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. CALCULATIONS1. 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-CHECKWe 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.Insert from Gofman 1990, Chap.8, Part 4: The government's best estimate in 1987 of the bomb's yield: 12-18 KT.
And:(699 bombs/yr) times (1.43) = 1000 bombs per year.