications and approximations you need to get to a numerical answer. I am most interested in
your getting the order of magnitude right for each step (i.e. within a factor of 2 or 3); and critically
evaluating whether that order of magnitude makes sense in the bigger picture. If you are missing a
number, estimate it in the most reasonable way you can come up with (and make clear that you are
doing so and how). Also, some of the later steps can be done even if you can’t do the earlier ones, so
try each step independently. Please explain how you are trying to solve each step, so that I can give
you partial credit even if you don’t get the final answer right.
(a) In a typical EI ion source, an emission current of 2.5 mA is used. What is the electron flux
(electrons / s ) on this source? What is the speed of the electrons if their energy is 70 eV? What is the
associated wavelength? Can you explain why 70 eV electrons are most effective at ionizing almost any
molecule? (as compared with electrons with different kinetic energies).
Electron path
Effective
Ionization
Volume
Filament
(b) Assume that the actual ionization volume is a cube of 4 mm side, and that 100% of the source
pressure of 10-7 Torr is due to N2. What is the ion current detected by the mass spectrometer? Assume
that ions formed in the ionization volume are transmitted to the detector with 30% efficiency. Note that
the EI cross section of N2 is 2.7 A2 (1A = 10-10 m). Refer to the course notes for the interpretation of
the EI cross section.
(c) What is the probability that a given electron that leaves the filament actually ionizes a nitrogen
molecule?
(d) What is the probability that a molecule that crosses the ionizer volume at its thermal speed only
once (at 300K) is ionized? (this is the “ionization efficiency”).
(e) (Bonus Points, not required) Create an animation of “the view from the filament” in Igor. Draw a
square which is the projection of the ionization volume as viewed from the filament. Have one N2
molecule with the total cross section of all the N2 molecules in the ionization volume (or larger if
needed to see it). Have that “molecule” undergo specular reflection at the boundaries of the ionization
volume (as if the ionizer was a closed box). Then have electrons impact randomly in the square at the
appropriate rate. Change the color of the N2 molecule when it is ionized. Are the results of the
simulation consistent with those of parts (b)-(d)?
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Problem 5.4- Electrospray Ionization Charge States.
Below are two expanded views of an electrospray mass spectrum of an unknown biomolecule collected
with the Orbitrap high-resolution mass spectrometer in the CU-Boulder Mass Spectrometry Facility.
The first spectrum shows a charge envelope between m/z 650 and 1150.
(a) Using knowledge of the m/z values for the peaks of the envelope, assign charge states to all peaks
having relative abundance > 15 and determine the mass of unknown compound (Da).
(d) Using data from the second mass spectrum, which is an expanded view of the region between m/z
737.2 and 738.8, re-calculate the charge of the peak at m/z 738.02307.
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