Fission product yield

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Long-lived
fission products
Prop:
Unit:
t½
Ma
Yield
%
Q *
KeV
βγ
*
99Tc 0.211 6.1385 294 β
126Sn 0.230 0.1084 4050 βγ
79Se 0.327 0.0447 151 β
93Zr 1.53 5.4575 91 βγ
135Cs 2.3  6.9110 269 β
107Pd 6.5  1.2499 33 β
129I 15.7  0.8410 194 βγ
Hover underlined: more info

Nuclear fission splits a heavy nucleus such as uranium or plutonium into two lighter nuclei, which are called fission products. Yield refers to the fraction of a fission product produced per fission.

Yield can be broken down by:

  1. Individual isotope
  2. Chemical element spanning several isotopes of different mass number but same atomic number.
  3. Nuclei of a given mass number regardless of atomic number. Known as "chain yield" because it represents a decay chain of beta decay.

Isotope and element yields will change as the fission products undergo beta decay, while chain yields do not change after completion of neutron emission by a few neutron-rich initial fission products (delayed neutrons), with halflife measured in seconds.

A few isotopes can be produced directly by fission, but not by beta decay because the would-be precursor with atomic number one greater is stable and does not decay. Chain yields do not account for these "shadowed" isotopes; however, they have very low yields (less than a millionth as much as common fission products) because they are far less neutron-rich than the original heavy nuclei.

Yield is usually stated as percentage per fission, so that the total yield percentages sum to 200%. Less often, it is stated as percentage of all fission products, so that the percentages sum to 100%. Ternary fission, about 0.2% to 0.4% of fissions, also produces a third light nucleus such as helium-4 (90%) or tritium (7%).

Medium-lived
fission products
Prop:
Unit:
t½
a
Yield
%
Q *
keV
βγ
*
155Eu 4.76 .0803 252 βγ
85Kr 10.76 .2180 687 βγ
113mCd 14.1 .0008 316 β
90Sr 28.9 4.505 2826 β
137Cs 30.23 6.337 1176 βγ
121mSn 43.9 .00005 390 βγ
151Sm 96.6 .5314 77 β

Mass vs. yield curve[edit]

From Fluoride volatility: Blue elements have volatile fluorides or are already volatile; green elements do not but have volatile chlorides; red elements have neither, but the elements themselves are volatile at very high temperatures. Yields at 100,1,2,3 years after fission, not considering later neutron capture, fraction of 100% not 200%. Beta decay Kr-85Rb, Sr-90Zr, Ru-106Pd, Sb-125Te, Cs-137Ba, Ce-144Nd, Sm-151Eu, Eu-155Gd visible.
Fission product yields by mass for thermal neutron fission of U-235, Pu-239, a combination of the two typical of current nuclear power reactors, and U-233 used in the thorium cycle

If a graph of the mass or mole yield of fission products against the atomic number of the fragments is drawn then it has two peaks, one in the area zirconium through to palladium and one at xenon through to neodymium. This is because the fission event causes the nucleus to split in an asymmetric manner.[1] Yield vs. Z - This is a typical distribution for the fission of uranium. Note that in the calculations used to make this graph the activation of fission products was ignored and the fission was assumed to occur in a single moment rather than a length of time. In this bar chart results are shown for different cooling times (time after fission).

Because of the stability of nuclei with even numbers of protons and/or neutrons the curve of yield against element is not a smooth curve. It tends to alternate.

In general, the higher the energy of the state that undergoes nuclear fission, the more likely a symmetric fission is, hence as the neutron energy increases and/or the energy of the fissile atom increases, the valley between the two peaks becomes more shallow; for instance, the curve of yield against mass for Pu-239 has a more shallow valley than that observed for U-235, when the neutrons are thermal neutrons. The curves for the fission of the later actinides tend to make even more shallow valleys. In extreme cases such as 259Fm, only one peak is seen.

Yield is usually expressed relative to number of fissioning nuclei, not the number of fission product nuclei, that is, yields should sum to 200%.

The table in the next section gives yields for notable radioactive (with halflife greater than one year, plus iodine-131) fission products, and (the few most absorptive) neutron poison fission products, from thermal neutron fission of U-235 (typical of nuclear power reactors), computed from [1].

The yields in the table sum to only 45.5522%, including 34.8401% which have halflife greater than one year:

t½ in years yield
1 to 5 2.7252%
10 to 100 12.5340%
2 to 300,000 6.1251%
1.5 to 16 million 13.4494%

The remainder and the unlisted 54.4478% decay with halflife less than one year into nonradioactive nuclei.

This is before accounting for the effects of any subsequent neutron capture, e.g.:

  • 135Xe capturing a neutron and becoming nonradioactive 136Xe, rather than decaying to 135Cs which is radioactive with a halflife of 2.3 million years
  • Nonradioactive 133Cs capturing a neutron and becoming 134Cs which is radioactive with a halflife of 2 years
  • Many of the fission products with mass 147 or greater such as Promethium-147, Samarium-149, Samarium-151, Europium-155 have significant cross sections for neutron capture, so that one heavy fission product atom can undergo multiple successive neutron captures.

Besides fission products, the other types of radioactive products are

Ordered by yield (thermal neutron fission of U-235)[edit]

Yield Isotope Halflife Comment
6.7896% caesium-133 133Cs 134Cs 2.065 y neutron capture (29 barns) slowly converts stable 133Cs to 134Cs, which itself is low-yield because beta decay stops at 134Xe; can be further converted (140 barns) to 135Cs
6.3333% iodine1-35 135I 135Xe 6.57 h most important neutron poison; neutron capture converts 10%–50% of 135Xe to 136Xe; remainder decays (9.14h) to 135Cs (2.3My)
6.2956% zirconium 93Zr 1.53 My
6.1% molybdenum 99Mo 65.94 h Its daughter nuclide 99mTc is important in medical diagnosing.
6.0899% caesium-137 137Cs 30.17 y
6.0507% technetium 99Tc 211 ky Candidate for disposal by nuclear transmutation
5.7518% strontium 90Sr 28.9 y
2.8336% iodine131 131I 8.02 d
2.2713% promethium 147Pm 2.62 y
1.0888% samarium-149 149Sm virtually stable 2nd most significant neutron poison
0.6576% iodine-129 129I 15.7 My Candidate for disposal by nuclear transmutation
0.4203% samarium-151 151Sm 90 y neutron poison; most will be converted to stable 152Sm
0.3912% ruthenium 106Ru 373.6 d
0.2717% krypton 85Kr 10.78 y
0.1629% palladium 107Pd 6.5 My
0.0508% selenium 79Se 327 ky
0.0330% europium 155Eu 155Gd 4.76 y both neutron poisons, most will be destroyed while fuel still in use
0.0297% antimony 125Sb 2.76 y
0.0236% tin 126Sn 230 ky
0.0065% gadolinium 157Gd stable neutron poison
0.0003% cadmium 113mCd 14.1 y neutron poison, most will be destroyed while fuel still in use
Yields at 100,1,2,3 years after fission, probably of Pu-239 not U-235 because left hump is shifted right, not considering later neutron capture, fraction of 100% not 200%. Beta decay Kr-85Rb, Sr-90Zr, Ru-106Pd, Sb-125Te, Cs-137Ba, Ce-144Nd, Sm-151Eu, Eu-155Gd visible.

Ordered by mass number[edit]

Yield Isotope
0.0508% selenium-79
0.2717% krypton-85
5.7518% strontium-90
6.2956% zirconium-93
6.0507% technetium-99
0.3912% ruthenium-106
0.1629% palladium-107
0.0003% cadmium-113m
0.0297% antimony-125
0.0236% tin-126
0.6576% iodine-129
2.8336% iodine-131
6.7896% caesium-133 caesium-134
6.3333% iodine-135 xenon-135 caesium-135
6.0899% caesium-137
2.2713% promethium-147
1.0888% samarium-149
0.4203% samarium-151
0.0330% europium-155 gadolinium-155
0.0065% gadolinium-157

Ordered by halflife[edit]

Yield Isotope Halflife Comment
2.8336% 131I 8.02d Important in nuclear explosions and accidents but not in cooled spent nuclear fuel
0.3912% 106Ru 373.6d
6.7896% 133Cs 134Cs 2.065y neutron capture converts a few percent of nonradioactive 133Cs to 134Cs, which has low direct yield because beta decay stops at 134Xe
2.2713% 147Pm 2.62y
0.0297% 125Sb 2.76y
<0.0330% 155Eu 155Gd 4.76y both neutron poisons, most will be destroyed by neutron capture while still in reactor
0.2717% 85Kr 10.78y Current nuclear reprocessing releases it to atmosphere
<0.0003% 113mCd 14.1y most will be destroyed by neutron capture while still in reactor
5.7518% 90Sr 28.9y One of two principal medium-term radiation and heat sources
6.0899% 137Cs 30.17y One of two principal medium-term radiation and heat sources
<0.4203% 151Sm 90y Most will be destroyed by neutron capture while still in reactor
6.0507% 99Tc 211ky Dominant radiation source among FP in period about ×104 to ×106 years; mobile in environment; candidate for disposal by nuclear transmutation
0.0236% 126Sn 230ky
0.0508% 79Se 327ky
6.2956% 93Zr 1.53My
<6.3333% 135Cs 2.3My
0.1629% 107Pd 6.5My
0.6576% 129I 15.7My Mobile in environment; candidate for disposal by nuclear transmutation
<1.0888% 149Sm nonradioactive neutron poison
<0.0065% 157Gd nonradioactive neutron poison

Ordered by thermal neutron neutron absorption cross section[edit]

Barns Yield Isotope t½ Comment
2,650,000 6.3333% iodine-135 135I 135Xe 6.57 h Most important neutron poison; neutron capture rapidly converts 135Xe to 136Xe; remainder decays (9.14 h) to 135Cs (2.3 My)
254,000 0.0065% gadolinium 157Gd neutron poison, but low yield
40,140 1.0888% samarium-149 149Sm 2nd most important neutron poison
20,600 0.0003% cadmium 113mCd 14.1 y most will be destroyed by neutron capture
15,200 0.4203% samarium-151 151Sm 90 y most will be destroyed by neutron capture
3,950 0.0330% europium 155Eu 155Gd 4.76 y both neutron poisons
96 2.2713% promethium 147Pm 2.62 y
80 2.8336% iodine-131 131I 8.02 d
29
140
6.7896% caesium-133 133Cs 134Cs
2.065 y
neutron capture converts a few percent of nonradioactive 133Cs to 134Cs, which has very low direct yield because beta decay stops at 134Xe; further capture will add to long-lived 135Cs
20 6.0507% technetium 99Tc 211 ky candidate for disposal by nuclear transmutation
18 0.6576% iodine-129 129I 15.7 My candidate for disposal by nuclear transmutation
2.7 6.2956% zirconium 93Zr 1.53 My transmutation impractical
1.8 0.1629% palladium 107Pd 6.5 My
1.66 0.2717% krypton 85Kr 10.78 y
0.90 5.7518% strontium 90Sr 28.9 y
0.15 0.3912% ruthenium 106Ru 373.6 d
0.11 6.0899% caesium-137 137Cs 30.17 y
0.0297% antimony 125Sb 2.76 y
0.0236% tin 126Sn 230 ky
0.0508% selenium 79Se 327 ky

References[edit]

  1. ^ fissionyield