1.6 Energy Release in Fission
19
1.6 Energy Release in Fission
Neutron-induced uranium fission can happen in a multiplicity of ways, with a wide
variety of resulting products. Empirically, equal division of the bombarded nucleus
is quite unlikely; the most likely mass ratio for the products is about 1.5.
To understand the energy release in fission, consider the splitting of a
235 U
nucleus into barium and krypton (the Hahn-Strassmann fission-discovery situation),
accompanied by the release of three neutrons:
1
0 n +
235
92 U →
141
56 Ba +
92
36 Kr + 3 (
1
0 n).
(1.42)
The -values are
⎧
⎪ ⎪ ⎨
⎪ ⎪ ⎩
1
0 n
= 8.071
235
92 U
= 40.921
141
56 Ba
= −79.726
92
36 Kr
= −68.79,
(1.43)
giving Q = 173.3 MeV.
The fission energy latent in a single kilogram of
235 U is enormous. With an atomic
weight of 235 gr mol
−1 , 1 kg of
235 U comprises about 4.26 mol or 2.56 × 10
24 atoms.
At 173 MeV/reaction, the potential fission energy amounts to 4.43 × 10
32 eV, or 7.1
× 10
13 J. Explosion of one ton of TNT liberates about 4.2 × 10
9 J, so the energy
released by fission of 1 kg of
235 U is equivalent to nearly 17 kilotons (kt) of TNT.
The explosive yield of the Little Boy uranium bomb dropped on Hiroshima has been
estimated at about 13 kilotons (Penney et al. 1970), from which we can infer that
only some 0.8 kilograms of
235 U actually underwent fission. Upon considering that
Little Boy contained about 53 kg of
235 U, we can appreciate that the first fission
weapons were rather inefficient devices despite their enormous explosive yields.
Weapon efficiency is examined in detail in Chap. 2.
In writing the above reaction, it was assumed that three neutrons were released
in the process. If one is to have any hope of sustaining a neutron-moderated chain
reaction, it is clear that, on average, at least one neutron will have to be liberated
per fission event. Soon after the discovery of fission, a number of researchers began
looking for evidence of these “secondary” neutrons, and proof of their existence was
not long in coming. On March 16, 1939, two independent teams at Columbia University submitted letters to The Physical Review reporting their discovery: Anderson,
Fermi and Hanstein (1939), and Szilard and Zinn (1939). Both groups estimated
about two neutrons emitted per each captured. Their papers were published on April
15. In Paris on April 7, Halban et al. (1939) submitted a paper to Nature in which they
reported 3.5 ± 0.7 neutrons liberated per fission; their paper was published on April
22. The French group, however, made a subtle error in their analysis which resulted
in overestimating the number of neutrons per fission; when corrected, their results
indicated 2.6 ± 0.6, very much in line with the modern value (Turner 1940; Weart
19
1.6 Energy Release in Fission
Neutron-induced uranium fission can happen in a multiplicity of ways, with a wide
variety of resulting products. Empirically, equal division of the bombarded nucleus
is quite unlikely; the most likely mass ratio for the products is about 1.5.
To understand the energy release in fission, consider the splitting of a
235 U
nucleus into barium and krypton (the Hahn-Strassmann fission-discovery situation),
accompanied by the release of three neutrons:
1
0 n +
235
92 U →
141
56 Ba +
92
36 Kr + 3 (
1
0 n).
(1.42)
The -values are
⎧
⎪ ⎪ ⎨
⎪ ⎪ ⎩
1
0 n
= 8.071
235
92 U
= 40.921
141
56 Ba
= −79.726
92
36 Kr
= −68.79,
(1.43)
giving Q = 173.3 MeV.
The fission energy latent in a single kilogram of
235 U is enormous. With an atomic
weight of 235 gr mol
−1 , 1 kg of
235 U comprises about 4.26 mol or 2.56 × 10
24 atoms.
At 173 MeV/reaction, the potential fission energy amounts to 4.43 × 10
32 eV, or 7.1
× 10
13 J. Explosion of one ton of TNT liberates about 4.2 × 10
9 J, so the energy
released by fission of 1 kg of
235 U is equivalent to nearly 17 kilotons (kt) of TNT.
The explosive yield of the Little Boy uranium bomb dropped on Hiroshima has been
estimated at about 13 kilotons (Penney et al. 1970), from which we can infer that
only some 0.8 kilograms of
235 U actually underwent fission. Upon considering that
Little Boy contained about 53 kg of
235 U, we can appreciate that the first fission
weapons were rather inefficient devices despite their enormous explosive yields.
Weapon efficiency is examined in detail in Chap. 2.
In writing the above reaction, it was assumed that three neutrons were released
in the process. If one is to have any hope of sustaining a neutron-moderated chain
reaction, it is clear that, on average, at least one neutron will have to be liberated
per fission event. Soon after the discovery of fission, a number of researchers began
looking for evidence of these “secondary” neutrons, and proof of their existence was
not long in coming. On March 16, 1939, two independent teams at Columbia University submitted letters to The Physical Review reporting their discovery: Anderson,
Fermi and Hanstein (1939), and Szilard and Zinn (1939). Both groups estimated
about two neutrons emitted per each captured. Their papers were published on April
15. In Paris on April 7, Halban et al. (1939) submitted a paper to Nature in which they
reported 3.5 ± 0.7 neutrons liberated per fission; their paper was published on April
22. The French group, however, made a subtle error in their analysis which resulted
in overestimating the number of neutrons per fission; when corrected, their results
indicated 2.6 ± 0.6, very much in line with the modern value (Turner 1940; Weart