PH437 - Nuclear Physics
Spring 2007
Dr. Daniel K. Marble
Electrodynamics
Homework Set #2 : 50 marks
This homework set contains material that you have covered in your previous physics classes and
is due at the beginning of next class (lesson #3). These problems have been assigned to ensure
that you have necessary skills and solution techniques for material that will be covered during
PH437 thus all work must be shown to obtain credit.
Reminder: Discussion with classmates is encouraged.
1.
A nucleus can often be successfully modeled as a uniformly charged sphere. Given a
nucleus of atomic number Z and radius R:
a) show that the electrostatic energy (Coulomb repulsion energy) stored in the nucleus is
3  e 2  Z2

given by the formula: E  
5  4  o  R
b) Calculate the Coulomb repulsion energy for a carbon nucleus of radius 2.747 fm.
2.
In homework set #1, you were required to calculate the binding energies for two mirror
nuclei (39Ca and 39K). Both of these nuclei have approximately the same radius but have
different binding energies due to their different Coulomb repulsion energies as they have
different atomic numbers. Use the binding energy results from homework assignment #1
(39Ca : 326 MeV and 39K : 334 MeV) along with your results from problem #1 to solve
for the radius of these two nuclei.
3.
A proton fired from an accelerator interacts with a stationary proton in a target through
the Coulomb force as shown below:
v
p
p
r
Given that the radius of a proton, R, is 1.2 fm (1 fm = 1x10-15 m), what is the minimum
energy required for an incident proton to make contact with the target proton as shown
below:
p
p
r
4.
A proton beam is obtained from an accelerator by accelerating the proton through an
electric potential difference of Vo as shown in the diagram below. A perpindicular
magnetic field of 4.00 T will select a proton beam for an experiment by passing the beam
through hole in a metal plate as shown in the diagram.What magnetic field would be
required for this experimental setup if the proton beam was replaced by an oxygen beam
with a charge state of +2 for the same accelerating potential, Vo. Assume that the proton
is traveling at non-relativistic energies.
`
Vo
o
Accelerator
5.
Magnet
A proprietary electrical amplifier has been developed for ACME corporation by a
contractor. Your boss, Dr. Wiley E. Coyote needs to know the voltage gain of the
amplifier. Since the device is proprietary, the contractor has refused to give Dr. Coyote a
schematic of the device. Thus, Dr. Coyote has setup the following circuit in order to
experimentally determine the voltage gain of the device using a 10 volt input signal with
a variable frequency and a voltmeter to measure the amplifier’s output voltage.
+
10V
Amp
V
-
Input
Output
Using this circuit, Dr. Coyote has made the following set of experimental measurements
of output voltage Vs frequency, . Dr. Coyote has asked to you to use the definition of
voltage gain, A v   
Vout
, and his experimental data to determine the formula for the
Vinput
voltage gain of the amplifier as a function of frequency. (Hint: Graph the data using
different types of graph paper.)
 (rad/s)
Vout (Volts)
100.1
2341
300.1
142.00.1
500.1
86.00.1
700.1
52.00.1
900.1
32.00.1
1100.1
19.000.01