PH437 - Nuclear Physics
Spring 2008
Homework Set #5
This homework set contains material on the Rutherford model of the atom and Rutherford
scattering.
1.
An incident particle of mass M1 scatters at an angle of  (with respect to its incident
direction) off a target nuclei of mass M2 due to Rutherford scattering. The ratio of the
scattered energy to incident energy of the projectile is called the kinematic factor, K, and
is one of the most important quantities that must be calculated in order to analyze the
scattering energy spectrum. Using the fact that Rutherford scattering is an elastic
collision, prove that the formula for the kinematic factor is given by the equation:
K
2.
E1
E0
2


 M1 cos  1   M1  sin 2  
 M2

 M2 


M1


1


M2


2
Rutherford backscattering spectrometry is performed using a 2 MeV alpha beam and a
particle detector at 171 degrees on a series of thin elemental foils. Calculate the energy of
the detected alpha particle if the thin foil is composed of:
a) 197Au
b) 32S
c) 64Zn
d) 12C
e) 13C
3.
The following research breakthrough was reported in “Physics News Update” by the
American Institute of Physics on January 8, 1997:
A NEW ELECTROLUMINESCENT DEVICE:
A new electroluminescent device uses 1/10th the voltage of previous devices. Head-mounted displays
(small enough to fit into a visor) in automobile, aircraft, and microsurgery environments won’t be practical
until the conversion of electricity into tiny parcels of light can be done using small currents and voltages.
At
the heart of a thin-film electroluminescent (TFEL) device is a host material such as ZnS doped with
luminescing centers such as Mn atoms. On either side of this material are insulating layers which serve as
suppliers of electrons. High electric fields, supplied by a voltage applied across the whole sandwich,
launch electrons into ZnS where they strike a manganese atom, which emits a photon. A new TFEL
concept developed at Georgia Tech (Christopher Summers, chris.summers@gtri.gatech.edu) employs much thinner
insulating layers, which permits the electrons to reach their necessary velocity using much less voltage: 1525 V instead of the customary 150-200 V. The efficiency of the new device is still low and the cost of
growing the crystalline insulating layers is comparatively high, but the low-voltage requirements, and the
smaller circuitry this will permit, may make the approach worthwhile. (C.J. Summers et al., upcoming
article in Applied Physics Letters).
After reading this report, Dr. Donald Duck, Director of Materials Research at Acme
Corp., contacted Dr. Dave Morton of the Army Research Lab and received funding to
develop quality manganese doped ZnS films for ARL. Dr. Duck has made thin films of
ZnS on a thin carbon foil backing. Dr. Duck needs to know the stoichiometry of his
film (ratio of S to Zn), the manganese doping concentration (ratio of Mn to S) and is also
worried about possible processing contamination by the following impurities: Au, O, H,
and Al. To answer these questions, Dr. Duck has supplied your boss, Dr. Wiley Coyote,
with a thin test film for analysis using Rutherford backscattering. Mr. T. Devil, your RBS
technician, has obtained an RBS spectrum with peak energies and heights listed in the
following table using a 2 MeV alpha beam with the detector at 171 degrees. Dr. Coyote
has asked you to analyze the spectrum and supply Dr. Duck with the following
information:
a)
the stochiometry of the film (ratio of S to Zn)
b)
the doping concentration of the Mn (ratio of Mn to Zn)
c)
the name of any impurities detected in the film
d)
tell Dr. Duck if there are any impurities in his list that you can not detect with
RBS.
Peak Energy(MeV)
Counts
Peak Energy (MeV)
Counts
0.504
894
1.213
18620
0.565
10
1.249
848
0.724
40
1.496
1453
1.100
1240
1.568
71240
4.
The following experimental data is similar to that obtained using the LC-400 Van de
Graaff accelerator by CDT Bull during the spring of 1996 for protons scattered off a
carbon foil as a function of proton beam energy.
Beam Energy (keV)
Counts
Beam Energy (keV)
Counts
255
237601
355
115096
265
213599
365
107074
275
198347
375
103147
285
184488
385
87232
295
168572
400
79313
305
162859
410
43635
315
152683
420
31718
325
142864
430
67415
335
128982
440
144886
345
122999
450
207407
Assuming that all data points were taken with the same experimental geometry and for
the same number of incident protons, determine all energy regions where the scattering
data indicates that the scattering between the proton and the carbon atom was Rutherford.
(Hint: Plot the data on the appropriate type of graph and check for the Rutherford
scattering energy dependence)
5.
Determine the Rutherford scattering cross sections for 150 keV protons scattered at 171
degrees off 197Au and 12C. Remember to apply electron shielding corrections if necessary.