Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: theThinker on 19/09/2016 16:47:56
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Hello all,
We currently have data (e.g. official from CODATA) about the "missing mass" or binding energy per nucleon available for most nuclide of the elements. I'll like to know what physics or specific formula is used to determine such mass difference of the proton and neutron when they are in the bound states within nuclides.
My vague understanding is that they are done through mass spectrometry. In the case where the charge-to-mass ratio is measured by magnetic deflection, then the main (or only formula) that it depends on is the Lorentz magnetic force : F=q(v x B). C-12 may be standardized to say 12 Dalton. Comparing the deflections of the other nuclide with C-12 will give us the mass of all other nuclide.
Can someone comment if this is basically correct.
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Yes, mass spectrometry is how this is done. This includes deflection in a magnetic field (often quadrupole), but also time-of-flight mass spectrometry (https://en.wikipedia.org/wiki/Time-of-flight_mass_spectrometry)
https://en.wikipedia.org/wiki/Mass_spectrometry#Mass_selection
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In some cases you could do the determination with a gas density balance.
The isotopes can be detected because they give the wrong weights in chemical analysis
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I'll like to know what physics or specific formula is used to determine such mass difference of the proton and neutron when they are in the bound states within nuclides.
The above answers describe how binding energy is measured experimentally.
Unfortunately, the theory of how to calculate the missing mass mathematically is a bit more complex.
With electrons in atoms, There is just one particle type (the electron), of a single mass, interacting via a single electromagnetic force with a tiny nucleus, subject to the Pauli Exclusion Principle. The energy of each shell is defined by the Schroedinger equation, and can be easily measured using spectroscopy; mostly visible light, with some in the ultraviolet and many in the infra-red.
With forces in the nucleus, the situation is much more complex. There are now two particle types (protons and neutrons).
- The protons interact via the electromagnetic force, but the neutrons do not.
- The Pauli Exclusion Principle applies to Protons and Neutrons separately, so the protons and neutrons have different energy levels.
- Protons and Neutrons interact via the Strong Nuclear force (the weak nuclear force can be almost ignored in stable atoms)
- Protons and Neutrons seem to like hanging around in groups of 4 (Alpha particles).
- The Protons and Neutrons have different masses
- Gamma rays to probe the nucleus are much harder to manipulate than visible light
- With all of these variables, it is not quite certain how many protons and neutrons can fit into each energy level; different theories predict different numbers.
There is good agreement between theory and experiment for stable nuclei that have already been measured in the laboratory. However, the test of a good theory is that it will predict the results for heavy nuclei that have not yet been produced in the lab; we don't have a theory that could confidently do this. Not helped by the fact that:
- these physically large nuclei exceed the range of the strong nuclear force
- these heavy nuclei are unstable, and the weak nuclear force plays a larger role.
See: https://en.wikipedia.org/wiki/Nuclear_shell_model
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In some cases you could do the determination with a gas density balance.
The isotopes can be detected because they give the wrong weights in chemical analysis
Hello,
Your answer may be about something else. I think the missing mass, the difference between free nucleons and bound nucleons should be very small so that chemical techniques may not have the precision to measure it.
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I'll like to know what physics or specific formula is used to determine such mass difference of the proton and neutron when they are in the bound states within nuclides.
The above answers describe how binding energy is measured experimentally.
Unfortunately, the theory of how to calculate the missing mass mathematically is a bit more complex.
With electrons in atoms, There is just one particle type (the electron), of a single mass, interacting via a single electromagnetic force with a tiny nucleus, subject to the Pauli Exclusion Principle. The energy of each shell is defined by the Schroedinger equation, and can be easily measured using spectroscopy; mostly visible light, with some in the ultraviolet and many in the infra-red.
With forces in the nucleus, the situation is much more complex. There are now two particle types (protons and neutrons).
- The protons interact via the electromagnetic force, but the neutrons do not.
- The Pauli Exclusion Principle applies to Protons and Neutrons separately, so the protons and neutrons have different energy levels.
- Protons and Neutrons interact via the Strong Nuclear force (the weak nuclear force can be almost ignored in stable atoms)
- Protons and Neutrons seem to like hanging around in groups of 4 (Alpha particles).
- The Protons and Neutrons have different masses
- Gamma rays to probe the nucleus are much harder to manipulate than visible light
- With all of these variables, it is not quite certain how many protons and neutrons can fit into each energy level; different theories predict different numbers.
There is good agreement between theory and experiment for stable nuclei that have already been measured in the laboratory. However, the test of a good theory is that it will predict the results for heavy nuclei that have not yet been produced in the lab; we don't have a theory that could confidently do this. Not helped by the fact that:
- these physically large nuclei exceed the range of the strong nuclear force
- these heavy nuclei are unstable, and the weak nuclear force plays a larger role.
Hello Evan,
I think there is still very much to learn about the the forces within the nucleus - it would be a miracle if we say our nuclear shell model is complete.
About the CODATA for the binding energy, I think it should be raw unadulterated experimental figures given to us, not after "fine tuning" to conform to Michelin standards!
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We currently have data (e.g. official from CODATA) about the "missing mass" or binding energy per nucleon available for most nuclide of the elements. I'll like to know what physics or specific formula is used to determine such mass difference of the proton and neutron when they are in the bound states within nuclides.
I think I know what you may be looking for and if I'm right then the mass that you're looking for comes from mass-energy equivalence. The energy, and thus mass, comes from the strong force which holds nuclides together. So the formula that you're looking for is E = mc0.
Is that what you were looking for?
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Hello,
Your answer may be about something else. I think the missing mass, the difference between free nucleons and bound nucleons should be very small so that chemical techniques may not have the precision to measure it.
"
I'm guessing you don't know how good modern chemistry is.
Consider manganese and its fluorides (Manganese and fluorine only have one stable isotope which makes things easier).
If there was no "mass defect" then the atomic masses would be exactly the same as the nucleon number
Fluorine would be 19 exactly and manganese would be 55 exactly.
So if I took a gram of manganese and reacted it with fluorine the product (MnF2) would weigh exactly
(55+19+19 )/55 i.e.
1.6909090909 grams
However if I did the experiment I would get
(54.938045 +18.998403+18.998403)/54.938045 i.e 1.69163 grams
That's a 0.04% change in mass and a good balance would detect it with no difficulty.
With beryllium fluoride you get a bigger effect
5.21616
vs
5.222
That's more than a 0.1% change.
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"
Hello,
Your answer may be about something else. I think the missing mass, the difference between free nucleons and bound nucleons should be very small so that chemical techniques may not have the precision to measure it.
"
I'm guessing you don't know how good modern chemistry is.
Consider manganese and its fluorides (Manganese and fluorine only have one stable isotope which makes things easier).
If there was no "mass defect" then the atomic masses would be exactly the same as the nucleon number
Fluorine would be 19 exactly and manganese would be 55 exactly.
So if I took a gram of manganese and reacted it with fluorine the product (MnF2) would weigh exactly
(55+19+19 )/55 i.e.
1.6909090909 grams
However if I did the experiment I would get
(54.938045 +18.998403+18.998403)/54.938045 i.e 1.69163 grams
That's a 0.04% change in mass and a good balance would detect it with no difficulty.
With beryllium fluoride you get a bigger effect
5.21616
vs
5.222
That's more than a 0.1% change.
Hello chemist,
I got distinction in "O" level chemistry!
I still can't grasp the significance of your 0.04%. All along, I have the idea that mass defect plays a significant/measurable part only in nuclear interactions - a little mass makes a lot of energy through E=mc². But chemistry means chemical bonds. I still don't quite digest that burning of wood by our earliest ancestors involve mass defect.
Anyway, I have some vague idea that they even seem to account for mass defects about total mass of electrons in atoms and molecules. I still have to accept and learn.
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We currently have data (e.g. official from CODATA) about the "missing mass" or binding energy per nucleon available for most nuclide of the elements. I'll like to know what physics or specific formula is used to determine such mass difference of the proton and neutron when they are in the bound states within nuclides.
I think I know what you may be looking for and if I'm right then the mass that you're looking for comes from mass-energy equivalence. The energy, and thus mass, comes from the strong force which holds nuclides together. So the formula that you're looking for is E = mc0.
Is that what you were looking for?
I actually was asking for confirmation and further comments by experts about the use of the magnetic force formula q (v x B) as the basis if magnetic deflection is the way with mass spectrometry. I seems somehow the experimental measurement of the mass defect must be in good agreement with the actual energy in nuclear interactions based on E=m₀c².
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I actually was asking for confirmation and further comments by experts about the use of the magnetic force formula q (v x B) as the basis if magnetic deflection is the way with mass spectrometry.
I'm not clear on what you mean by "expert." I'm a professional physicist (retired). My area of expertise is relativity. To know relativity you come to learn about its applications, i.e. what is it used for. And one of the things I know about this subject is how a charged particle moves in an EM field. If the mass of a particle is measured a mass spectrometer is used which is basically a cyclotron. But you can look all this up by searching the internet. But I'll be as much help as I can with your inquires.
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Hello chemist,
I got distinction in "O" level chemistry!
I still can't grasp the significance of your 0.04%. All along, I have the idea that mass defect plays a significant/measurable part only in nuclear interactions - a little mass makes a lot of energy through E=mc². But chemistry means chemical bonds. I still don't quite digest that burning of wood by our earliest ancestors involve mass defect.
Anyway, I have some vague idea that they even seem to account for mass defects about total mass of electrons in atoms and molecules. I still have to accept and learn.
The significance of the 0.4% is that it is not zero.
If the mass defect was zero you would get a different ratio of masses of elements in compounds.
You can measure that ratio in a chemistry lab.
Since the mass changes are real, you are right in saying that you have to accept and learn.
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"
Hello,
Your answer may be about something else. I think the missing mass, the difference between free nucleons and bound nucleons should be very small so that chemical techniques may not have the precision to measure it.
"
I'm guessing you don't know how good modern chemistry is.
Consider manganese and its fluorides (Manganese and fluorine only have one stable isotope which makes things easier).
If there was no "mass defect" then the atomic masses would be exactly the same as the nucleon number
Fluorine would be 19 exactly and manganese would be 55 exactly.
So if I took a gram of manganese and reacted it with fluorine the product (MnF2) would weigh exactly
(55+19+19 )/55 i.e.
1.6909090909 grams
However if I did the experiment I would get
(54.938045 +18.998403+18.998403)/54.938045 i.e 1.69163 grams
That's a 0.04% change in mass and a good balance would detect it with no difficulty.
With beryllium fluoride you get a bigger effect
5.21616
vs
5.222
That's more than a 0.1% change.
Hello chemist,
I got distinction in "O" level chemistry!
I still can't grasp the significance of your 0.04%. All along, I have the idea that mass defect plays a significant/measurable part only in nuclear interactions - a little mass makes a lot of energy through E=mc². But chemistry means chemical bonds. I still don't quite digest that burning of wood by our earliest ancestors involve mass defect.
Anyway, I have some vague idea that they even seem to account for mass defects about total mass of electrons in atoms and molecules. I still have to accept and learn.
I believe the point of Bored's comment was not that chemical reactions result in lost or gained mass (it does, but the energies involved are so small that the mass change is negligible). The point was that, even for isotopically pure elements, like fluorine and iridium, the atomic masses are not just multiples of the same atomic mass unit. If, for instance, iridium trifluoride were made up of these "perfect" mass elements, then there would be 3x19/(3x19 +192) or 22.89% fluorine by mass. However, it is actually measureably 3x18.998/(3x18.998 +192.217) = 22.87% fluorine...