Download 1. Two particles are observed to emerge from a nuclear interaction

PH437 - Nuclear Physics
Spring 2008
Dr. Daniel K. Marble
Homework Set #4 : 50 marks
Due Next Friday
This homework set contains material on the Thomson model of the atom and Geiger-Marsden
scattering experiment.
Reminder: In order to obtain full credit, you must show all work including deriving any
equations that are not in your notes or textbook. Make sure that you indicate on each line of a
problem, the physics that you are using (my posted solutions indicate what I expect). It is your
responsibility to indicate what you are doing. I will not guess!! Answers by themselves are worth
little to no credit!! Finally, each problem should be worked out neatly. I am going to take of
credit for sloppy work.
1.
If a non-relativistic particle of mass, M1, and kinetic energy, E1, collides with a
stationary free particle of mass, M2, show that the maximum energy, E2, that can be
transfered to the particle with mass M2 in an elastic collision is given by the formula:
E2 
2.
4 M1M2
 M1  M2 2
E1
What is the maximum energy that can be transfered to a free stationary electron through
an elastic collision with a 6 MeV alpha particle.
3.
Does your answer in part 2, justify our neglecting interactions between the alpha particle
and the gold atom’s electrons in the famous Geiger-Marsden 1909 scatterin experiment?
Fully explain your reasoning using any calculations required!!
4.
In the diagram below, a 6 MeV alpha particle is scattered by an iron atom
Alpha

r
R
Fe Atom
a)
Using the Thomson model of the atom, calculate the maximum scattering angle
for the alpha particle if the radius of the iron atom is approximately 1 angstron.
b)
Using your results from part (a), calculate the root-mean-square scattering angle
expected for a 6 MeV alpha beam passing through a uniform 100 g/cm2 iron
scattering foil according to the Thomson model.
5.
ACME corporation is attempting to market a low cost modern version of J.J. Thomson’s
experimental apparatus to measure the charge-to-mass ratio of the electron for high
school physics classes. Dr. Wiley E. Coyote, has asked you to check out the experimental
setup before it is marketed. You obtain the following experimental data using the
Thomson appartus with a magnetic field of 1.00 mT and electrodes that are 5.00 cm in
length and seperated by a 1.00 cm gap.
Plate Voltage (Volts)
Deflection Angle (rad)
3000
0.02830.0001
6000
0.01440.0001
9000
0.00930.0001
12000
0.00700.0001
15000
0.00580.0001
a)
Determine the charge-to-mass ratio for the electron from your data.
b)
Does your experimental result confirm the presently accepted value for the
charge-to-mass ratio of the electron to within your experimental uncertainty.
Hint: Graph your data on the three different types of graph paper in order to obtain the
basic form of the equation. Using this information, choose a new x-variable such
that you can replot your data as a straight line on linear graph paper. You can now
use the data regression capabilities of Quattro Pro or Excel to answer the questions.