PH437 - Nuclear Physics
Spring 2008
Dr. Daniel K. Marble
Classical Mechanics and Special Relativity
Homework Set #1 : 40 points
This homework set contains material that you have covered in your previous physics classes and
is due next Wed. 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.
1.
The new MGH-Northeast Proton Therapy Center under construction at Massachusetts
General Hospital, MGH, in Boston will use an accelerator to produce a 230 MeV proton
beam to kill both benign and malignant tumors in patients. As chief design physicist for
the principle contractor, ACME corporation ( a subsidiary of Roadrunner International),
you’ve been asked by your boss Dr. Wiley E. Coyotte to provide the hospital’s oversight
committee with the following information:
A.
the total energy of the proton.
B.
the magnitude of the linear momentum of the proton.
C.
the speed of the proton.
D.
what accelerating potential is required to accelerate the proton up to this energy (assume
a single accelerating potential)?
2.
The 0 meson decays into a proton (rest mass of 938 MeV/c2) and a negative pion, -,
(rest mass of 140 MeV/c2). Given that the 0 meson is at rest in the lab frame and that
both the proton and pion are emitted at non-relativistic energies, calculate the kinetic
energy of the pion if the proton is detected with 4.90 MeV of kinetic energy.
3.
Two particles are observed to emerge from a nuclear interaction with velocities at right
angles to each other. Each particle has a rest mass of 2.00 GeV/c2 and a linear momentum
of magnitude 1.00 GeV/c. It is hypothesized that the two particles are the only decay
products of a single short-lived particle. Calculate the rest mass of the parent particle.
P1
P2
4.
When protons and neutrons are combined to form a nucleus, mass is converted to energy
in order to bind the nucleons together (binding energy). Thus, the resultant nucleus has
less mass than the original nucleons and the difference in mass is called the “mass
defect.” Calculate the mass defect, and then use Einstein’s mass-energy equivalence
relation to calculate the binding energy for the following two nuclei (Hint: See Beiser pg
397 or Das and Ferbel pp 29-30):
a) 39Ca
atomic mass: 38.970718 u
b) 39K
atomic mass: 38.963707 u