Even and odd atomic nuclei

Source: Wikipedia, the free encyclopedia.

In

nuclear models, such as the nuclear shell model. This difference of nuclear binding energy between neighbouring nuclei, especially of odd-A isobars, has important consequences for beta decay
.

The

nuclear spin
is zero for even-Z, even-N nuclei, integer for all even-A nuclei, and odd half-integer for all odd-A nuclei.

Even vs. odd mass number (A).
Even Odd Total
Stable 150 101 251
Long-lived 26 9 35
All primordial 176 110 286

The

nuclear decay. Unstable nuclides with a nonoptimal number of neutrons or protons decay by beta decay (including positron decay), electron capture, or other means, such as spontaneous fission and cluster decay
.

Even mass number

Even-mass-number nuclides, which comprise 150/251 = ~60% of all stable nuclides, are

180m
73
Ta
), all having a non-zero integer spin.

Pairing effects

Even/odd Z, N (Hydrogen-1 included as OE)
p,n EE OO EO OE Total
Stable 145 5 53 48 251
Long-lived 22 4 4 5 35
All primordial 167 9 57 53 286

Beta decay of an

116
Cd
has a half-life of 2.9×1019 years. This makes for a larger number of stable even–even nuclides, with some mass numbers having two stable nuclides, and some elements (atomic numbers) having as many as seven
.

For example, the extreme stability of helium-4 due to a double pairing of two protons and two neutrons prevents any nuclides containing five or eight nucleons from existing for long enough to serve as platforms for the buildup of heavier elements via

alpha particles, making beryllium the only even-numbered element that is monoisotopic
.

Even proton, even neutron

There are 145 stable even–even nuclides, forming ~58% of the 251 stable nuclides. There are also 22 primordial long-lived even–even nuclides. As a result, many of the 41 even-numbered elements from 2 to 82 have

208
82
Pb
is the final decay product of 232
90
Th
,[2] a primordial radionuclide with an even proton and neutron number. 238
92
U
is another notable primordial radionuclide with a half life of 4.468 billion years,[3] and produces almost half of all radioactive heat within the Earth.[4]

All even–even nuclides have spin 0 in their ground state, due to the Pauli exclusion principle (See Pairing Effects for more details).

Odd proton, odd neutron

Only five stable nuclides contain both an odd number of protons and an odd number of neutrons. The first four "odd–odd" nuclides occur in low mass nuclides, for which changing a proton to a neutron or vice versa would lead to a very lopsided proton–neutron ratio (

gamma decay, or internal conversion is greatly inhibited if the only decay possible between isobar nuclides (or in the case of 180m
73
Ta
between nuclear isomers of the same nuclide) involves high multiples of a change in spin of 1 unit, the "preferred" change of spin that is associated with rapid decay. This high-spin inhibition of decay is the cause of the five heavy stable or long-lived odd-proton, odd-neutron nuclides discussed above. For an example of this effect where the spin effect is subtracted, tantalum-180, the odd–odd low-spin (theoretical) decay product of primordial tantalum-180m, itself has a half life of only about eleven hours.[8]

Many odd–odd radionuclides (like tantalum-180) with comparatively short half lives are known. Almost invariably, these decay by positive or negative beta decay, in order to produce stable even–even isotopes which have paired protons and paired neutrons. In some odd–odd radionuclides where the ratio of protons to neutrons is neither excessively large nor excessively small (i.e., falling too far from the ratio of maximal stability), this decay can proceed in either direction, turning a proton into a neutron, or vice versa. An example is

64
30
Zn
.

Of the nine primordial odd–odd nuclides (five stable and four radioactive with long half lives), only

10
5
B
are minority isotopes of elements that are themselves rare compared to other light elements, while the other six isotopes make up only a tiny percentage of the natural abundance of their elements. For example, 180m
73
Ta
is thought to be the rarest of the 251 stable nuclides
.

None of the primordial (i.e., stable or nearly stable) odd–odd nuclides have spin 0 in the ground state. This is because the single unpaired neutron and unpaired proton have a larger nuclear force attraction to each other if their spins are aligned (producing a total spin of at least 1 unit), instead of anti-aligned. See deuterium for the simplest case of this nuclear behavior.

Odd mass number

For a given odd mass number, there is exactly one beta-stable nuclide. There is not a difference in binding energy between even–odd and odd–even comparable to that between even–even and odd–odd, leaving other nuclides of the same mass number (isobars) free to beta decay toward the lowest-mass nuclide. For mass numbers of 147, 151, and 209+, the beta-stable isobar of that mass number has been observed to undergo alpha decay. (In theory, mass number 143 to 155, 160 to 162, and 165+ can also alpha decay.) This gives a total of 101 stable nuclides with odd mass numbers. There are another nine radioactive primordial nuclides (which by definition all have relatively long half lives, greater than 80 million years) with odd mass numbers.

Odd-mass-number nuclides are fermions, i.e., have half-integer spin. Generally speaking, since odd-mass-number nuclides always have an even number of either neutrons or protons, the even-numbered particles usually form part of a "core" in the nucleus with a spin of zero. The unpaired nucleon with the odd number (whether proton or neutron) is then responsible for the nuclear spin, which is the sum of the orbital angular momentum and spin angular momentum of the remaining nucleon. In all, 29 of the 110 primordial odd-mass nuclides have spin 1/2, 30 have spin 3/2, 24 have spin 5/2, 17 have spin 7/2, and nine have spin 9/2.[citation needed]

The odd-mass number stable nuclides are divided (roughly evenly) into odd-proton–even-neutron, and odd-neutron–even-proton nuclides, which are more thoroughly discussed below.

Odd proton, even neutron

These 48 stable nuclides, stabilized by their even numbers of paired neutrons, form most of the stable isotopes of the odd-numbered elements; the very few odd–odd nuclides comprise the others. There are 41 odd-numbered elements with Z = 1 through 81, of which 30 (including hydrogen, since zero is an even number) have one stable odd-even isotope, the elements technetium (
43
Tc
) and promethium (
61
Pm
) have no stable isotopes, and nine elements: chlorine (
17
Cl
), potassium (
19
K
), copper (
29
Cu
), gallium (
31
Ga
), bromine (
35
Br
), silver (
47
Ag
), antimony (
51
Sb
),

The last two were only recently found to undergo alpha decay, with half-lives greater than 1018 years.

Even proton, odd neutron

Even–odd long-lived
Decay
Half-life
113
48
Cd
beta 7.7×1015
a
147
62
Sm
alpha 1.06×1011
a
235
92
U
alpha 7.04×108
a

These 53 stable nuclides have an even number of protons and an odd number of neutrons. By definition, they are all isotopes of even-Z elements, where they are a minority in comparison to the even–even isotopes which are about 3 times as numerous. Among the 41 even-Z elements that have a stable nuclide, only two elements (argon and cerium) have no even–odd stable nuclides. One element (tin) has three. There are 24 elements that have one even–odd nuclide and 13 that have two even–odd nuclides. The lightest example of this type of nuclide is

207
82
Pb
.

Of 34 primordial radionuclides there exist three even–odd nuclides (see table at right), including the

fissile 235
92
U
. Because of their odd neutron numbers, the even–odd nuclides tend to have large neutron capture
cross sections, due to the energy that results from neutron-pairing effects.

These stable even-proton odd-neutron nuclides tend to be uncommon by abundance in nature, generally because in order to form and contribute to the primordial abundance, they must have escaped capturing neutrons to form yet other stable even–even isotopes, during both the

9
4
Be
are the most naturally abundant isotopes of their element, the former only by a small margin, and the latter only because the expected beryllium-8 has lower binding energy than two alpha particles and therefore immediately alpha decays
.

Odd neutron number

Neutron number parity
N Even Odd
Stable 193 58
Long-lived 27 8
All primordial 220 66

fast neutrons
. Only
195
78
Pt
have an odd neutron number and are the most naturally abundant isotope of their element.

References

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  2. .
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  4. .
  5. .
  6. ^ "Radiation and Radioactive Decay. Radioactive Human Body". Harvard Natural Sciences Lecture Demonstrations. Retrieved July 2, 2016.
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  14. ^ Dumé, Belle (2003-04-23). "Bismuth breaks half-life record for alpha decay". Physicsweb.
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