This is my final post on E=mc2 and the myth that such a formula was related to the development of the atomic bombs
used in 1945, and developed in the Manhattan Project.
I quote here the words of Robert Serber, a Manhattan's physicist, who wrote his memoirs in a small book by 1992,
currently sold by Amazon. The book, which contain several documents declassified and memories from 1943-1945,
was edited by Richard Rhodes. I strongly recommend to read the book (12 chapters), which tell about obstacles,
fears, discussions, doubts and many anecdotes for the whole Manhattan Project (2 1/2 years).
The Los Alamos Primer
The first lectures on how to build an Atomic Bomb
University of California Press
1992 by Robert Serber (edited by Richard Rhodes)
and can be read at this link: https://www.academia...s_Alamos_Primer
From the American Heritage Foundation: https://www.atomiche...e/robert-serber
Robert Serber (1909-1997) was an American physicist. He was recruited by J. Robert Oppenheimer to work on
the Manhattan Project. Serber was tasked with explaining the basic principles and goals of the project to all
incoming scientific staff. Moving to Los Alamos in 1943, he gave lectures to members of the Manhattan Project
about the design and construction of atomic bombs known as the “Los Alamos Primer."
While at Los Alamos, Serber developed the first good theory of bomb disassembly hydrodynamics.
After the Trinity Test in July 1945, Serber traveled to Tinian Island to assist in the construction of the bomb, as a
special consultant to Project Alberta. While there, he reassured Col. Paul Tibbets, pilot of the Enola Gay, that the
bomb's blast would not harm the plane. In early September 1945, Serber was part of the first American team to enter
Hiroshima and Nagasaki, assessing the bombs' damage and collecting debris for testing on their five-week mission.
From the Chapter 2: Energy of Fission Process, I take some excerpts here, related with energy per gram of atom
and Serber's comment about the complete disconnexion between atomic energy and the "myth" of Einstein's E=mc2.
In my words:
1) The fission's energy release per gram of U-235 (as kinetic energy due to electrostatic repulsion) is 7.1017 erg/gram.
2) The energy conversion of 1 gram of mass, in Einstein's E=mc2, is 9.1020 erg/gram.
3) Einstein's formula E=mc2 has a difference 1285.71 times higher and is unrelated to nuclear fission (Serber words).
In Robert Serber words (Chapter 2: Energy of Fission Process):
The direct energy release in the fission process is of the order of 170 Mev per atom.
To start with a simpler particle than an atom, let’s look at two electrons pushed together. If you
released them, they would fly apart with an amount of energy equal to the work that went into pushing
them together. That energy E is given by the formula
E = e2/R (1)
where e is the electron charge,e2 is e multiplied by itself, and R is the distance between the particles.
The electrostatic energy thus ends up as kinetic energy, the energy of motion.
Now let’s consider the electrostatic energy in the uranium nucleus.
The uranium nucleus contains 92 protons, each of which has the same charge as an electron, though of opposite
sign — particles of opposite sign attract each other,those of the same sign repel. So the uranium nucleus has a
charge 92 times as great as an electron; it’s positive rather than negative, + rather than -, but since only the
square of the charge is involved, that difference doesn’t matter in equation (1). The numerator of (1) is thus 92
times bigger than for a chemical reaction. For our purposes, 922 is close enough to call 1002. So the numerator for
a uranium atom would be greater by a factor of 1002, 100 times 100, or 10,000 (104).
The uranium nucleus is also much smaller than an atom. In an atom, the distance R is 10-8 cm (cm meaning centimeters).
The radius of the uranium nucleus is 10-12 cm, which is 104 times smaller. The electrostatic energy for a uranium nucleus
is therefore 104 for the numerator and another 104 for the denominator, for a total of 108 times greater than the
electrostatic energy between atoms or molecules. When a uranium nucleus fissions, much of this energy is released as
kinetic energy in the two fission fragments that fly apart. Suppose that the uranium nucleus broke in half. Each fragment
would have half the charge. The numerator of equation (1) would be a quarter as big—a half times a half. Since the volume
is proportional to the cube of the radius, the radius would be smaller by a factor of
2-3/2 = 1/1.26
So each fragment would have an electrostatic energy of about a third of the total and the two fragments about two-thirds.
That leaves a third left over for the reaction energy. Thus we see that the energy of fission is about 108 —one hundred
million times — greater than the energy of a chemical reaction, confirming the statement that it’s “considerably more than 107.”
This is 170·106 · 4.8·10-10/300 = 2.7·10-4 erg/nucleus. Since the weight of 1 nucleus of 25 is 3.88·10-22 gram/nucleus the energy
release is 7·1017 erg/gram.
The energy release in TNT is 4·1010 erg/gram or 3.6·1016 erg/ton. Hence 1 kg of 25 ≈ 20000 tons of TNT
Somehow the popular notion took hold long ago that Einstein’s theory of relativity, in particular his famous equation E=mc2,
plays some essential role in the theory of fission. Albert Einstein had a part in alerting the United States government to
the possibility of building an atomic bomb, but his theory of relativity is not required in discussing fission.
The theory of fission is what physicists call a non relativistic theory, meaning that relativistic effects are too small
to affect the dynamics of the fission process significantly. Section 2 of the Primer gives a more exact calculation of the
ratio of the energy released by the fission of a gram of uranium to the energy released by the explosion of a gram of TNT.
---------------- End of quotes ----------------------------------------------------
Finally, this is a copy of the original page Serber prepared by 1943 to give 5 lectures to every physicist (at Los Alamos facilities),
in April 1943, before they were assigned to different (compartmentalized) tasks. The charge of the electron 4.8.10-10 was given
by then in Electrostatic Units, and due this the division by 300 is to obtain ergs from eV (that is what physicists used by then in US).
Edited by rhertz, 12 June 2019 - 10:53 PM.