Download Nuclear Final Exam

For the question 1-3, answer 2 out of the three questions. Each
question will be worth about 25 points each. These questions 1-3 are
the toughest questions of the final—Good Luck! As Victor says, these are
“Crocodiles”.
1. Assume that virtual π mesons are emitted and absorbed by a nucleus.
From this assumption, and the π meson mass, and the uncertainty
principle, estimate the range of the nuclear potential r0.
2. In a nuclear decay an electron is emitted with an energy of about 1 MeV
and an alpha particle with about 5 MeV. At one time both the electron
and the alpha particle were thought to have been present inside the
nucleus and to have escaped during the decay. Use the uncertainty
principle to show that the electron could not have been inside the
nucleus but the alpha particle could have. Assume neither particle
looses much energy as it is emitted. Carefully indicate your reasoning
behind your calculations.
3. Cs55137 is a common laboratory radioactive source of electrons and gamma rays.
Eight percent of the time Cs55137 beta decays to the ground state of Ba56137. The
net atomic mass difference between the two isotopes is 1.18 MeV/c2. A 180
degree spectrometer is used to measure the beta decay spectrum. The
spectrometer has a radius R = 5.2 cm.
(a) Write down the reaction for the beta decay.
(b) Calculate the maximum momentum of the beta decay electron/positron.
Express the result in MeV/c.
(c) What is the vector direction of the spectrometer magnetic field relative to the
drawing?
(d) What is the magnetic field setting of the spectrometer for the maximum
energy of the electron/positron to arrive at the detector? Provide a numerical
answer with units.
Answer question 4, it is a middle complexity type problem, it is not really that
hard once you understand the statistical view of the problem, I expect to see a
derivation of the total probability here. (10 pt problem)
4. Lets say that you’re a nuclear physicsts who is working on determining the
nuclear potential. You will have to determine the barrier for alpha decay. You then
find the data given below from Georgia State University Hyper Physics Web site.
You can go on line and get the answer, but you must tell me how this works! Is
this a good approximation? Do you think that it will work the same for all isotopes?
The shape of the barrier must obviously be taken into account since it drops rapidly.
But it is instructive to calculate the half-life for a rectangular barrier of that height
and width. Using the barrier penetration calculation gives a half-life of 1.5 x 10^7
seconds, about 13 orders of magnitude longer than the observed half-life. This gives
some insight into the large range of alpha half-lives; the tunneling probability
depends very strongly on the nature of the barrier. The probability depends
exponentially on the height and width, and in this case the height is dropping like 1/r
with distance from the nucleus.
A better tunneling probability can be obtained by
breaking the barrier into segments and multiplying
the successive tunneling probabilities according to
the basic rules for combining probabilities. The
calculated tunneling probabilities for the segments
are shown in the table.
Segment height
Probability
of tunneling
21.9
1.20 x10^-5
16.4
1.74 x 10^-4
13.2
1.43 x 10^-3
11.0
.98 x 10^-2
9.4
.85 x 10^-1
Product of
probabilities
?
Details of calculation
For Question 5-11, answer 4 questions from the list. Each question that you
answer will be worth about 10 pts per problem. These are the basic problems.
The complexity of these are ranked as “baby crocodiles”.
5.
Find for me some common ranges of the barrier and energy of emitted particle
from decay. Here I will give you the A’s and Z’s and you do numerical
calculations on the range and energy. Consider that all of these elements emit
alpha if results seems seems reasonable.
a. A=235, Z=84, find the range and energy; A=240, Z=84, find range and
energy; A=240. Z= 85, find the range and energy; A=210, Z = 85, find the
range and energy; A=18, Z=9, find the range and energy.
b. Why do you think that the last value doesn’t seem reasonable?
c. What do you know about alpha decay in the heavier element isotopes?
What can be said about the lower mass isotopes??
6.
What are alpha particles? What are Beta Particles? What are Gammas?
7.
What is meant by the mean free path length of these three types of radiations
of Betas, alphas, and Gammas? Which of the three do we need to be worried
about? This is a example of attenuation from lab #9.
8.
9.
10.
11.
Do Question number 1 from page 429.
Do problem number 2 on page 429.
Do problem number 3 on page 429.
Do problem number 5 on page 430.
The proposed due date for these problems will not be due until study periods, which is
on May 1st 2006. You will need to have the final completed and turned in by my box
or handed in not latter than 5:00 pm on May 5st! I will have grades ready to turn in
by May 2nd! Your lab test #11 half-life is already in this final.