Largest empty sphere

In this chart of nuclides, isobars occur along diagonal lines running from the lower right to upper left. The line of beta-stability includes the observationally stable nuclides shown in black; disconnected 'islands' are a consequence of the Mattauch isobar rule.

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Isobars are atoms (nuclides) of different chemical elements that have the same number of nucleons. Correspondingly, isobars differ in atomic number (or number of protons) but have the same mass number. An example of a series of isobars would be ⁴⁰S, ⁴⁰Cl, ⁴⁰Ar, ⁴⁰K, and ⁴⁰Ca. The nuclei of these nuclides all contain 40 nucleons; however, they contain varying numbers of protons and neutrons.

The term "isobars" (originally "isobares") for nuclides was suggested by Alfred Walter Stewart in 1918. It is derived from the Greek word isos, meaning "equal" and baros, meaning "weight".

Mass

The same mass number does not imply neither the same mass of nuclei, nor equal atomic masses of corresponding nuclides. From the Weizsäcker's formula for the mass of a nucleus

$m(A,Z)=Zm_{p}+Nm_{n}-a_{V}A+a_{S}A^{2/3}+a_{C}{\frac {Z^{2}}{A^{1/3}}}+a_{A}{\frac {(N-Z)^{2}}{A}}-\delta (A,Z)$

where mass number Template:Mvar equals to the sum of atomic number Template:Mvar and number of neutrons Template:Mvar, and Template:Mvar, Template:Mvar, Template:Mvar, Template:Mvar, Template:Mvar, Template:Mvar are constants, one can see that the mass depends on Template:Mvar and Template:Mvar non-linearly, even for a constant mass number. For odd Template:Mvar, it is admitted that Buying, selling and renting HDB and personal residential properties in Singapore are simple and transparent transactions. Although you are not required to engage a real property salesperson (generally often known as a "public listed property developers In singapore agent") to complete these property transactions, chances are you'll think about partaking one if you are not accustomed to the processes concerned.

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Another method by way of which you could find out whether the agent is sweet is by checking the feedback, of the shoppers, on the website. There are various individuals would publish their comments on the web site of the Singapore property agent. You can take a look at these feedback and the see whether it will be clever to hire that specific Singapore property agent. You may even get in contact with the developer immediately. Many Singapore property brokers know the developers and you may confirm the goodwill of the agent by asking the developer. and the mass dependence on Template:Mvar is convex (or on Template:Mvar or Buying, selling and renting HDB and personal residential properties in Singapore are simple and transparent transactions. Although you are not required to engage a real property salesperson (generally often known as a "public listed property developers In singapore agent") to complete these property transactions, chances are you'll think about partaking one if you are not accustomed to the processes concerned.

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<even A>...</even A>For even Template:Mvar the Template:Mvar term has the form:

$\delta (A,Z)=(-1)^{Z}a_{P}A^{-{\frac {1}{2}}}$

where Template:Mvar is another constant. This term, subtracted from the mass expression above, is positive for even-even nuclei and negative for odd-odd nuclei. This means that even-even nuclei, which have not a strong neutron excess or neutron deficiency, have higher binding energy than their odd-odd isobar neighbors. It implies that even-even nuclei are (relatively) lighter and more stable. The difference is especially strong for small Template:Mvar. This effect is also predicted (qualitatively) by other nuclear models and has important consequences.

Stability

The Mattauch isobar rule states that if two adjacent elements on the periodic table have isotopes of the same mass number, (at least) one of these isobars must be a radionuclide (radioactive). In cases of three isobars of sequential elements where the first and last are stable (this is often the case for even-even nuclides, see above), branched decay of the middle isobar may occur; e.g. radioactive iodine-126 has an almost equal probabilities for two decay modes, which lead to different daughter isotopes: tellurium-126 and xenon-126.

No observationally stable isobars exist for mass numbers 5 (decays to helium-4 plus a proton or neutron), 8 (decays to two helium-4 nuclei), 147, 151, as well as for 209 and above. Two observationally stable isobars exist for 36, 40, 46, 50, 54, 58, 64, 70, 74, 78, 80, 84, 86, 92, 94, 96, 98, 102, 104, 106, 108, 110, 112, 114, 120, 122, 123, 126, 132, 134, 136, 138, 142, 144, 146, 148, 154, 156, 158, 160, 162, 164, 168, 170, 176, 180, 184, 186, 192, 196, 198 and 204. Three observationally stable isobars exist for 124.

See also

• Isotopes (nuclides having the same number of protons)
• Isotones (nuclides having the same number of neutrons)
• Nuclear isomers (different excited states of the same nuclide)
• Magic number (physics)
• Electron capture

Bibliography

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