15-13. The world’s first nuclear reactor was designed and built by Enrico Fermi in
1942. It consisted of a checkerboard of three dimensional alternating blocks of a
graphite moderator and fissile U-235. The fuel was natural grade uranium
containing just 0.7% U-235 because no one had yet solved the problem of how to
enrich it beyond its natural state.
The resonance escape probability for an infinite (no neutron loss) homogeneous
core is about 0.648. Predict k if = 1.000, = 1.931, f = 0.750 and p = 0.648. If
you calculate k 1.000, how did Fermi get it achieve criticality?
Need: Fermi’s secret to make a graphite moderated reactor natural uranium
reactor work.
15-14. Find the Error in This Solution: You have a radioactive sample consisting of
1025 atoms. It is decaying at a rate of 1021 per second. What is the residual activity after
24 hours?
Need: Residual activity of a radioisotope after 24 hours.
Know: Original amount is 1025 atoms decaying at a rate of 1021 per second.
15
15-15. How much radiation in Becquerel’s3 (radiation particles/s) is released by
the burning of 8,000 metric tons/day of coal in a power plant? (The low level
radiation is there because uranium is slightly radioactive and widespread in
minerals4 of all types including coal.)
Assume coal contains 10.0% by weight of ash. If the coal contains 10.0 parts per million
(ppm) of
U
238
92
the ash contains 100. ppm of
U
238
92
. The half life of
U
238
92
is 4.468 billion
years. There are 8 other radioactive isotopes per disintegration of
U
238
92
.
Need: Radiation from burning 8,000 metric tons/day of coal.
Know: Coal is 10.0% ash containing 100. ppm
U
238
92
decaying by particle decay
with t½ of 4.468 billion years or 1.41 × 1017 seconds. Avogadro’s number is 6.023×
1026 particles/238 kg of
U
238
92
.
U
238
92
U
238
92
U
238
92
15-16. Milk, which is easily contaminated by I-131, can be made into cheese5 and aged
for a few months so it will become wholesome again. How long should you wait?
Need: How long to age radioactive cheese.
Know: I-131 has a half life of 8. days. The decay law for radioactive atoms
is
tt
eCC 2/1
/693.0
0
. Assume 3 – 6 months (90 – 180 days) is enough to render the I-131
harmless.
2/10
tC
5 After contamination of central European farms by the Chernobyl nuclear disaster in the Ukraine in 1986,
the Poles did indeed convert their contaminated milk into cheese and then aged it for several months.
15-17. A particularly long lived isotope is 237Np with a half–life of 2.2 million years so
that its radioactivity is long lasting6. How many Bq does 1.00 mg of it produce?
Need: Disintegration rate of 1.00 mg of Np in Bq, i.e., disintegrations per s.
13
2/1
1094.6
dt
15-18. What does it mean when a nuclear reactor is to be moderated by graphite and
cooled by helium? Can you sketch such a reactor?
Need: Graphite moderated reactor and helium cooled.
15-19. While not concerned with nuclear power, the analytical tools you have mastered
can be used to give a lower limit on the age of the Earth.
4.47 billion years.
The measurement depends on small zircon crystals (ZrSiO4) that, when molten, can
dissolve uranium compounds (but they will not dissolve lead compounds). Liquid zircons
will freeze at about 2,500C trapping any uranium in them. This uranium will eventually
decay to stable Pb-206, which is then trapped within the zircon crystal.
In one zircon crystal the ratio of U-238/Pb206 was determined to be 0.888. When was the
Earth last molten?
Need: The age of the Earth.
7 For those versed with even a smattering of calculus, the first step is the rate of production of Pb is equal to
dU
dPb
20. You are a nuclear engineer in the now defunct Soviet Union, which was a heavy–
handed dictatorship tolerating neither criticism nor behavior contrary to the official line.
You are shown a proposed design for the Chernobyl reactor that is destined to explode in
1986 causing about 30 “immediate” deaths and inflicting thyroid damage on thousands
(perhaps tens of thousands) of other victims (particularly the young). You immediately
see that the reactor has no secondary containment and, perhaps as bad, the last 60 cm. of
the control rods are coated with a heavy layer of a graphite moderator. You point out to
the engineer-in-chief that a sudden insertion of withdrawn control rods all the way into
the core of the reactor will not shut it down as expected, but will increase the nuclear
reactions by virtue of the extra moderation via the graphite coating. Furthermore, lacking
a secondary containment vessel, there could be disastrous widespread consequences. The
engineer–in-chief takes you aside and says the reactor is designed to be economical8. The
design must stand essentially as is. He warns you to be careful because, if you bring it up
again, the Soviet oversight authorities may send you to jail.
What should the engineer do?
a) Work within the system to get the best reactor he can under the
circumstances
b) Still insist on changes to make the reactor safer including changes he has
been warned to ignore.
c) Resign and seek a new job, a job that will surely be a serious demotion
given the Soviet’s aversion to explicit or implicit criticism.
Use an Ethical Decision Matrix and the NSPE Code of Engineering Ethics
Options →
NSPE
Canons
a: Go along with
the decision
b: Insist on design
changes
c: Quit your job
Hold
paramount
the safety,
health and
welfare of the
public.
This is definitely
contrary to this
canon.
There is great
personal risk; you
would likely
balance your own
safety vs. that of the
public
This is a difficult
decision because
the system may
regard you as a
refusnik in the
Soviet Union.
Perform
services only
in the area of
your
Yes. This is your
field of expertise.
This is what you
should do – but few
would have the
courage.
You might not find
another nuclear
engineering job and
would end up in a
22
competence
minor job outside
of your area of core
competence.
Issue public
statements
only in an
objective and
truthful
manner
NA
NA
Having quit, you
could try to make
public statements to
prevent Chernobyl
– but it’s not likely
you will have a
voice.
Act for each
employer or
client as
faithful
agents or
trustees
Yes. Being silent
would satisfy this
canon.
This maybe within
your expertise, but
your employer
might not agree!
His view will
prevail.
NA. The media are
all controlled by the
regime. You can’t
go public.
Avoid
deceptive acts
No, this is
deceptive to the
public.
This is your best
bet to reduce
consequences of
what has been
decided against
your better
judgment.
This complies
exactly with the
canons. Anything
else is deceptive to
some degree.
Conduct
themselves
honorably …
Hardly honorable.
This is honorable
but probably
ineffective.
Honorable but
surely ineffective.
The personal stakes are so high that you really can’t be expected do a); b) is probably the
best you can manage but it’s the slippery slope to making other concessions to the
system, and c) maybe satisfying but will exclude you from an effective voice. b) is your
best bet.
21. You are a nuclear engineer designing the nuclear reactor complex in Fukushima,
Japan. It contains six virtually identical reactors. Japan is of course a democracy but one
imbued with a culture of respect for one’s elders. During a design review for the nuclear
complex, you notice that all the secondary cooling systems have a common design based
on diesel-electric generators to run the cooling pumps. You realize that a common failure
mode exists. Anything that knocks out one generator could do the same to all of the
reactors. Very politely you explain your concerns to the engineer–in-chief who tells you
the design has been fixed as a compromise between absolute safety and safety based on
an extremely unlikely event. And, based on the virtually zero likelihood of a common
mode failure, the design stands. Remember, in Japan, consensus is very important. Are
you OK with the engineer-in–chief’s decision?
What should the engineer do?
a) Work within the system to get the best reactor he can under the
circumstances
b) Still insist on changes to make the reactor complex safer including
changes he has been warned to ignore.
c) Resign and seek a new job, a job that could be a demotion given the
Japanese aversion to explicit or implicit criticism of their collective
decision making.
Use an Ethical Decision Matrix and the NSPE Code of Engineering Ethics
Options →
NSPE
Canons
a: Go along with
the decision
b: Insist on design
changes
c: Quit your job
Hold
paramount
the safety,
health and
welfare of the
public.
This is definitely
contrary to this
canon.
Yes. You clearly
should push
changes in the
design.
This might benefit
the general public
but working within
the system could be
more beneficial.
Perform
services only
in the area of
your
competence
Yes. This is your
field of expertise
This is what you
should do – but it
would be contrary
to cultural Japanese
norms.
You probably could
find another job but
perhaps less
prestigious than the
current one.
Issue public
statements
only in an
NA
Yes, even as an
employee you have
access to public
Yes, But another
job may be hard to
find having been
24
objective and
truthful
manner
media. You could
truthfully inform
the public but you
would be unfaithful
to your employer.
disloyal to your
previous employer.
Act for each
employer or
client as
faithful
agents or
trustees
Yes. Being silent
would satisfy this
canon.
This is within your
expertise.
If you quit, lots of
TV stations or
newspapers would
love to print your
story. But it’s not
faithful to your old
employer.
Avoid
deceptive acts
No, this is clearly
deceptive to the
public.
This is your best
bet to reduce
consequences of
what has been
decided against
your better
judgment.
This complies
exactly with the
canons. Anything
else is deceptive.
Conduct
themselves
honorably …
Hardly honorable.
This is honorable
and could be
effective.
Honorable and also
possibly effective.
So this engineer has the same dilemma as the Soviet engineer. But quitting and going
public is more practical in Japan than it was in the Soviet Union. Probably c) is your best
choice of action.