X-ray Spectroscopy
What are the energy levels for each value of n? For the hydrogen atom with
nuclear charge Z=1 and 1 orbital electron,
En 
( 13.6eV )
n2
(2)
For a single electron bound to a nucleus of charge Z, the electron is more tightly bound:
the energy levels are given by
En 
( 13.6eV ) Z 2
n2
(3)
If an electron in an excited state drops from the level ninitial to nfinal, a photon is emitted.
The energy of this photon is given by
 1
1 
En  13.6 Z 2  2  2  eV
n

 i nf 
(4)
In multi-electron atoms, the 1-electron energy levels are substantially changed by
electron-electron interactions. However, Moseley showed that for the K and K  x-rays,
the effect of the additional electrons on the energy levels can be treated by replacing Z in
Eq. 4 by an effective Z equal to Z-1. The reduced value of Z can be rationalized as arising
from the screening of the nuclear charge by the partially filled n= 1 orbital in the initial
(excited) state of the atom.
Thus the energy of the K x-ray (ninitial = 2 to nfinal = 1) is then given by
E  E2  E1  (13.6eV )( Z  1) 2 (
1 1
 )
12 22
(5)
For the K  X-ray, Eq. 5 must be modified to take into account that ninitial = 3:
1 1
E  E3  E1  (13.6eV )( Z  1) 2  2  2 
1 3 
Fig. Energy levels showing the K and L series of transitions that give rise to the
corresponding x-ray wavelengths.
(6)
Procedure:
I.
Familiarize yourself with the x-ray generation system and the
spectrometer.
a. Check the zero setting of the spectrometer angle. This is done by loosening
the ‘Motor Lock Screws’ and slightly translating the Stepper Motor to the
left to disengage it from the central axle gear. Then swing the arm with the
Geiger-Muller Tube to the 100o position on the 2 scale. At this position
the scored line on the large circular aluminum plate underneath the ‘Gear
Locking Nut’ should have its ruling aligned with the 50o scale close to it.
If not, while keeping the ruling aligned with the 50o mark, loosen the ‘Gear
Locking Nut’ and rotate the arm to 100o. Then retighten the ‘Gear Locking
Nut’ without changing either of the two settings. Re-engage the motor and
tighten the ‘Motor Lock Screws’. The unit is now properly zeroed. If this
step is done incorrectly your results will be gibberish. If you have to
perform this step of unlocking the ‘Gear Locking Nut’, please inform
Prof. Bonin.
b. Choose GM tube setting (400-500 volts) and make sure the counter and the
stepper motor control box both have their power turned on.
c. Understand that the crystal deflection angle θ and the detector angle are
mechanically linked.
Fig. 1: The Tel-X-Ometer x-ray tube and spectrometer.
II.
III.
Open the xray program. First turn on the Dell computer until it is booted in
Windows XP. Then click on the ‘xray’ icon to open the directory with the
program we need to run. Double click on the file entitled ‘Tel-x-Ometer v1.05’.
Familiarize yourself with the interface window for the experiment. This
will allow you to set the important operating paramenters to take an xray
scattering spectrum, and to save the scattering data to a file. First – go the
the ‘Operate’ item on the top menu in the Tel-x-Ometer window and click
on it and then select ‘Change to Run Mode’ (at the bottom of the list).
a. There are seven main areas on the Instrumentation window: Controls,
Indicators, Calibration, Arm Orientation, Data Acquisition (Fixed Time),
Data Acquisition (Count Limited), and Counts vs. Angle Plot. See the
screenshot figure below. Note: this is an editable item so please do not edit
any of the interface other than to enter values of parameters that have
fields. Two critical buttons are on the menu bar under the FileEdit … menu
bar: the run continuous icon (two bent arrows) and the stop icon (red
hexagon).
Fig. 2: The Labview window for data acquisition and instrument control of the Tel-xOmeter x-ray tube and spectrometer.
b. Arm Orientation: set to Right Side (default).
c. Click the ‘run’ icon on the menu bare and under Calibration, click the
‘Calibrate’ bar. The stepper motor will move the GM tube to a minimum
angle – enter the value of this angle in the child window that opened up and
click ‘OK’. The motor will then move to the maximum value - enter the
value of this angle in the second child window that opened up and click
‘OK’.
d. Under Controls, enter 26.00 into the ‘Move to angle’ field and click on the
push button just to the right of this field. The GM tube should move to 26
degrees.
e. Under Data Acquisition (Fixed Time), set it up to do a rough scan of the
region between 26 and 36 degrees. Enter ‘2’ in the step resolution (this
corresponds to how large an angle each stepper motor step will be in
sixteenths of a degree, e.g. if step resolution is 2 then each step will be 1/8
of a degree). Next enter ‘2.00’ in the Time/step(sec) field – this will
determine how long we will collect counts at each data point. For now, do
not click Save data to file, but do this for your final scans.
f. Collect a very short data set to educate yourself on the procedure for
collecting and saving real scattering data.
1. install NaCl crystal with rough face toward the x-ray beam – see
Fig. 2;
2. collect data between 26 and 35 degrees, 2 second accumulation
time; Click the ‘Acquire Data’ button to begin collecting data in
the range of angles you entered. The ‘Counts vs Angle Plot’ will
begin graphing the data.
3. store the data on hard disk as “your name_1”.
IV.
V.
Estimate what you expect to observe when analyzing the x-ray emission
spectrum with a NaCl crystal. Note that the anode material in the x-ray tube is
Cu (Z= 29).
1. Compute the energy and wavelength of the Kα and Kβ lines of Cu.
2. Compute the expected angles for first-order Bragg diffraction of
these x-rays from the NaCl crystal, for which the spacing d =
0.282 nm.
Do the real experiments
a. Measure and save the data for the x-ray spectrum of the system, using the
NaCl crystal as grating, between 25 and 40 degrees. Enter ‘2’ in the step
resolution. You should click Save data to file. You should see 2 peaks
close together. Note that the angles that are recorded by the x-ray
spectrometer are 2, so they are twice the angle of scattering. Thus if you
see a peak at 50° on the spectrometer then the scattering angle is  = 25°.
b. Repeat for 40-80° with NaCl crystal.
c. Explain the spectrum observed between 25° and 40°. Your results should
be pretty close to those computed in part III.
d. Explain the spectrum seen between 40 and 80°. Hint: consider two
possibilities: second order diffraction of Kα and Kβ photons, or first order
diffraction of Lα, Lβ photons. For L transitions, the final state is nfinal = 2.
e. When you close the program (Labview) DO NOT SAVE ANYTHING.