Difference between revisions of "NucPhys I HomeworkProblems"
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1.) Show that the mean-square charge radius of a uniformly charged sphere is <math><r^2> = 3R^2/5</math> | 1.) Show that the mean-square charge radius of a uniformly charged sphere is <math><r^2> = 3R^2/5</math> | ||
− | 2.) Using the definition of the form factor <math>F(q^2)</math> and probably an integral table, | + | 2.) Using the definition of the form factor <math>F(q^2)</math> and probably an integral table, calculate <math>F(q^2)</math> when |
a.):<math>\rho(r) =\left \{ {\rho_0 \;\;\;\; r<R \atop 0 \;\;\;\; r>R} \right .</math> | a.):<math>\rho(r) =\left \{ {\rho_0 \;\;\;\; r<R \atop 0 \;\;\;\; r>R} \right .</math> |
Revision as of 22:35, 8 March 2008
Chapter 2
Set 1
1.) In your own words, describe what the "Standard Model" of physics is using 2 to 5 paragraphs. Your paragraphs should include the concepts of the 4 fundamental forces of physics, QED, and QCD at a minimum. Any sentences in which a string of 5 or more words match a sentence that is found on the internet will be evidence of cheating.
2.) Solve the Schrodinger equation for the following potential:
. Assume particles are incident from , don't try to normalize but do express the wave function in terms of one coefficient.
Set 2
1.) Given the following barrier potential
show that the transmission coefficient is
when
Assume particles are incident from
and .Set 3
1.) Starting with Shrodinger's time-independent equation, derive the wave functions for a 2-D simple harmonic oscillator. Your derivation should take advantage of separation of variables and you are not required to normalize the wave function.
Set 4
1.) Show that the mean-square charge radius of a uniformly charged sphere is
2.) Using the definition of the form factor
and probably an integral table, calculate whena.):
b.)
c.)
Set 5
1.) a.) find the binding energy difference between O-15 and N-15
b.) compute the nuclear radius of O-15 and N-15 assuming the above binding energy is due to the coulomb energy.
2.) Muonic X-rays
a.) Calculate the energies of muonic K-line X-rays from Fe assuming a point nucleus and using a one-electron model..
b.) Calculate the energy correction (\Delta E) due to the finite nuclear size.
3.) Find the binding energy using the semi-empirical mass formula for
a.) Ne-21
b.) Fe-57
c.) Bi-209
d.) Fm-256
4.) Find the nuetron separation energies for
a.) Li-7
b.) Zr-91
c.) U-236
5.) Find the proton separation energies for
a.) Ne-20
b.) Mn-55
c.) Au-197
Set 500
5.) Several nuclei decay by the emmission of an alpha particle. An alpha particle (He-4) is a tighlty bound nuclear containing 2 protons and 2 neutrons in which the energy needed to remove one neutron is 20.5 MeV. One model for this decay process views the alpha particle as being bound to the nucleus via a spherical potential well.
Once outside the nucleus, the alpha particle is repelled via Coulombs law
The original nucleus had a charge
and the alpha particle has a charge .Use the WKB approximation to show that the transmissivity (T : transmission coefficient) is:
- Media:GamowFormula.pdf Gamow's formula
where
- and and .