S1xty
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| Joined: 25 Oct 2009 |
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| 02 May 2015 09:45 PM |
And carbon 12 is exactly 12.
How to calculate amu. I thought it was just the neutrons + protons, but clearly Carbon 13 does not have an extra .0034 neutrons
Filterrrrr blockkkk
OT was to incoherent to answer this |
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S1xty
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| Joined: 25 Oct 2009 |
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S1xty
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| Joined: 25 Oct 2009 |
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| 02 May 2015 09:50 PM |
| Mass defects in the isotope samples. |
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morash
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S1xty
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| Joined: 25 Oct 2009 |
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| 02 May 2015 09:58 PM |
| That's not taken into consideration in amu because their mass is infinitesimal compared to protons and neutrons |
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| 02 May 2015 10:00 PM |
mass is relative to the proton when it comes to numbers like "12" and "13".
a proton, for all intents and purposes has the same mass as a neutron and since carbon 13 is an isotope of carbon(12), it gains an extra neutron.
the 0.0034 is just the error in the instrument used to measure the mass, because again mass is relative so it could be off by whatever that error is plus or minus. |
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| 02 May 2015 10:19 PM |
Polymorphic has the right idea about the isotopes. Carbon-13 is an isotope and has undergone a process to change the number of neutrons in the atom (now an ion). This could be a form of radioactive decay (likely β decay or a combination of other decay patterns [known as a series]). The difference in mass lies therein. Protons and neutrons do not have the same mass. However, I do not believe the error lies in the instruments. The value is calculated to 2 significant figures; the 3 must be certain (based on their measurements). I believe the difference may be due to uncertainty principles; if this is the case, we'll never know the exact mass, even with technological developments. However, it seems they are fairly certain about the difference in mass between the isotopes of carbon. |
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mathchamp
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| Joined: 22 Oct 2007 |
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| 02 May 2015 11:06 PM |
Wrong section, first of all.
Carbon-12's mass is exactly 12u because the atomic mass unit (amu) is DEFINED such that 1 amu = 1/12 the mass of C-12, i.e. mass of C-12 is 12 amu by definition.
Other isotopes and nuclides have masses that are not exact integers, and it has nothing to do with measurement error.
First of all, both protons and neutrons are a bit less than 1% heavier than 1 amu (the neutron is also slightly heavier than the proton). This is why H-1 has an atomic mass of 1.0078u, since this is the mass of a proton (1.0073u) and electron (0.0005u).
Secondly, there is a concept known as "mass defect", where the mass of an atomic nucleus is less than the sum of the masses of the individual protons and neutrons. For example, the mass of 6 protons, 6 neutrons, and 6 electrons is 12.0989u, but when these are combined to form Carbon-12, the total mass is only 12.0000u. The mass defect for C-12 is thus 0.0989u. Thus, the mass of each proton and neutron has decreased by 0.0082u (1/12 of the total mass defect) on forming the C-12 nucleus.
This mass defect actually corresponds to a "binding energy", which is the energy needed to separate an atom into its individual protons, neutrons, and electrons. The binding energy is calculated from the mass defect using E=mc^2. For C-12, the binding energy is 92.16 MeV, or 7.680 MeV per nucleon (6 protons + 6 neutrons = 12 nucleons).
Conversely, the binding energy is the amount of energy released when protons and neutrons come together to form nuclei. This is how our Sun works. The proton-proton chain reaction converts hydrogen into helium. One helium nucleus has a lower mass than four protons, and this difference is converted into energy and released as heat.
The binding energy per nucleon is the reason why some isotopes have a lower mass (in amu) than their mass number (protons+neutrons) and others have a higher mass than their mass number. Some examples:
Hydrogen-1 has no nuclear binding energy (since the nucleus is just a proton), thus its mass is 1.0078u, which is significantly more than 1. The mass is simply the sum of proton and electron mass (if you ignore the very small binding energy between the proton and electron - this binding energy is 13.6 eV, or 0.0000136 MeV).
Helium-4 has a very large binding energy per nucleon (7.075 MeV) for its size. However, the binding energy per nucleon is still less than that of C-12, and thus the atomic mass is 4.0026u, slightly more than 4.
Carbon-12 has a binding energy per nucleon of 7.680 MeV and an atomic mass of exactly 12u. Carbon-13 has a slightly lower binding energy per nucleon of 7.470 MeV, and also has more neutrons (which are heavier) than protons, which is why its atomic mass is 13.0034u and not 13u.
Nickel-62 has the highest binding energy per nucleon by the above definition, of 8.795 MeV, thus it is actually lighter than 62u (its mass is 61.9283u).
Uranium-238 has an atomic mass of 238.0508u, but its constituent particles add to 239.9850u, corresponding to a mass defect of 1.9342u, or 0.0081u per nucleon (binding energy of 7.570 MeV per nucleon). Its atomic mass is slightly more than 238u both due to having a weaker binding energy per nucleon than C-12 and by having many more neutrons (146) than protons (92). |
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| 02 May 2015 11:12 PM |
Yes, exactly what mathchamp said. Thank you! I haven't been through much chemistry; I'm more of a physics guy. However, I can tell you that the mass of a nucleus is less than the mass of its nucleons! |
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| 02 May 2015 11:18 PM |
| I love physics! I plan on becoming some sort of physicist, perhaps an astrophysicist. |
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S1xty
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| Joined: 25 Oct 2009 |
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| 03 May 2015 11:12 AM |
| interesting. I'll have to learn more about binding energy or whatever |
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