Marvelous P110/120'ers: As fossil fuel supplies dwindle we turn to alternatives (biomass, wind, solar...) and nuclear fission. This set of exercises is oriented principally toward energy from nuclear fission in light water reactors. Chapter 6 in Ristinen and Kraushaar is an excellent chapter on this subject. Also, we will spend most of this week discussing nuclear energy. You are also encouraged to discuss these questions with each other and with me. I am available most of the time. Stop by or send e-mail: brabson@indiana.edu. Ben
1.) Which of the following are
high potential energy arrangements for two electric charges? (3 correct
responses!) (Ans: Remember that it takes work
to pull attractive objects apart or to push repulsive objects together!)
a.)
-
- (two negative charges
far apart)
b.) +
+ (two positive charges
far apart)
c.)
++
(two positive charges close together)
d.)
+-
(a positive charge near a negative charge)
e.)
+
- (a positive
charge far from a negative charge)
f.)
--
(two negative charges close together)
2.) Give a brief description
of the entire oxygen atom. You might want to first discuss the nucleus
(size and composition), and then the whole atom (size and composition).
Words like electron, proton, neutron, positive, negative, neutral, and
sizes like 10-10 m or 10-14 m, could conceivably
creep into your description. (Ans: On reserve
in the Swain West Library for P120, Romer's, Energy: An Introduction to
Physics, p 567 has a nice description of atoms and nuclei.)
3.) Almost all of the mass of the oxygen
atom you described in problem 2 is in its nucleus? Explain why.
(Ans:
Masses are discussed in R&K, p 173. The key lies in discovering how
much an electron weighs compared to a proton or neutron )
4.) An atom has a certain number
of protons a certain number of neutrons in its nucleus and a certain number
of electrons in orbit around the nucleus. Which of these numbers
determines the name of the element? Try out your answer on the two
isotopes of Carbon, stable
126C6 and radioactive
146C8.
Explain how your answer does the job. [Hint: See
page 174 in R & K].
5.) Consider the radioactive
Uranium-235 nucleus, 235U. How many protons and how many
neutrons does it contain? [Ans: You need a
periodic table or a chemistry friend who knows which element Uranium is.
Hydrogen has 1 proton, Helium has 2 protons, ... Uranium has...]
6.) Neutrons bombard uranium
(23994Pu). If a neutron and this Plutonium
nucleus stick together to form a new nucleus, the new nucleus must be:
a.) 24094Pu146
b.) 23994Pu145
c.)23995Pu144
d.) 24094Am146
e.) 24095Am147
[Hint: This problem has two parts. First,
you must decide on the number of protons and neutrons in the new nucleus,
and then you must use the naming convention of problem 4 to figure out
what to call it.]
7.) Consider a nuclear reaction where the total rest mass before the reaction is greater than the total rest mass after. Do you have to supply energy to make this reaction happen (endothermic) or does the reaction release energy when it takes place (exothermic)? [Hint: Einstein's DE = Dmc2 where DE is the change in energy or DE = Eafter - Ebefore and Dm = mafter - mbefore].
8.) Consider the possible forces
between a proton and another proton that are very close together.
Three candidate forces, GRAVITIONAL, ELECTRIC,
and STRONG. Between
the proton and proton these three forces are respectively:
a.) attractive,
repulsive, zero
b.) zero,
zero, attractive
c.) attractive,
zero, attractive
d.) attractive,
repulsive,
attractive
e.) zero,
zero, repulsive
[Hint: It's the mass of two objects that insures that they are gravitationally attractive. When are two objects attracted or repelled by electric forces? When are two objects attracted by the strong force that holds the nucleus together?]
9.) In this fission process what
(??) is missing ? 10n
+ 23592U ---> 23692U
---> 14357La + 9035Br
+ ??
a.) 30H b.) 3 protons
c.) 2 neutrons d.) 3 neutrons e.) none
of these.
[Hint: Conservation of charge says that the
number of charges on each side of the arrow must balance. Also conservation
of baryon number says that the total number of protons + neutrons must
balance.]
10.) Calculate the number of
joules that can be obtained from the fissioning of one mole (235 grams)
of 235U, assuming 200 MeV average energy release per fission.
[Ans:
1.93 x 10+13 Joules]. Most folks in the US use
consume an average of 11,000 watts of power. How long would the energy
from 235 grams of Uranium last you at this rate?
[Ans: 55.4 years]
[Hint: The front cover of R & K gives
the energy conversion of 1 eV = 1.60 x 10-19 Joules, so 1 MeV
= 1.60 x 10-13 Joules.]
11.) Thinking about problem 10, how
much natural uranium does it take to provide a mole (235 grams) of
235U?
[Ans:
33.6 kg] [Hint: Only 0.7% of natural uranium is U-235.]
12.) When a neutron hits a Uranium-235
nucleus, 23592U, the nucleus often absorbs the neutron
and the new nucleus fissions, breaking apart into fission fragments and
a number of neutrons. If a sufficient quantity of 23592U
is present, a chain reaction can take place. What is meant by a chain
reaction? [Ans: R&K, p173]
13.) Exponential growth happens
when the number of new objects (babies, for example) is proportional to
the number of old ones (parents). Exponential decay of a parent
sample of radioactive nuclei takes place because the number of decays is
proportional to:
a.) the time allowed
for a single decay.
b.) the mass of the nucleus
decaying.
c.) the number of parent
nuclei in the sample.
d.) the number of daughter
nuclei in the sample.
e.) the number of nucleons
in the decaying nucleus.
[Aside: The number of decays per second is
also called the activity. It is the activity that we actually measure,
not the number of parent nuclei present. Both the number of parents
and the activity decrease exponentially.]
14.) As a sample of a radioactive
isotope decays, its half-life:
a.) decreases by 1/2
each half life.
b.) remains the same.
c.) doubles each half-life.
d.) may increase or decrease
depending on the isotope.
e.) would follow a straight
line if plotted on semilogarithmic paper.
[Hint: Think about what happens to the doubling
time in exponential growth. Suppose your bank pays 7%/year.
Then, from the rule of 70, your account doubles after 10 years. Now
what is the doubling time of your account? That is, how long will
it take your account to double again?]
15.) In 1995 the US is electric power
production was approximately 450 GWe (A typical large power plant produces
about 1 gigawatt of electric power). Roughly what fraction of that
electric power came from geothermal sources in the US in 1995? Where are
the major geothermal sources? [Hint: The fraction
you will get is very small. Geothermal energy is discussed in detail
starting on p. 158 in R & K.]
16.) There is a vast reservoir of thermal
energy in the Earth's interior stored as hot rock. Where did/does
this energy come from?
a.) Energy from the decay
of radioactive nuclei like natural uranium.
b.) Energy from solar
neutrinos interacting with the Earth.
c.) Tidal forces from
the Moon-Earth interaction.
d.) Primordial heat energy
remaining from the origin of the solar system.
e.) Energy from the release
of gravitational potential energy as the Earth is gravitationally compressed.
[Hint: We will discuss this in class when
we address Geothermal energy. Also, R&K, p158.]
17.) A tidal estuary, 1.0 km.
wide and 100.0 km. long, has a high tide 10 meters above low tide.
Using the fact that a cubic meter of water has a mass of 1000 kg, find
the mass of water available for use in generating power. [Ans:
1012 kg ]
18.) Power can be generated both
during the 6 1/4 hour period as the tide comes in and again during the
6 1/4 hour period as the tide goes out. On average, how much
power can be generated by the tidal bay of the previous problem?
(Use g = 10 N/kg.) [Ans: 2.22 x 109.
If you get an answer that disagrees by 2 with this answer, then think carefully
about the average height of the water as it goes from high tide to low
tide and explain why this matters.]
19.) To heat your house for one
season in Bloomington takes about 107 Kcal. You could
get this heat by cooling off the rock under your yard by, say, 10
0C. If your yard is 30 m x 30 m, how deep a layer of rock (h)
must you cool to extract this much heat? The specific heat of rock
is 0.21 Kcal/kg/0C and the density of rock is about 3000 kg/m3.
[Ans: 1.8 m.]
20.) In a particular fusion reaction
, d + t ---> 42He +
n, it is observed that the mass of the final state particles (42He
+ n) is less than the mass of the initial state (d + t) by about 3.1 x
10-29 kg. How much energy in MeV is realeased in this
reaction? 1 MeV = 1.6 x 10-13 J. [Ans:
2.8 x 10-12 J or 17.6 MeV , Hint: See problem 7's answer. How
does this compare with the energy released in one fission reaction discussed
in problem 10?]