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[[File:NuclideMap stitched small preview.png|thumb|right|300px|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]].]] | |||
{{About|concept in nuclear physics|further meanings|Isobar (disambiguation){{!}}Isobar}} | |||
'''Isobars''' are atoms ([[nuclide]]s) of different [[chemical element]]s that have the same number of [[nucleon]]s. Correspondingly, isobars differ in [[atomic number]] (or number of [[proton]]s) but have the same [[mass number]]. An example of a series of isobars would be [[Sulfur-40|<sup>40</sup>S]], [[Chlorine-40|<sup>40</sup>Cl]], [[Argon-40|<sup>40</sup>Ar]], [[Potassium-40|<sup>40</sup>K]], and [[Calcium-40|<sup>40</sup>Ca]]. The nuclei of these nuclides all contain 40 nucleons; however, they contain varying numbers of protons and neutrons.<ref>[[#refSprawls1993|Sprawls (1993)]]</ref> | |||
The term "isobars" (originally "isobares") for nuclides was suggested by [[Alfred Walter Stewart]] in 1918.<ref>http://jnm.snmjournals.org/content/19/6/581.full.pdf</ref> It is derived from the [[Greek language|Greek]] word ''isos'', meaning "equal" and ''baros'', meaning "weight".<ref>[http://www.etymonline.com/index.php?term=isobar Etymology Online]</ref> | |||
== Mass == | |||
The same mass number does not imply neither the same [[invariant mass|mass]] of [[atomic nucleus|nuclei]], nor equal [[atomic mass]]es of corresponding nuclides. From the [[Semi-empirical mass formula|Weizsäcker's formula]] for the mass of a nucleus | |||
: <math>m(A,Z) = Z m_p + N m_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)</math> | |||
where mass number {{mvar|A}} equals to the sum of atomic number {{mvar|Z}} and number of neutrons {{mvar|N}}, and {{mvar|m<sub>p</sub>}}, {{mvar|m<sub>n</sub>}}, {{mvar|a<sub>V</sub>}}, {{mvar|a<sub>S</sub>}}, {{mvar|a<sub>C</sub>}}, {{mvar|a<sub>A</sub>}} are constants, one can see that the mass depends on {{mvar|Z}} and {{mvar|N}} non-linearly, even for a constant mass number. For [[odd number|odd]] {{mvar|A}}, it is admitted that {{math|1=''δ'' = 0}} and the mass dependence on {{mvar|Z}} is [[convex function|convex]] (or on {{mvar|N}} or {{math|''N'' − ''Z''}}, it does not matter for a constant {{mvar|A}}). This explains that [[beta-decay]] is energetically favorable for [[neutron-rich]] nuclides, and [[positron decay]] is favorable for strongly [[neutron-deficient]] nuclides. Both [[decay mode]]s do not change the mass number, hence an original nucleus and its [[decay product|daughter]] nucleus are isobars. In both aforementioned cases, a heavier nucleus decays to its lighter isobar. | |||
{{anchor|even A}}For [[even number|even]] {{mvar|A}} the {{mvar|δ}} term has the form: | |||
:<math>\delta(A,Z) = (-1)^Z a_P A^{-\frac 1 2}</math> | |||
where {{mvar|a<sub>P</sub>}} is another constant. This term, [[subtraction|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 [[nuclear binding energy|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 {{mvar|A}}. This effect is also predicted (qualitatively) by other [[nuclear model]]s 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 [[#even A|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.<ref>via [[Stable isotope]]; cf. [[observationally stable]] and note also more recently discovered decays: [[Isotopes of europium|Eu-151]] and [[Isotopes of bismuth|Bi-209]]</ref> | |||
==See also== | |||
* [[Isotope]]s (nuclides having the same number of protons) | |||
* [[Isotone]]s (nuclides having the same number of neutrons) | |||
* [[Nuclear isomer]]s (different excited states of the same nuclide) | |||
* [[Magic number (physics)]] | |||
* [[Electron capture]] | |||
==Bibliography== | |||
{{cite book | |||
|last= Sprawls | |||
|first= Perry | |||
|title= Physical Principles of Medical Imaging | |||
|url= http://www.sprawls.org/ppmi2/ | |||
|accessdate= 28 April 2010 | |||
|edition= 2 | |||
|year= 1993 | |||
|publisher= Medical Physics Publishing | |||
|location= [[Madison, Wisconsin|Madison, WI]] | |||
|isbn= 0-8342-0309-X | |||
|chapter= 5 – Characteristics and Structure of Matter | |||
|ref= refSprawls1993 | |||
}} | |||
==References== | |||
<references/> | |||
{{DEFAULTSORT:Isobar (Nuclide)}} | |||
[[Category:Nuclear physics]] | |||
Latest revision as of 11:53, 20 March 2013
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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.[1]
The term "isobars" (originally "isobares") for nuclides was suggested by Alfred Walter Stewart in 1918.[2] It is derived from the Greek word isos, meaning "equal" and baros, meaning "weight".[3]
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
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.
Professional agents are readily available once you need to discover an condominium for hire in singapore In some cases, landlords will take into account you more favourably in case your agent comes to them than for those who tried to method them by yourself. You need to be careful, nevertheless, as you resolve in your agent. Ensure that the agent you are contemplating working with is registered with the IEA – Institute of Estate Brokers. Whereas it might sound a hassle to you, will probably be worth it in the end. The IEA works by an ordinary algorithm and regulations, so you'll protect yourself in opposition to probably going with a rogue agent who prices you more than they should for his or her service in finding you an residence for lease in singapore.
There isn't any deal too small. Property agents who are keen to find time for any deal even if the commission is small are the ones you want on your aspect. Additionally they present humbleness and might relate with the typical Singaporean higher. Relentlessly pursuing any deal, calling prospects even without being prompted. Even if they get rejected a hundred times, they still come again for more. These are the property brokers who will find consumers what they need eventually, and who would be the most successful in what they do. 4. Honesty and Integrity
This feature is suitable for you who need to get the tax deductions out of your PIC scheme to your property agency firm. It's endorsed that you visit the correct site for filling this tax return software. This utility must be submitted at the very least yearly to report your whole tax and tax return that you're going to receive in the current accounting 12 months. There may be an official website for this tax filling procedure. Filling this tax return software shouldn't be a tough thing to do for all business homeowners in Singapore.
A wholly owned subsidiary of SLP Worldwide, SLP Realty houses 900 associates to service SLP's fast rising portfolio of residential tasks. Real estate is a human-centric trade. Apart from offering comprehensive coaching applications for our associates, SLP Realty puts equal emphasis on creating human capabilities and creating sturdy teamwork throughout all ranges of our organisational hierarchy. Worldwide Presence At SLP International, our staff of execs is pushed to make sure our shoppers meet their enterprise and investment targets. Under is an inventory of some notable shoppers from completely different industries and markets, who've entrusted their real estate must the expertise of SLP Worldwide.
If you're looking for a real estate or Singapore property agent online, you merely need to belief your instinct. It is because you don't know which agent is sweet and which agent will not be. Carry out research on a number of brokers by looking out the internet. As soon as if you find yourself certain that a selected agent is dependable and trustworthy, you'll be able to choose to utilize his partnerise find you a house in Singapore. More often than not, a property agent is considered to be good if she or he places the contact data on his web site. This is able to imply that the agent does not thoughts you calling them and asking them any questions regarding properties in Singapore. After chatting with them you too can see them of their office after taking an appointment.
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., it does not matter for a constant Template:Mvar). This explains that beta-decay is energetically favorable for neutron-rich nuclides, and positron decay is favorable for strongly neutron-deficient nuclides. Both decay modes do not change the mass number, hence an original nucleus and its daughter nucleus are isobars. In both aforementioned cases, a heavier nucleus decays to its lighter isobar.
<even A>...</even A>For even Template:Mvar the Template:Mvar term has the form:
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.[4]
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
20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534
References
- ↑ Sprawls (1993)
- ↑ http://jnm.snmjournals.org/content/19/6/581.full.pdf
- ↑ Etymology Online
- ↑ via Stable isotope; cf. observationally stable and note also more recently discovered decays: Eu-151 and Bi-209