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The Frisch–Peierls memorandum was the first technical exposition of a practical
nuclear weapon A nuclear weapon is an explosive device that derives its destructive force from nuclear reactions, either fission (fission bomb) or a combination of fission and fusion reactions (thermonuclear bomb), producing a nuclear explosion. Both bomb ...
. It was written by expatriate German-Jewish physicists
Otto Frisch Otto Robert Frisch FRS (1 October 1904 – 22 September 1979) was an Austrian-born British physicist who worked on nuclear physics. With Lise Meitner he advanced the first theoretical explanation of nuclear fission (coining the term) and first ...
and Rudolf Peierls in March 1940 while they were both working for
Mark Oliphant Sir Marcus Laurence Elwin Oliphant, (8 October 1901 – 14 July 2000) was an Australian physicist and humanitarian who played an important role in the first experimental demonstration of nuclear fusion and in the development of nuclear weapo ...
at the
University of Birmingham The University of Birmingham (informally Birmingham University) is a Public university, public research university located in Edgbaston, Birmingham, United Kingdom. It received its royal charter in 1900 as a successor to Queen's College, Birmingha ...
in Britain during World War II. The memorandum contained the first calculations about the size of the
critical mass In nuclear engineering, a critical mass is the smallest amount of fissile material needed for a sustained nuclear chain reaction. The critical mass of a fissionable material depends upon its nuclear properties (specifically, its nuclear fiss ...
of
fissile In nuclear engineering, fissile material is material capable of sustaining a nuclear fission chain reaction. By definition, fissile material can sustain a chain reaction with neutrons of thermal energy. The predominant neutron energy may be ty ...
material needed for an
atomic bomb A nuclear weapon is an explosive device that derives its destructive force from nuclear reactions, either fission (fission bomb) or a combination of fission and fusion reactions (thermonuclear bomb), producing a nuclear explosion. Both bomb ...
. It revealed that the amount required might be small enough to incorporate into a bomb that could be delivered by air. It also anticipated the strategic and moral implications of nuclear weapons. It helped send both Britain and America down a path which led to the
MAUD Committee The MAUD Committee was a British scientific working group formed during the Second World War. It was established to perform the research required to determine if an atomic bomb was feasible. The name MAUD came from a strange line in a telegram fr ...
, the
Tube Alloys Tube Alloys was the research and development programme authorised by the United Kingdom, with participation from Canada, to develop nuclear weapons during the Second World War. Starting before the Manhattan Project in the United States, the Bri ...
project, the
Manhattan Project The Manhattan Project was a research and development undertaking during World War II that produced the first nuclear weapons. It was led by the United States with the support of the United Kingdom and Canada. From 1942 to 1946, the project ...
, and ultimately the
atomic bombings of Hiroshima and Nagasaki The United States detonated two atomic bombs over the Japanese cities of Hiroshima and Nagasaki on 6 and 9 August 1945, respectively. The two bombings killed between 129,000 and 226,000 people, most of whom were civilians, and remain the onl ...
.


Background


Rudolf Peierls

Rudolf Peierls was born in Berlin in 1907. He studied
physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which re ...
at the
University of Berlin Humboldt-Universität zu Berlin (german: Humboldt-Universität zu Berlin, abbreviated HU Berlin) is a German public research university in the central borough of Mitte in Berlin. It was established by Frederick William III on the initiative o ...
, at the
University of Munich The Ludwig Maximilian University of Munich (simply University of Munich or LMU; german: Ludwig-Maximilians-Universität München) is a public research university in Munich, Germany. It is Germany's sixth-oldest university in continuous operati ...
under
Arnold Sommerfeld Arnold Johannes Wilhelm Sommerfeld, (; 5 December 1868 – 26 April 1951) was a German theoretical physicist who pioneered developments in atomic and quantum physics, and also educated and mentored many students for the new era of theoretical ...
, the University of Leipzig under
Werner Heisenberg Werner Karl Heisenberg () (5 December 1901 – 1 February 1976) was a German theoretical physicist and one of the main pioneers of the theory of quantum mechanics. He published his work in 1925 in a Über quantentheoretische Umdeutung kinematis ...
, and
ETH Zurich (colloquially) , former_name = eidgenössische polytechnische Schule , image = ETHZ.JPG , image_size = , established = , type = Public , budget = CHF 1.896 billion (2021) , rector = Günther Dissertori , president = Joël Mesot , aca ...
under
Wolfgang Pauli Wolfgang Ernst Pauli (; ; 25 April 1900 – 15 December 1958) was an Austrian theoretical physicist and one of the pioneers of quantum physics. In 1945, after having been nominated by Albert Einstein, Pauli received the Nobel Prize in Physics fo ...
. After receiving his
DPhil A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is ...
from Leipzig in 1929, he became an assistant to Pauli in Zurich. In 1932, he was awarded a
Rockefeller Fellowship The Rockefeller Foundation is an American private foundation and philanthropic medical research and arts funding organization based at 420 Fifth Avenue, New York City. The second-oldest major philanthropic institution in America, after the Carn ...
, which he used to study in Rome under
Enrico Fermi Enrico Fermi (; 29 September 1901 – 28 November 1954) was an Italian (later naturalized American) physicist and the creator of the world's first nuclear reactor, the Chicago Pile-1. He has been called the "architect of the nuclear age" and ...
, and then at the
Cavendish Laboratory The Cavendish Laboratory is the Department of Physics at the University of Cambridge, and is part of the School of Physical Sciences. The laboratory was opened in 1874 on the New Museums Site as a laboratory for experimental physics and is name ...
at the
University of Cambridge , mottoeng = Literal: From here, light and sacred draughts. Non literal: From this place, we gain enlightenment and precious knowledge. , established = , other_name = The Chancellor, Masters and Schola ...
under Ralph H. Fowler. Due to
Adolf Hitler's rise to power Adolf Hitler's rise to power began in the newly established Weimar Republic in September 1919 when Hitler joined the '' Deutsche Arbeiterpartei'' (DAP; German Workers' Party). He rose to a place of prominence in the early years of the party. B ...
in Germany, he elected to not return home in 1933, but to remain in Britain. He worked with
Hans Bethe Hans Albrecht Bethe (; July 2, 1906 – March 6, 2005) was a German-American theoretical physicist who made major contributions to nuclear physics, astrophysics, quantum electrodynamics, and solid-state physics, and who won the 1967 Nobel Pr ...
at the
University of Manchester , mottoeng = Knowledge, Wisdom, Humanity , established = 2004 – University of Manchester Predecessor institutions: 1956 – UMIST (as university college; university 1994) 1904 – Victoria University of Manchester 1880 – Victoria Unive ...
, then at the Mond Laboratory at Cambridge. In 1937,
Mark Oliphant Sir Marcus Laurence Elwin Oliphant, (8 October 1901 – 14 July 2000) was an Australian physicist and humanitarian who played an important role in the first experimental demonstration of nuclear fusion and in the development of nuclear weapo ...
, the Australian, newly appointed professor of physics at the
University of Birmingham The University of Birmingham (informally Birmingham University) is a Public university, public research university located in Edgbaston, Birmingham, United Kingdom. It received its royal charter in 1900 as a successor to Queen's College, Birmingha ...
recruited him for a new chair there in applied mathematics.


Otto Frisch

Otto Robert Frisch was born in
Vienna en, Viennese , iso_code = AT-9 , registration_plate = W , postal_code_type = Postal code , postal_code = , timezone = CET , utc_offset = +1 , timezone_DST ...
in 1904. He studied physics at the
University of Vienna The University of Vienna (german: Universität Wien) is a public university, public research university located in Vienna, Austria. It was founded by Rudolf IV, Duke of Austria, Duke Rudolph IV in 1365 and is the oldest university in the Geogra ...
, from which he received his
DPhil A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is ...
in 1926. He worked at the Physikalisch-Technische Reichsanstalt in Berlin until 1930, when he obtained a position at the University of Hamburg under the
Nobel Prize The Nobel Prizes ( ; sv, Nobelpriset ; no, Nobelprisen ) are five separate prizes that, according to Alfred Nobel's will of 1895, are awarded to "those who, during the preceding year, have conferred the greatest benefit to humankind." Alfre ...
-winning scientist
Otto Stern :''Otto Stern was also the pen name of German women's rights activist Louise Otto-Peters (1819–1895)''. Otto Stern (; 17 February 1888 – 17 August 1969) was a German-American physicist and Nobel laureate in physics. He was the second most ...
. As non-Aryans, Stern and Frisch were dismissed after Hitler's accession. Stern found Frisch a position in Britain with
Patrick Blackett Patrick Maynard Stuart Blackett, Baron Blackett (18 November 1897 – 13 July 1974) was a British experimental physicist known for his work on cloud chambers, cosmic rays, and paleomagnetism, winning the Nobel Prize for Physics in 194 ...
at
Birkbeck College , mottoeng = Advice comes over nightTranslation used by Birkbeck. , established = , type = Public research university , endowment = £4.3 m (2014) , budget = £109 ...
at the
University of London The University of London (UoL; abbreviated as Lond or more rarely Londin in post-nominals) is a federal public research university located in London, England, United Kingdom. The university was established by royal charter in 1836 as a degree- ...
, and a grant from the
Academic Assistance Council The Council for At-Risk Academics (CARA) is a charitable British organisation dedicated to assisting academics in immediate danger, those forced into exile, and many who choose to remain in their home countries despite the serious risks they face ...
. He followed this with a five-year stint at the
Niels Bohr Institute The Niels Bohr Institute (Danish: ''Niels Bohr Institutet'') is a research institute of the University of Copenhagen. The research of the institute spans astronomy, geophysics, nanotechnology, particle physics, quantum mechanics and biophysics. ...
in
Copenhagen Copenhagen ( or .; da, København ) is the capital and most populous city of Denmark, with a proper population of around 815.000 in the last quarter of 2022; and some 1.370,000 in the urban area; and the wider Copenhagen metropolitan ...
with
Niels Bohr Niels Henrik David Bohr (; 7 October 1885 – 18 November 1962) was a Danish physicist who made foundational contributions to understanding atomic structure and quantum theory, for which he received the Nobel Prize in Physics in 1922. ...
where he increasingly specialised in
nuclear physics Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions, in addition to the study of other forms of nuclear matter. Nuclear physics should not be confused with atomic physics, which studies t ...
, particularly the physics of
neutron The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the nuclei of atoms. Since protons and neutrons beha ...
s, which had been discovered by
James Chadwick Sir James Chadwick, (20 October 1891 – 24 July 1974) was an English physicist who was awarded the 1935 Nobel Prize in Physics for his discovery of the neutron in 1932. In 1941, he wrote the final draft of the MAUD Report, which inspi ...
in 1932. Oliphant invited Frisch to come to the University of Birmingham in the summer of 1939. When the outbreak of the
Second World War World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposi ...
in September 1939 prevented his return to Copenhagen, Oliphant found him a position at the University of Birmingham.


Nuclear fission

During the Christmas holiday in 1938, Frisch visited his aunt
Lise Meitner Elise Meitner ( , ; 7 November 1878 – 27 October 1968) was an Austrian-Swedish physicist who was one of those responsible for the discovery of the element protactinium and nuclear fission. While working at the Kaiser Wilhelm Institute on rad ...
in Kungälv in Sweden, where she had relocated after Germany's annexation of Austria. While there she received the news that her former colleagues
Otto Hahn Otto Hahn (; 8 March 1879 – 28 July 1968) was a German chemist who was a pioneer in the fields of radioactivity and radiochemistry. He is referred to as the father of nuclear chemistry and father of nuclear fission. Hahn and Lise Meitner ...
and
Fritz Strassmann Friedrich Wilhelm Strassmann (; 22 February 1902 – 22 April 1980) was a German chemist who, with Otto Hahn in December 1938, identified the element barium as a product of the bombardment of uranium with neutrons. Their observation was the k ...
in Berlin had discovered that the collision of a neutron with a
uranium Uranium is a chemical element with the symbol U and atomic number 92. It is a silvery-grey metal in the actinide series of the periodic table. A uranium atom has 92 protons and 92 electrons, of which 6 are valence electrons. Uranium is weak ...
nucleus Nucleus ( : nuclei) is a Latin word for the seed inside a fruit. It most often refers to: *Atomic nucleus, the very dense central region of an atom *Cell nucleus, a central organelle of a eukaryotic cell, containing most of the cell's DNA Nucle ...
produced
barium Barium is a chemical element with the symbol Ba and atomic number 56. It is the fifth element in group 2 and is a soft, silvery alkaline earth metal. Because of its high chemical reactivity, barium is never found in nature as a free element. The ...
as one of its byproducts. Frisch and Meitner hypothesized that the uranium nucleus had split in two. They estimated the energy released at around 200 MeV, and Frisch appropriated the term fission from
biology Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditary ...
to describe it. Hahn's paper described the experiment and the finding of the barium byproduct. Meitner and Frisch's paper, dated 16 January 1939, explained the physics behind the phenomenon. Frisch went back to Copenhagen, where he was able to isolate the fragments produced by fission reactions. Frisch later recalled that: The news of the discovery of fission was brought to America by Bohr in January 1939. Bohr and John A. Wheeler set to work applying the
liquid drop model In nuclear physics, the semi-empirical mass formula (SEMF) (sometimes also called the Weizsäcker formula, Bethe–Weizsäcker formula, or Bethe–Weizsäcker mass formula to distinguish it from the Bethe–Weizsäcker process) is used to approxi ...
developed by Bohr and Fritz Kalckar to explain the mechanism of nuclear fission.
George Placzek George Placzek (; September 26, 1905 – October 9, 1955) was a Moravian physicist. Biography Placzek was born into a wealthy Jewish family in Brünn, Moravia (now Brno, Czech Republic), the grandson of Chief Rabbi Baruch Placzek.PDF He studied ...
, who was skeptical about the whole idea of fission, challenged Bohr to explain why uranium seemed to fission with both very fast and very slow neutrons. Bohr had an epiphany that the fission at low energies was due to the
uranium-235 Uranium-235 (235U or U-235) is an isotope of uranium making up about 0.72% of natural uranium. Unlike the predominant isotope uranium-238, it is fissile, i.e., it can sustain a nuclear chain reaction. It is the only fissile isotope that exis ...
isotope Isotopes are two or more types of atoms that have the same atomic number (number of protons in their nuclei) and position in the periodic table (and hence belong to the same chemical element), and that differ in nucleon numbers (mass numbers ...
, while at high energies it was due mainly to the more abundant
uranium-238 Uranium-238 (238U or U-238) is the most common isotope of uranium found in nature, with a relative abundance of 99%. Unlike uranium-235, it is non-fissile, which means it cannot sustain a chain reaction in a thermal-neutron reactor. However, i ...
isotope. The former makes up just 0.7% of natural uranium; while the latter accounts for 99.3%. On 16 April, Bohr, Placzek, Wheeler,
Eugene Wigner Eugene Paul "E. P." Wigner ( hu, Wigner Jenő Pál, ; November 17, 1902 – January 1, 1995) was a Hungarian-American theoretical physicist who also contributed to mathematical physics. He received the Nobel Prize in Physics in 1963 "for his con ...
and Leon Rosenfeld discussed whether it would be possible to use a
nuclear chain reaction In nuclear physics, a nuclear chain reaction occurs when one single nuclear reaction causes an average of one or more subsequent nuclear reactions, thus leading to the possibility of a self-propagating series of these reactions. The specific nu ...
to make an
atomic bomb A nuclear weapon is an explosive device that derives its destructive force from nuclear reactions, either fission (fission bomb) or a combination of fission and fusion reactions (thermonuclear bomb), producing a nuclear explosion. Both bomb ...
, and concluded that it was not. Bohr observed that "It would take the entire efforts of a country to make a bomb."


British response

In Britain, scientists also considered whether an atomic bomb was practical. At the
University of Liverpool , mottoeng = These days of peace foster learning , established = 1881 – University College Liverpool1884 – affiliated to the federal Victoria Universityhttp://www.legislation.gov.uk/ukla/2004/4 University of Manchester Act 200 ...
, Chadwick and the Polish refugee scientist Joseph Rotblat tackled the problem, but their calculations were inconclusive. At Cambridge,
Nobel Prize in Physics ) , image = Nobel Prize.png , alt = A golden medallion with an embossed image of a bearded man facing left in profile. To the left of the man is the text "ALFR•" then "NOBEL", and on the right, the text (smaller) "NAT•" then " ...
laureates
George Paget Thomson Sir George Paget Thomson, FRS (; 3 May 189210 September 1975) was a British physicist and Nobel laureate in physics recognized for his discovery of the wave properties of the electron by electron diffraction. Education and early life Thomson ...
and
William Lawrence Bragg Sir William Lawrence Bragg, (31 March 1890 – 1 July 1971) was an Australian-born British physicist and X-ray crystallography, X-ray crystallographer, discoverer (1912) of Bragg's law, Bragg's law of X-ray diffraction, which is basic for t ...
wanted the government to take urgent action to acquire
uranium ore Uranium ore deposits are economically recoverable concentrations of uranium within the Earth's crust. Uranium is one of the more common elements in the Earth's crust, being 40 times more common than silver and 500 times more common than gold. It ...
to keep it out of German hands. The Secretary of the
Committee for Imperial Defence The Committee of Imperial Defence was an important ''ad hoc'' part of the Government of the United Kingdom and the British Empire from just after the Second Boer War until the start of the Second World War. It was responsible for research, and so ...
,
Major General Major general (abbreviated MG, maj. gen. and similar) is a military rank used in many countries. It is derived from the older rank of sergeant major general. The disappearance of the "sergeant" in the title explains the apparent confusion of a ...
Hastings Ismay asked Sir
Henry Tizard Sir Henry Thomas Tizard (23 August 1885 – 9 October 1959) was an English chemist, inventor and Rector of Imperial College, who developed the modern "octane rating" used to classify petrol, helped develop radar in World War II, and led the f ...
for an opinion. Tizard was sceptical of the likelihood of an atomic bomb being developed, reckoning the odds of success at 100,000 to 1. Even at such long odds, the danger was sufficiently great to be taken seriously. It was not considered worthwhile to immediately acquire the uranium, but Tizard's Committee on the Scientific Survey of Air Defence was directed to conduct research into the feasibility of atomic bombs. Thomson, at
Imperial College London Imperial College London (legally Imperial College of Science, Technology and Medicine) is a public research university in London, United Kingdom. Its history began with Prince Albert, consort of Queen Victoria, who developed his vision for a cu ...
, and Oliphant, at the University of Birmingham, were tasked with carrying out a series of experiments on uranium. By February 1940, Thomson's team had failed to create a chain reaction in natural uranium, and he had decided that it was not worth pursuing.


Memorandum

As enemy aliens, at least until Peierls'
naturalisation Naturalization (or naturalisation) is the legal act or process by which a non-citizen of a country may acquire citizenship or nationality of that country. It may be done automatically by a statute, i.e., without any effort on the part of the in ...
papers came through in February 1940, Frisch and Peierls were excluded from the most important—and secret—war work being done by Oliphant's team at Birmingham, that on radar. However, Oliphant would ask Peierls a theoretical question about, say, the solution to
Maxwell's equations Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. ...
in a hemispheric cavity. Peierls knew that questions of this nature related to the work on microwave radar, and Oliphant was doubtless aware of this too, but the façade of secrecy was maintained. The nuclear investigation was not yet secret, so Frisch was available to work on it. He began experimenting with
uranium enrichment Enriched uranium is a type of uranium in which the percent composition of uranium-235 (written 235U) has been increased through the process of isotope separation. Naturally occurring uranium is composed of three major isotopes: uranium-238 (238 ...
through thermal diffusion, a process first demonstrated in Germany by Klaus Clusius. Progress was slow; the required equipment was not available, and the radar project had first call on the available resources. Francis Perrin had defined a
critical mass In nuclear engineering, a critical mass is the smallest amount of fissile material needed for a sustained nuclear chain reaction. The critical mass of a fissionable material depends upon its nuclear properties (specifically, its nuclear fiss ...
of uranium to be the smallest amount that could sustain a chain reaction, and had calculated the critical mass of uranium oxide (not metal) to be about . He reckoned that if a
neutron reflector A neutron reflector is any material that reflects neutrons. This refers to elastic scattering rather than to a specular reflection. The material may be graphite, beryllium, steel, tungsten carbide, gold, or other materials. A neutron ref ...
were placed around it of materials such as iron or lead which did not greatly impede fast neutrons, this might be reduced to . Peierls also attempted to simplify the problem by using the fast neutrons produced by fission, thus omitting consideration of moderator. He then calculated the critical mass of a sphere of uranium metal in a theoretical paper written in 1939. He later recalled that the size of the critical mass "was of the order of tons. It therefore appeared to me that the paper had no relevance to a nuclear weapon." However, Bohr had argued that the uranium-235 isotope was far more likely to capture neutrons, so fissile even using neutrons of low energy. Frisch wondered what would happen if he were able to produce a sphere of pure uranium-235. When he used Peierls' formula to calculate this, he received a startling answer. Peierls later observed that: Realising the sensitive nature of the document, Peierls typed it himself. One carbon copy was made. Today the original is in the
Bodleian Library The Bodleian Library () is the main research library of the University of Oxford, and is one of the oldest libraries in Europe. It derives its name from its founder, Sir Thomas Bodley. With over 13 million printed items, it is the second- ...
at
Oxford University Oxford () is a city in England. It is the county town and only city of Oxfordshire. In 2020, its population was estimated at 151,584. It is north-west of London, south-east of Birmingham and north-east of Bristol. The city is home to the ...
.


Non-technical

The memorandum was written in two parts. The first was an elegant and comprehensive outline of the implications of their calculations. It included a proposal that the best defence against such a weapon would be to develop one before Germany did so. In a few short pages these two scientists anticipated the policies of
deterrence Deterrence may refer to: * Deterrence theory, a theory of war, especially regarding nuclear weapons * Deterrence (penology), a theory of justice * Deterrence (psychology), a psychological theory * ''Deterrence'' (film), a 1999 drama starring K ...
which would shape
Cold War The Cold War is a term commonly used to refer to a period of geopolitical tension between the United States and the Soviet Union and their respective allies, the Western Bloc and the Eastern Bloc. The term '' cold war'' is used because t ...
geopolitics Geopolitics (from Greek γῆ ''gê'' "earth, land" and πολιτική ''politikḗ'' "politics") is the study of the effects of Earth's geography (human and physical) on politics and international relations. While geopolitics usually refers to ...
. The second was an explanation of the science supporting their conclusions. The memorandum opens with:


Calculations

Peierls' starting point was a paper by Francis Perrin, in which he had derived
critical mass In nuclear engineering, a critical mass is the smallest amount of fissile material needed for a sustained nuclear chain reaction. The critical mass of a fissionable material depends upon its nuclear properties (specifically, its nuclear fiss ...
calculations in terms of nuclear constants. The physicists considered a sphere, which has the minimum surface area for a given volume. A critical mass occurs when the number of neutrons produced equals the number that escape. Perrin assumed that the
mean free path In physics, mean free path is the average distance over which a moving particle (such as an atom, a molecule, or a photon) travels before substantially changing its direction or energy (or, in a specific context, other properties), typically as a ...
was much larger than the radius of the sphere. Peierls did not agree, and commenced his own calculations. A key insight came from Frisch, who wondered what would happen if, instead of natural uranium, someone gave you a sphere of the uranium-235 isotope. By definition, the mean free path is: :\ell = 1/\sigma n , where is the mean free path, is the number of target particles per unit volume, and is the effective fission cross section area. Peierls did not perform the calculation, leaving this task to Frisch. The chemistry of uranium was not well known at the time, and Frisch believed that its density was ; the true value is more like . The fission cross section value was more problematic. For this, Frisch turned to a 1939 ''Nature'' article by L. A. Goldstein, A. Rogozinski and R. J. Walen at the Radium Institute in Paris, who gave a value of . This was too large by an
order of magnitude An order of magnitude is an approximation of the logarithm of a value relative to some contextually understood reference value, usually 10, interpreted as the base of the logarithm and the representative of values of magnitude one. Logarithmic d ...
; a modern value is about . Using the values he had, Frisch calculated the value of the mean free path for uranium-235 using the
Avogadro constant The Avogadro constant, commonly denoted or , is the proportionality factor that relates the number of constituent particles (usually molecules, atoms or ions) in a sample with the amount of substance in that sample. It is an SI defining c ...
: :\ell = 1 / (1 \times 10^\ \mathrm)(15\ \mathrm)(6 \times 10^\ \mathrm / 235\ \mathrm) = 235/90\ \mathrm = 2.6\ \mathrm . Peierls and Frisch claimed that the critical radius was about 0.8 times the mean free path. From this, Frisch could calculate the volume of the sphere from the well-known equation: :V = \frac\pi r^3 = \frac\pi (2.6 \times 0.8\ \mathrm)^3 \approx 38\ \mathrm . The mass then comes out to be: :38\ \mathrm \times 15 \mathrm = 570\ \mathrm \approx 600\ \mathrm . Frisch and Peierls then considered the speed of a uranium fission chain reaction, exponential in nature, where "''τ'' is the time required for the neutron density to multiply by a factor ''e''." The available data was very approximate, but their central point – that a bomb was possible using fast (~2 MeV) neutrons – remains. Jeremy Bernstein remarked of this effort: "Let me make the same point by asking a somewhat different question but using the correct numbers. How much time does it take to fission a kilogram of 235U using fast neutrons?" Using modern values he found that to be "equal to about a microsecond, which makes the point about the rapidity of fission with fact icneutrons". In the original memorandum, if the neutrons had velocities of 109 cm/s, then they would have an average time between fission collisions of . Therefore, Bernstein's time for a kilogram of uranium-235 to fission is found by solving: :1000 \times (6 \times 10^ /\ 235) = e ^ , where was the mean time for fission neutron density to increase by ''e''. Given the doubling time :t^ = 2.6 \times 10^ \mathrm , this implied a mean fission exponential folding time of :\tau = t^ / ln(2) \approx 4.0 \times 10^\ \mathrm . This led to a calculation of the energy released, which Peierls reckoned as approximately: : E = 0.2 M (r^2/\tau^2) (\sqrt - 1) , where ''M'' is the mass of the sphere, ''r'' is the radius, and ''r''0 is the critical mass radius. The conclusion drawn was that a few kilograms would explode with the energy of thousands of tons of dynamite.


Influence

The memorandum was given to Oliphant, who passed it on to Tizard in his capacity as the chairman of the Committee for the Scientific Survey of Air Warfare (CSSAW). He in turn passed it to Thomson, the chairman of the committee to which the CSSAW had delegated responsibility for uranium research. Thomson's committee was about to disband. It had studied nuclear reactions in uranium, and the use of
graphite Graphite () is a crystalline form of the element carbon. It consists of stacked layers of graphene. Graphite occurs naturally and is the most stable form of carbon under standard conditions. Synthetic and natural graphite are consumed on lar ...
as a
neutron moderator In nuclear engineering, a neutron moderator is a medium that reduces the speed of fast neutrons, ideally without capturing any, leaving them as thermal neutrons with only minimal (thermal) kinetic energy. These thermal neutrons are immensely m ...
in a
nuclear reactor A nuclear reactor is a device used to initiate and control a fission nuclear chain reaction or nuclear fusion reactions. Nuclear reactors are used at nuclear power plants for electricity generation and in nuclear marine propulsion. Heat from n ...
, but its results had been negative, and it had concluded that the rate of capture of neutrons by the graphite was too great to make such a reactor a practical proposition. The Frisch–Peierls memorandum caused Thomson to reconsider. After discussions between Cockcroft, Oliphant and Thomson, CSSAW created the
MAUD Committee The MAUD Committee was a British scientific working group formed during the Second World War. It was established to perform the research required to determine if an atomic bomb was feasible. The name MAUD came from a strange line in a telegram fr ...
to investigate further. As enemy aliens, Peierls and Frisch were initially excluded from its deliberations, but they were later added to its technical subcommittee. The research from the MAUD committee was compiled in two reports, commonly known as the MAUD reports in July 1941. The first report, "Use of Uranium for a Bomb", discussed the feasibility of creating a super-bomb from uranium, which they now thought to be true. The second, "Use of Uranium as a Source of Power" discussed the idea of using uranium as a source of power, not just a bomb. The MAUD Committee and report helped bring about the British nuclear program, the
Tube Alloys Tube Alloys was the research and development programme authorised by the United Kingdom, with participation from Canada, to develop nuclear weapons during the Second World War. Starting before the Manhattan Project in the United States, the Bri ...
project. Not only did it help start a nuclear project in Britain but it helped jump-start the American project. Without the help of the MAUD Committee the American program, the
Manhattan Project The Manhattan Project was a research and development undertaking during World War II that produced the first nuclear weapons. It was led by the United States with the support of the United Kingdom and Canada. From 1942 to 1946, the project ...
, would have started months behind. Instead they were able to begin thinking about how to create a bomb, not whether it was possible. Historian
Margaret Gowing Margaret Mary Gowing (), (26 April 1921 – 7 November 1998) was an English historian. She was involved with the production of several volumes of the officially sponsored ''History of the Second World War'', but was better known for her books ...
noted that "events that change a time scale by only a few months can nevertheless change history." In August 1941, Oliphant was sent to the US to assist the Americans with microwave radar. He took the initiative to enlighten the scientific community there of the ground-breaking discoveries of the MAUD Committee. He travelled to Berkeley to meet with his friend
Ernest Lawrence Ernest Orlando Lawrence (August 8, 1901 – August 27, 1958) was an American nuclear physicist and winner of the Nobel Prize in Physics in 1939 for his invention of the cyclotron. He is known for his work on uranium-isotope separation f ...
, who soon caught his enthusiasm. Oliphant convinced the Americans to move forward with nuclear weapons, and his lobbying resulted in
Vannevar Bush Vannevar Bush ( ; March 11, 1890 – June 28, 1974) was an American engineer, inventor and science administrator, who during World War II headed the U.S. Office of Scientific Research and Development (OSRD), through which almost all wartim ...
taking the report directly to the president.
Leo Szilard Leo Szilard (; hu, Szilárd Leó, pronounced ; born Leó Spitz; February 11, 1898 – May 30, 1964) was a Hungarian-German-American physicist and inventor. He conceived the nuclear chain reaction in 1933, patented the idea of a nuclear ...
later wrote: "if Congress knew the true history of the atomic energy project, I have no doubt but that it would create a special medal to be given to meddling foreigners for distinguished services, and that Dr Oliphant would be the first to receive one."


Notes


References

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External links


Memorandum on the Properties of a Radioactive "Super-bomb"
:* Enclosure
On the Construction of a "Super-bomb" based on a Nuclear Chain Reaction in Uranium
{{DEFAULTSORT:Frisch-Peierls memorandum Nuclear history of the United Kingdom Science and technology during World War II Classified documents World War II documents 1940 documents Memoranda Collection of The National Archives (United Kingdom)