Download CHEM-5181 Homework 2 Mass Spectrometry and Chromatography

CHEM-5181 Homework 2
Mass Spectrometry and Chromatography, CU Boulder
Due before class by emailing experiments to [email protected] (under 5 MB)
NOTES
1. You must report the results (text and/or graphs) of your work in a Notebook in the experiment.
This is the work I will grade. It’s ok to use one Notebook for the entire assignment, although it
may be cleaner to keep the different questions in different experiments, at least for #4.
2. You should keep the waves for each question in their own DataFolder (this will make it easier for
me to look at your work.
3. Please follow the programming style conventions (below). You will receive additional points for
following these guidelines. These are especially for your benefit – they help make your code
clearer and easier to understand after you come back to it after a while. Remember, “write code
for the reader!”
4. For questions 1 and 2, you may wish to copy the command for the function into your Notebook,
highlight it, right-click, and choose “Execute Selection”. Then the results are written both in the
History and the Notebook.
Question 1: Energy, Wavelength, and Frequency.
Write a function that calculates and reports the frequency and wavelength of photons with a given energy
(in eV) and what range of the electromagnetic spectrum the photon is in. A sample output might look
like
"A photon with 100 eV of energy has a wavelength of 1.2e-8 m, a frequency of 2.4e16
Hz, and is in the UV portion of the electromagnetic spectrum."
Report these data in your notebook for photons with 1, 3, 20, and 70 eV.
Question 2: Velocity in an Electric Field.
Write a function that takes the mass (in amus) and charge of an ion (integer), its initial velocity (m/s) and
a desired final velocity (m/s) and returns** the electric potential the ion must climb up or down to
achieve the final velocity. Write in your notebook what law governs this relationship and show a simple
derivation of the equation used in your function.
Report the potential required for a singly-charged (+) Hg ion with initial velocity 10,000 m/s to reach a
final velocity of 100 m/s.
** Hint: use the Help to learn how to use “return” in a function. Note that when you return a value, the
function is trying to send a value, so you need a place to put that value. You can assign it to a variable or
print it.
Question 3: Speed Distribution of Gas Molecules
Write a function to calculate the Maxwell-Boltzmann distribution of speeds given the mass of the moving
object, the maximum speed for consideration, and the temperature. Declare any necessary constants as
constants, not variables.
a) Calculate and plot the speed probability distribution functions for 4He, 20Ne, 40Ar, and 132Xe at
298.15 K (check your work against the plot on the Wikipedia page for the Maxwell-Boltzmann
Distribution)
b) Calculate and append to the plot the speed probability distribution functions for 40Ar at 200 and
400 K.
c) Is there a temperature at which the speed probability distribution function of 40Ar is similar to the
speed probability distribution function for 20Ne at 298.15K? Append this to your plot.

Make good plots! Consider the following points:
1. Include axis labels (including units).
2. Make the trace appearances have something to do with the data. Group "like" traces by
using the same color, line style, etc.
3. Include a legend, and put the items in a "good" order and with good names.
Question 4: Trajectory of an Ion between Parallel Plates
Consider the following simple mass selector:
0.30
Distance Between Plates (m)
Inject Ions
0.1
0.25
0.20
0.9
0.30 m
0.9
0.15
0.10
0.05
0.1
Detector
0.00
0.0



0.1
0.20.50 m 0.3
Plate Length (m)
0.4
0.5
Two parallel plates, length 0.5 m, separated by 0.3 m. The maximum voltage across the plates
will be 10kV.
Ions are inserted at the left side at 90% of the distance between the plates. The ion's initial
velocity will be 5x104 m/s in the x-direction and 0 m/s in the y-direction. A detector of width
0.05 m is placed at the right side at 10% of the distance between the plates.
In this problem we will ignore edge effects of the electric field at the edges of the plates, i.e. the
field will be assumed to always be perpendicular to the plates (or the equipotential lines will be
assumed to always be parallel to the plates).
1. Make a plot of the plates and the electric field between the plates (assume the high voltage is on
the upper plate). (See note at the end for how to make arrows.) Paste the plot in your Notebook.
a. Make a "good" plot. Consider the following points:
 Include axis labels (with units).
 Make the aspect ratio of the plot approximately to scale in the x- and y- direction
(i.e., for this plot, the y-axis certainly shouldn't be longer than the x-axis!).
 Make the plate color distinct from the axis colors (make the more important one
the darker color).
2. Assume that the plates are aligned so that the electric field is in the same direction as
gravity. Can gravitational forces be neglected for this problem, or must they be included? Make
your discussion in your notebook, and include appropriate equations.
3. You will now calculate the trajectories (x, y) of ions that are inserted into the electric field.
a. Draw a force diagram for an ion between the plates and paste it in your notebook. You
can draw it in Powerpoint (select and copy all objects then paste in the notebook) or you
can type 'display" in the Igor command line, then type ctrl+t in the graph and use the
tools to draw the graph (note that you must type ctrl+t to close the tools or press the top
tool button before you can copy the graph).
b. Write (in the notebook) the equations of motion (acceleration, velocity, position) for the
x- and y-directions. These can be in the form "da_x/dt = ...".
c. Write an Igor function that will calculate the x- and y- position of an ion inserted into the
electric field.
i. The function should take arguments for the following:

The dimensions of the separated plates

The potential on each plate

The initial position and velocity of the ion at the point of insertion

The mass and charge of the inserted ion

The time step of the simulation (dt)
ii. The number of points in the waves used should be calculated in the function
based on the time for the ion to travel the horizontal distance and dt.
iii. The function should perform numerical integration by Euler's method
(acceleration -> velocity -> position).
4. Determine an appropriate dt for your simulations. You'll be doing a "grid independence test"
(i.e., showing that your solution doesn't depend on your time step). Run your function for a
singly-charged (+) ion with m = 100 amu with a fairly coarse time step, choosing some values for
the potential on each plate (these values don't matter much for this part of the problem). Then
halve dt (this doubles the number of time steps) until the solution changes by less than 1% in the
final x and y positions.
a. Plot the x- and y-positions on different bottom (or left) axes and arrange your plot so that
the x- and y-positions are displayed next to each other or above and below each
other. Put a plot in your notebook which shows that you have achieved grid
independence and report the time step that you settle on.
5. Make a "good plot" (similar to part 1) that shows the plates (but not the electric field) and the
detector. (You may wish to make a graph macro (ctrl+y, choose a new WindowName, and check
the box for New Graph Macro) at this point so that you can easily make this base again.) Add a
trace that shows the path of the ion from part 3. Implement the physical constraint of impaction
with a plate in the function so that if the ion impacts one of the plates, it stops moving. Put this
plot (with the modification showing impaction) in your Notebook.
6. "Tune your mass spectrometer" (i.e., adjust the voltages on the plates) so that your ion hits in the
middle of the detector.
7. Using the same voltage difference as in part 6, add traces for different ions that have the same
initial velocity to show ions that
a. hit the top and bottom of the detector (report the detection amu range at this voltage in
your notebook)
b. impact the bottom plate
c. impact the top plate
d. stops between the plates (doesn't reach the exit but doesn't impact the top or bottom plate)
e. exit through the right (detection) side of the spectrometer, but miss the detector and don't
impact a plate
f.
exit through the left (injection) side of the spectrometer, but don’t impact a plate

If any of these trajectories are impossible, explain why in your notebook.

Make sure that all of your traces can be identified and that your plot has a good legend
(including the tuning of the spectrometer). Copy the plot into your notebook.
You will now make new plots to explore the properties of the spectrometer.
8. Make a new plot (use your graph macro) and use the same tuning as in parts 6 & 7. Paste in your
notebook a plot that shows the trajectories of a singly-charged (+) ion with m = 100 amu with
different initial velocities so that the ion
a. hit the top and bottom of the detector (report the initial velocity range in your notebook)
b. impact the bottom plate
c. impact the top plate
d. stops between the plates (doesn't reach the exit but doesn't impact the top or bottom plate)
e. exist through the right (detector) side of the spectrometer, but miss the detector and don't
impact a plate
f.
exit through the left (injection) side of the spectrometer, but don’t impact a plate

If any of these trajectories are impossible, explain why in your notebook.

Make sure that all of your traces can be identified and that your plot has a good legend
(including the tuning of the spectrometer). Copy the plot into your notebook.
9. Based on the equations of motion, will an ion with m = 200 amu and q=2e follow the same
trajectory as an ion with m = 100 amu and q = 1e? Discuss in your notebook and include a plot to
support your argument.
10. Make a new plot and use the same tuning as in parts 6-8. Paste in your notebook a plot that
shows a few ions that enter the spectrometer with the same energy and a few ions that enter the
spectrometer with the same momentum. Discuss in your notebook whether this is a mass-tocharge selector, a kinetic energy selector, or a momentum selector.
Making Arrows
Arrows are a form of trace markers in Igor. Each point in a wave can have an arrow. The tail of the
arrow is located at the plotted point of the wave.
To create arrows, you need a two-dimensional matrix that describes the arrow length and angle.
Make/N=(10 , 2) arrowWave // make a wave with 10 rows and 2 columns.
// The number of rows in the arrowWave should be the
// same as the number of points in the wave you’re plotting.
The 0th column of the arrowWave describes the arrow length in image points (minimum = 4 points).
The 1th column of the arrowWave gives the arrow angle (in radians, 0 = horizontal pointing right).
You can fill the 0 column with the same value by
arrowWave[][0] = 10
// leaving the first [] empty implies “all” rows