Beta-decay stable isobars - AbsoluteAstronomy.com

Beta-decay stable isobar
Isobar (nuclide)
Isobars are atoms of different chemical elements that have the same number of nucleons. Correspondingly, isobars differ in atomic number but not in mass number. An example of a series of isobars would be 40S, 40Cl, 40Ar, 40K, and 40Ca...

s are the set of nuclides which cannot undergo beta decay

Beta decay

In nuclear physics, beta decay is a type of radioactive decay in which a beta particle is emitted from an atom. There are two types of beta decay: beta minus and beta plus. In the case of beta decay that produces an electron emission, it is referred to as beta minus , while in the case of a...

, that is, the transformation of a neutron

Neutron

The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...

to a proton

Proton

The proton is a subatomic particle with the symbol or and a positive electric charge of 1 elementary charge. One or more protons are present in the nucleus of each atom, along with neutrons. The number of protons in each atom is its atomic number....

or a proton to a neutron within the nucleus

Atomic nucleus

The nucleus is the very dense region consisting of protons and neutrons at the center of an atom. It was discovered in 1911, as a result of Ernest Rutherford's interpretation of the famous 1909 Rutherford experiment performed by Hans Geiger and Ernest Marsden, under the direction of Rutherford. The...

. A subset of these nuclides are also stable with regards to double beta decay

Double beta decay

Double beta decay is a radioactive decay process where a nucleus releases two beta rays as a single process.In double-beta decay, two neutrons in the nucleus are converted to protons, and two electrons and two electron antineutrinos are emitted...

or theoretically higher simultaneous beta decay, as they have the lowest energy of all nuclides with the same mass number

Mass number

The mass number , also called atomic mass number or nucleon number, is the total number of protons and neutrons in an atomic nucleus. Because protons and neutrons both are baryons, the mass number A is identical with the baryon number B as of the nucleus as of the whole atom or ion...

.

This set of nuclides is also known as the line of beta stability, a term already in common use in 1965

Introduction

The line of beta stability can be defined mathematically by finding the nuclide with the greatest binding energy

Binding energy

Binding energy is the mechanical energy required to disassemble a whole into separate parts. A bound system typically has a lower potential energy than its constituent parts; this is what keeps the system together—often this means that energy is released upon the creation of a bound state...

for a given mass number, by a model such as the classical semi-empirical mass formula

Semi-empirical mass formula

In nuclear physics, the semi-empirical mass formula is used to approximate the mass and various other properties of an atomic nucleus...

developed by C. F. Weizsäcker

Carl Friedrich von Weizsäcker

Carl Friedrich Freiherr von Weizsäcker was a German physicist and philosopher. He was the longest-living member of the research team which performed nuclear research in Germany during the Second World War, under Werner Heisenberg's leadership...

. These nuclides are local maxima in terms of binding energy for a given mass number.

β decay
Beta decay
In nuclear physics, beta decay is a type of radioactive decay in which a beta particle is emitted from an atom. There are two types of beta decay: beta minus and beta plus. In the case of beta decay that produces an electron emission, it is referred to as beta minus , while in the case of a...

stable / even N
Mass number
The mass number , also called atomic mass number or nucleon number, is the total number of protons and neutrons in an atomic nucleus. Because protons and neutrons both are baryons, the mass number A is identical with the baryon number B as of the nucleus as of the whole atom or ion...
#βDS:	One	Two	Three
2-34	17
36-58	6	6
60-72	5	2
74-116	2	19	1
118-154	2	11	6
156-192	5	14
194-210	6	3
212-260	6	19
Total	48	75	7

All odd mass numbers have only one beta decay stable nuclide.

Among even mass number, seven (96, 124, 130, 136, 148, 150, 154) have three beta-stable nuclides. None have more than three, all others have either one or two.

From 2 to 34, all have only one.
From 36 to 72, only eight (36, 40, 46, 50, 54, 58, 64, 70) have two, and the remaining 11 have one.
From 74 to 122, only three (88, 90, 118) have one, and the remaining 22 have two.
From 124 to 154, only one (140) has one, six have three, and the remaining 9 have two.
From 156 to 260, only seventeen have one, and the remaining 36 have two.

All primordial nuclide

Primordial nuclide

In geochemistry and geonuclear physics, primordial nuclides or primordial isotopes are nuclides found on the earth that have existed in their current form since before Earth was formed. Only 288 such nuclides are known...

s are beta decay stable, with the exception of ⁴⁰K, ⁵⁰V, ⁸⁷Rb, ¹¹³Cd, ¹¹⁵In, ¹²³Te, ¹³⁸La, ¹⁷⁶Lu, and ¹⁸⁷Re. In addition, ^180mTa has not been observed to decay, but is believed to undergo beta decay with an extremely long half-life (over 10¹⁵ years). All elements except technetium

Technetium

Technetium is the chemical element with atomic number 43 and symbol Tc. It is the lowest atomic number element without any stable isotopes; every form of it is radioactive. Nearly all technetium is produced synthetically and only minute amounts are found in nature...

and promethium

Promethium

Promethium is a chemical element with the symbol Pm and atomic number 61. It is notable for being the only exclusively radioactive element besides technetium that is followed by chemical elements with stable isotopes.- Prediction :...

have at least one beta-stable isotope.

List of known beta-decay stable isobars

Theoretically predicted double beta-decay

Double beta decay

(if not dominated by alpha decay

Alpha decay

Alpha decay is a type of radioactive decay in which an atomic nucleus emits an alpha particle and thereby transforms into an atom with a mass number 4 less and atomic number 2 less...

or spontaneous fission

Spontaneous fission

Spontaneous fission is a form of radioactive decay characteristic of very heavy isotopes. Because the nuclear binding energy reaches a maximum at a nuclear mass greater than about 60 atomic mass units , spontaneous breakdown into smaller nuclei and single particles becomes possible at heavier masses...

) is shown by arrows, i.e. arrows point towards the lightest-mass isobar. There are currently known to be 358 beta-decay stable nuclides.

	Even N Neutron number The neutron number, symbol N, is the number of neutrons in a nuclide.Atomic number plus neutron number equals mass number: Z+N=A....	Odd N
Even Z Atomic number In chemistry and physics, the atomic number is the number of protons found in the nucleus of an atom and therefore identical to the charge number of the nucleus. It is conventionally represented by the symbol Z. The atomic number uniquely identifies a chemical element...	Even A Mass number The mass number , also called atomic mass number or nucleon number, is the total number of protons and neutrons in an atomic nucleus. Because protons and neutrons both are baryons, the mass number A is identical with the baryon number B as of the nucleus as of the whole atom or ion...	Odd A
Odd Z	Odd A	Even A

All beta-decay stable isobars with A ≤ 260 sorted by mass number
Odd A	Even A	Odd A	Even A	Odd A	Even A	Odd A	Even A
¹H	²H	³He	⁴He	⁵He (n)	⁶Li	⁷Li	⁸Be (α)
⁹Be	¹⁰B	¹¹B	¹²C	¹³C	¹⁴N	¹⁵N	¹⁶O
¹⁷O	¹⁸O	¹⁹F	²⁰Ne	²¹Ne	²²Ne	²³Na	²⁴Mg
²⁵Mg	²⁶Mg	²⁷Al	²⁸Si	²⁹Si	³⁰Si	³¹P	³²S
³³S	³⁴S	³⁵Cl	³⁶S←³⁶Ar	³⁷Cl	³⁸Ar	³⁹K	⁴⁰Ar←⁴⁰Ca
⁴¹K	⁴²Ca	⁴³Ca	⁴⁴Ca	⁴⁵Sc	⁴⁶Ca→⁴⁶Ti	⁴⁷Ti	⁴⁸Ti
⁴⁹Ti	⁵⁰Ti←⁵⁰Cr	⁵¹V	⁵²Cr	⁵³Cr	⁵⁴Cr←⁵⁴Fe	⁵⁵Mn	⁵⁶Fe
⁵⁷Fe	⁵⁸Fe←⁵⁸Ni	⁵⁹Co	⁶⁰Ni	⁶¹Ni	⁶²Ni	⁶³Cu	⁶⁴Ni←⁶⁴Zn
⁶⁵Cu	⁶⁶Zn	⁶⁷Zn	⁶⁸Zn	⁶⁹Ga	⁷⁰Zn→⁷⁰Ge	⁷¹Ga	⁷²Ge
⁷³Ge	⁷⁴Ge←⁷⁴Se	⁷⁵As	⁷⁶Ge→⁷⁶Se	⁷⁷Se	⁷⁸Se←⁷⁸Kr	⁷⁹Br	⁸⁰Se→⁸⁰Kr
⁸¹Br	⁸²Se→⁸²Kr	⁸³Kr	⁸⁴Kr←⁸⁴Sr	⁸⁵Rb	⁸⁶Kr→⁸⁶Sr	⁸⁷Sr	⁸⁸Sr
⁸⁹Y	⁹⁰Zr	⁹¹Zr	⁹²Zr←⁹²Mo	⁹³Nb	⁹⁴Zr→⁹⁴Mo	⁹⁵Mo	⁹⁶Zr→⁹⁶Mo←⁹⁶Ru
⁹⁷Mo	⁹⁸Mo→⁹⁸Ru	⁹⁹Ru	¹⁰⁰Mo→¹⁰⁰Ru	¹⁰¹Ru	¹⁰²Ru←¹⁰²Pd	¹⁰³Rh	¹⁰⁴Ru→¹⁰⁴Pd
¹⁰⁵Pd	¹⁰⁶Pd←¹⁰⁶Cd	¹⁰⁷Ag	¹⁰⁸Pd←¹⁰⁸Cd	¹⁰⁹Ag	¹¹⁰Pd→¹¹⁰Cd	¹¹¹Cd	¹¹²Cd←¹¹²Sn
¹¹³In	¹¹⁴Cd→¹¹⁴Sn	¹¹⁵Sn	¹¹⁶Cd→¹¹⁶Sn	¹¹⁷Sn	¹¹⁸Sn	¹¹⁹Sn	¹²⁰Sn←¹²⁰Te
¹²¹Sb	¹²²Sn→¹²²Te	¹²³Sb	¹²⁴Sn→¹²⁴Te←¹²⁴Xe	¹²⁵Te	¹²⁶Te←¹²⁶Xe	¹²⁷I	¹²⁸Te→¹²⁸Xe
¹²⁹Xe	¹³⁰Ba→¹³⁰Xe←¹³⁰Te	¹³¹Xe	¹³²Xe←¹³²Ba	¹³³Cs	¹³⁴Xe→¹³⁴Ba	¹³⁵Ba	¹³⁶Xe→¹³⁶Ba←¹³⁶Ce
¹³⁷Ba	¹³⁸Ba←¹³⁸Ce	¹³⁹La	¹⁴⁰Ce	¹⁴¹Pr	¹⁴²Ce→¹⁴²Nd	¹⁴³Nd	¹⁴⁴Nd (α)←¹⁴⁴Sm
¹⁴⁵Nd	¹⁴⁶Nd→¹⁴⁶Sm (α)	¹⁴⁷Sm	¹⁴⁸Nd→¹⁴⁸Sm (α)←¹⁴⁸Gd (α)	¹⁴⁹Sm	¹⁵⁰Nd→¹⁵⁰Sm←¹⁵⁰Gd (α)	¹⁵¹Eu	¹⁵²Sm←¹⁵²Gd (α)
¹⁵³Eu	¹⁵⁴Sm→¹⁵⁴Gd←¹⁵⁴Dy (α)	¹⁵⁵Gd	¹⁵⁶Gd←¹⁵⁶Dy	¹⁵⁷Gd	¹⁵⁸Gd←¹⁵⁸Dy	¹⁵⁹Tb	¹⁶⁰Gd→¹⁶⁰Dy
¹⁶¹Dy	¹⁶²Dy←¹⁶²Er	¹⁶³Dy	¹⁶⁴Dy←¹⁶⁴Er	¹⁶⁵Ho	¹⁶⁶Er	¹⁶⁷Er	¹⁶⁸Er←¹⁶⁸Yb
¹⁶⁹Tm	¹⁷⁰Er→¹⁷⁰Yb	¹⁷¹Yb	¹⁷²Yb	¹⁷³Yb	¹⁷⁴Yb←¹⁷⁴Hf (α)	¹⁷⁵Lu	¹⁷⁶Yb→¹⁷⁶Hf
¹⁷⁷Hf	¹⁷⁸Hf	¹⁷⁹Hf	¹⁸⁰Hf←¹⁸⁰W (α)	¹⁸¹Ta	¹⁸²W	¹⁸³W	¹⁸⁴W←¹⁸⁴Os
¹⁸⁵Re	¹⁸⁶W→¹⁸⁶Os (α)	¹⁸⁷Os	¹⁸⁸Os	¹⁸⁹Os	¹⁹⁰Os←¹⁹⁰Pt (α)	¹⁹¹Ir	¹⁹²Os→¹⁹²Pt
¹⁹³Ir	¹⁹⁴Pt	¹⁹⁵Pt	¹⁹⁶Pt←¹⁹⁶Hg	¹⁹⁷Au	¹⁹⁸Pt→¹⁹⁸Hg	¹⁹⁹Hg	²⁰⁰Hg
²⁰¹Hg	²⁰²Hg	²⁰³Tl	²⁰⁴Hg→²⁰⁴Pb	²⁰⁵Tl	²⁰⁶Pb	²⁰⁷Pb	²⁰⁸Pb
²⁰⁹Bi (α)	²¹⁰Po (α)	²¹¹Po	²¹²Po←²¹²Rn	²¹³Po	²¹⁴Po←²¹⁴Rn	²¹⁵At	²¹⁶Po→²¹⁶Rn
²¹⁷Rn	²¹⁸Rn←²¹⁸Ra	²¹⁹Fr	²²⁰Rn→²²⁰Ra	²²¹Ra	²²²Ra	²²³Ra	²²⁴Ra←²²⁴Th
²²⁵Ac	²²⁶Ra→²²⁶Th	²²⁷Th	²²⁸Th	²²⁹Th	²³⁰Th←²³⁰U	²³¹Pa	²³²Th→²³²U
²³³U	²³⁴U	²³⁵U	²³⁶U←²³⁶Pu	²³⁷Np	²³⁸U→²³⁸Pu	²³⁹Pu	²⁴⁰Pu
²⁴¹Am	²⁴²Pu←²⁴²Cm	²⁴³Am	²⁴⁴Pu→²⁴⁴Cm	²⁴⁵Cm	²⁴⁶Cm→ ²⁴⁶Cf	²⁴⁷Bk	²⁴⁸Cm→²⁴⁸Cf
²⁴⁹Cf	²⁵⁰Cf	²⁵¹Cf	²⁵²Cf←²⁵²Fm	²⁵³Es	²⁵⁴Cf (SF), ²⁵⁴Fm	²⁵⁵Fm	²⁵⁶Fm (SF)
²⁵⁷Fm	²⁵⁸Fm (SF), ²⁵⁸No (SF)	²⁵⁹Md (SF)	²⁶⁰Fm (SF), ²⁶⁰No (SF)

Known beta-decay stable isobars with A > 260 sorted by mass number
²⁶¹Md	²⁶²No (SF), ²⁶²Rf (SF)	²⁶³No (SF)	²⁶⁴No , ²⁶⁴Rf	²⁶⁵Lr (SF)	²⁶⁶Rf (SF)	²⁶⁷Rf (SF)	²⁶⁸Rf (SF)

All beta-decay stable nuclides with A ≥ 209 were observed to decay by alpha decay except some where spontaneous fission dominates.

Beta decay towards minimum mass

Beta decay generally causes isotopes to decay towards the isobar with the lowest mass (highest binding energy) with the same mass number, those not in italics in the table above. Thus, those with lower atomic number

Atomic number

In chemistry and physics, the atomic number is the number of protons found in the nucleus of an atom and therefore identical to the charge number of the nucleus. It is conventionally represented by the symbol Z. The atomic number uniquely identifies a chemical element...

and higher neutron number

Neutron number

The neutron number, symbol N, is the number of neutrons in a nuclide.Atomic number plus neutron number equals mass number: Z+N=A....

than the minimum-mass isobar undergo beta-minus decay, while those with higher atomic number and lower neutron number undergo beta-plus decay

Positron emission

Positron emission or beta plus decay is a type of beta decay in which a proton is converted, via the weak force, to a neutron, releasing a positron and a neutrino....

. However, there are four nuclides that are exceptions, in that the majority of their decays are in the opposite direction:

Chlorine-36 Chlorine-36 Chlorine-36 is an isotope of chlorine. Chlorine has two stable isotopes and one radioactive environmental isotope: the cosmogenic isotope 36Cl. The ratio of 36Cl to stable 37Cl in the environment is ~700 × 10−15. Its half-life is 301,000 ± 4,000 years. The long half-life of 36Cl makes it...	35.96830698	Potassium-40 Potassium-40 Potassium-40 is a radioactive isotope of potassium which has a very long half-life of 1.248 years, or about 39.38 seconds.Potassium-40 is a rare example of an isotope which undergoes all three types of beta decay. About 89.28% of the time, it decays to calcium-40 with emission of a beta particle...	39.96399848	Silver-108	107.905956	Promethium-146	145.914696
2% to Sulfur-36	35.96708076	11.2% to Argon-40	39.9623831225	3% to Palladium-108	107.903892	37% to Samarium-146	145.913041
98% to Argon-36	35.967545106	89% to Calcium-40	39.96259098	97% to Cadmium-108	107.904184	63% to Neodymium-146	145.9131169

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