Adapted from Vol.117, No. 105, July 8, 1971, of the
Congressional Record
by John W. Gofman, for the Committee for Nuclear Responsibility,
Post Office Box 421993, San Francisco CA 94142.
Preface by Egan O'Connor for CNR: The calculations below
establish that ONE large nuclear power plant, during ONE year of
operation, produces as much long-lived radioactive poison (fission
products) as produced by the explosion of about 1,000 Hiroshima
bombs.
The calculations were placed into the Congressional Record by
U.S. Senator Mike Gravel, Democrat from Alaska, on July 8, 1971,
and their "bottom line" was widely cited throughout the world.
Decades later, CNR could find only a very poor copy of the
Congressional Record --- so poor that very few of the exponents
were legible. So, we asked Dr. Gofman to adapt the presentation
into a better format (below). In our computer-program, the symbol
^ indicates that the next number is an exponent.
John W. Gofman, M.D., Ph.D., has a doctorate in
nuclear/physical chemistry. He is the co-discoverer of
uranium-233, founder of the Biomedical Research Division of the
Livermore National Laboratory, and Professor of Molecular and Cell
Biology at the University of California, Berkeley.
The Fission-Product Equivalence between
Nuclear Reactors and Nuclear Weapons
(By John W. Gofman)
What is desired here is a determination which compares
production of long-lived fission products (for example,
strontium-90 or cesium-137) by nuclear power reactors, with such
production by nuclear weapons. In particular, we shall determine
what Kilotonnage of atomic FISSION bombs (the Hiroshima bomb was a
fission bomb) is required to produce an inventory of long-lived
fission products equivalent to the inventory within a 1000
Megawatt (electrical) nuclear generating station which has
operated for one year.
The energy of the reactor and of the bomb are totally from
nuclear fission. Thus, when we compare equal ENERGY production, we
will automatically compare equal production of fission-products.
Listed below are certain physical conversion factors and
parameters of relevance, together with the source of such
information.
Energy Units: 1 Kilowatt-hour equals 8.6 x 10^5 gram-calories.
Reference: "Handbook of Chemistry and Physics," 44th Edition,
1962-1963, at p.3305 (Units and Conversion Factors). Chemical
Rubber Publishing Co., Cleveland, Ohio.
Equivalents of 1 Kiloton of TNT: 1 Kiloton TNT equals 10^12
gram-calories. 1 Kiloton TNT equals 1.15 x 10^6 Kilowatt-hours. KT
means Kiloton. Reference: "The Effects of Nuclear Weapons," Samuel
Glasstone, Editor. Published by the U.S. Atomic Energy Commission.
Revised Edition, February 1964. At page 14, Chapter 1, Table 1.41.
U.S. Government Printing Office, Washington, D.C.
Yield of Hiroshima Bomb: 1 Hiroshima Bomb is roughly 20
Kilotons TNT. Reference: Ibid., page 6, Chapter I.
* PART 1. CALCULATIONS
1. In one year of operation of a nuclear reactor, long-lived
fission products that have been manufactured will not have decayed
significantly. Hence, the inventory at the end of one year will be
almost precisely equivalent to the total quantity of such fission
products that has been produced.
2. The nuclear generating station will be taken as 33%
efficient in the conversion of thermal to electrical energy. Thus,
3000 Megawatts (thermal) yields 1000 Megawatts (electrical). The
calculation can be correspondingly modified for any other
efficiency value chosen (see Part 3).
3. The nuclear generating station will be presumed to
operate at full power throughout the year. The calculation can
readily be modified for any deviation from 100% operation over the
full year (see Part 3).
Now, 1 year of operation represents 24 hours/day times 365
days/yr, or 8760 hours/yr of operation.
If 1 Kilowatt-hour represents 8.6 x 10^5 gram-calories, then 1
Megawatt-hour represents a thousand-fold more, or 8.6 x 10^8
gram-calories.
Therefore, gram-calories per Megawatt-year (or 8760
Megawatt-hours) equal (8.76 x 10^3 Megawatt-hours) times (8.6 x
10^8 gram-calories per Megawatt-hour), or 7.53 x 10^12
gram-calories. And per 3000 Megawatt-years, the number is
3000-fold larger, or 2.26 x 10^16 gram-calories.
And there are 1 x 10^12 gram-calories per Kiloton TNT.
Therefore, a reactor at 3000 Megawatts (thermal) for one year
is equivalent to (2.26 x 10^16 gram-calories) divided by (1 x
10^12 gram-calories per Kiloton TNT), or 2.26 x 10^4 Kilotons.
Now, taking 1 Hiroshima bomb as 20 Kilotons (KT), we can say
3000 Megawatts (thermal) for 1 year represents 2.26 x 10^4 KT
(22,600 Kilotons), divided by 20 Kilotons per bomb, or 1130
Hiroshima bombs equivalent.
Reminders: This number (1130) applies to a 1000-Megawatt
(electrical) nuclear power reactor --- see Point 2, above. Also:
The energy of the reactor and of the bomb are totally from nuclear
fission. Hence, if we have compared equal ENERGY production, we
have automatically compared equal fission-product production. And
since, for long-lived fission products, we can neglect the decay,
we conclude that the inventory of long-lived fission products in a
3000 Megawatt (thermal) reactor, per year of constant operation,
is equal to the long-lived fission-products produced by explosion
of about 1130 Hiroshima bombs.
* PART 2. ERROR-CHECK
We can check this calculation by an alternative approach,
using Kilowatt-hours instead of gram-calories. We listed at the
outset that 1 Kiloton TNT represents 1.15 x 10^6 Kilowatt-hours.
Also: 3000 Megawatts (thermal) for 1 year represents (3 x 10^3
Megawatts) x (8.760 x 10^3 hours/yr), or 2.628 x 10^7
Megawatt-hours/yr. For Kilowatt-hours/yr, the number is 1000-fold
higher, or 2.628 x 10^10.
Therefore, 3000 Megawatts (thermal) for 1 year represents
(2.628 x 10^10 Kilowatt-hours) divided by (1.15 x 10^6
Kilowatt-hours per Kiloton TNT), or 2.29 x 10^4 Kilotons.
Converting to Hiroshima-bomb equivalent, we have (22,900
Kilotons) divided by (20 Kilotons/bomb), or 1145 Hiroshima bombs.
(Within rounding-off errors, the result is the same as the 1130
Hiroshima bombs obtained in Part 1 --- which is, of course,
expected.)
* PART 3. SOME POSSIBLE MODIFICATIONS
(1) It is claimed that, in the future, nuclear reactors may
operate at 40% efficiency (thermal to electrical) instead of the
33% efficiency assumed in these calculations. In such a case, the
Hiroshima bomb equivalent would be 1130 times (33 / 40), or 932
Hiroshima bombs for 1,000 Megawatts (electrical) or 2,500
Megawatts (thermal) per year.
(2) One might, for any calculation, consider that the
reactor will not operate at 100% power throughout the year.
Estimates like 75% have been suggested.
If a 1000-Megawatt electrical plant, with 33% efficiency,
operates 75% of the year, then Hiroshima-bomb equivalent = (0.75)
x (1130 bombs), or 848 bombs per year.
If a 1000-Megawatt electrical plant, with 40% efficiency,
operates 75% of the year, then Hiroshima-bomb equivalent = (0.75)
x (932 bombs), or 699 bombs per year.
(3) The Hiroshima Kilotonnage was taken as "roughly" 20
Kilotons in our calculations. Dr. Herbert York, in his book "Race
to Oblivion," suggests that the Hiroshima bomb may have been 14
Kilotons (KT).
In Part 1, we calculated that we have the equivalent of 2.26 x
10^4 Kilotons TNT from operating 3000 Megawatts (thermal) for one
year. If one Hiroshima bomb is 14 KT, then such operation produces
long-lived fission-products equal to (22,600 Kilotons) divided by
(14 Kilotons/bomb), or 1614 Hiroshima-bombs instead of the 1130
calculated in Part 1. And the results in (2) above would also
become higher by a factor of (20 KT / 14 KT), or 1.43. So:
(848 bombs/yr) times (1.43) = 1213 bombs per year.
And:
(699 bombs/yr) times (1.43) = 1000 bombs per year.
Insert from Gofman 1990, Chap.8, Part 4: The government's best
estimate in 1987 of the bomb's yield: 12-18 KT.
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