Variations in mass between elements
Alan Meyer
about "daltons" or the atomic mass units ("AMU")used to describe
the mass of atoms.
The Wikipedia gives the masses of protons and neutrons as
follows:
protons = 1.672621637(83)x10-27 kg
neutrons = 1.67492729(28)x10-27 kg
One dalton or AMU is defined as 1/12 the mass of Carbon-12. One
might think from that that one dalton is the average of the mass
of one proton and one neutron. I'm fine with this so far.
Now comes the difficulty for me.
The mass of Oxygen-16 is given in the periodic table as:
15.994914. I presume that this number is derived empirically and
is accurate.
Oxygen-16 has the exact same ratio of protons, neutrons, and
electrons as Carbon-12 does. In both cases, the ratios are
1:1:1.
So why doesn't the mass of Oxygen-16 = 16.00000... daltons?
Are the protons or neutrons somehow lighter? Is there some
component of carbon that is not a proton, neutron or electron and
that is missing or found in a different proportion in oxygen? Is
there some exotic quantum or relativistic effect that diverts
mass away from the oxygen atom? Do the masses of protons and
neutrons differ from each other under certain circumstances?
I've chosen oxygen for comparison with carbon, but the problem
exists for all of the elements. None of the isotopes of elements
have masses that form an exact multiple of their numbers of
protons and neutrons in comparison with the number of protons and
neutrons of carbon.
How should we understand this?
Thanks.
Alan
Stephan Bird
hr4ge4$a01$1...@news.eternal-september.org, Alan Meyer wrote:
> How should we understand this?
Have a look at binding energy, and related terms.
stephan
Frank
Alan Meyer
Thank you Frank and Stephan. I have read several elementary
chemistry texts and was always confounded by the fact that
the periodic tables showed non-integral daltons for isotopes,
but never saw the explanation of it in any of them.
Alan
David Bostwick
>I have a question about the mass of protons and neutrons, and
>about "daltons" or the atomic mass units ("AMU")used to describe
>the mass of atoms.
>
>The Wikipedia gives the masses of protons and neutrons as
>follows:
>
> protons = 1.672621637(83)x10-27 kg
> neutrons = 1.67492729(28)x10-27 kg
>
>One dalton or AMU is defined as 1/12 the mass of Carbon-12. One
>might think from that that one dalton is the average of the mass
>of one proton and one neutron. I'm fine with this so far.
>
>Now comes the difficulty for me.
>
>The mass of Oxygen-16 is given in the periodic table as:
>15.994914. I presume that this number is derived empirically and
>is accurate.
>
>Oxygen-16 has the exact same ratio of protons, neutrons, and
>electrons as Carbon-12 does. In both cases, the ratios are
>1:1:1.
>
>So why doesn't the mass of Oxygen-16 = 16.00000... daltons?
>
It used to be that way, until 12C replaced 16O as the standard. But of
course, 12C wasn't 12.0... at that time.
David Bostwick
Now let's complicate things by getting into mass spectrometry, and the
difference between average mass and monoisotopic mass. I've been telling
students the difference for 30+ years, and some of them never get it.
ChemDraw is not always your friend.
Alan Meyer
> Now let's complicate things by getting into mass spectrometry, and the
> difference between average mass and monoisotopic mass. I've been telling
> students the difference for 30+ years, and some of them never get it.
> ChemDraw is not always your friend.
I think I get that one.
From my initial, cursory reading of the Wikipedia article on binding
energy, it looks to me like binding energy is similar to lattice
energy in a crystal - but involves many more orders of magnitude of
energy because the nuclear forces are many orders of magnitude
greater than the electrostatic forces that bind ions to each other.
Does that sound reasonable? Or am I barking up the wrong tree?
Alan
Androcles
"Alan Meyer" <ame...@yahoo.com> wrote in message
news:hr4u0i$98q$1...@news.eternal-september.org...
F = GmM/r^2, but r is very small.
Let M = M = 1
let r = 1, then F = G1*1/(1*1) = G
let r = 0.1, then F = G * 100
let r = 0.01, then F = G * 10000
let r = 0.001, then F = G * 1,000,000
You are barking up the right tree at the wrong squirrel.
dlzc
On Apr 26, 1:44 pm, Alan Meyer <amey...@yahoo.com> wrote:
> David Bostwick wrote:
> > Now let's complicate things by getting into mass
> > spectrometry, and the difference between average
> > mass and monoisotopic mass. I've been telling
> > students the difference for 30+ years, and some of
> > them never get it. ChemDraw is not always your
> > friend.
>
> I think I get that one.
>
> From my initial, cursory reading of the Wikipedia
> article on binding energy, it looks to me like binding
> energy is similar to lattice energy in a crystal -
Pretty close.
> but involves many more orders of magnitude of
> energy because the nuclear forces are many orders
> of magnitude greater than the electrostatic forces that
> bind ions to each other.
>
> Does that sound reasonable? Or am I barking up the
> wrong tree?
You've got it. The amount of energy liberated in fission / fusion of
a few nanograms (even though large masses are applied) of matter is
much larger than even tons of TriNitroToluene.
David A. Smith
Martin Brown
> I have a question about the mass of protons and neutrons, and
> about "daltons" or the atomic mass units ("AMU")used to describe
> the mass of atoms.
>
> The Wikipedia gives the masses of protons and neutrons as
> follows:
>
> protons = 1.672621637(83)x10-27 kg
> neutrons = 1.67492729(28)x10-27 kg
>
> One dalton or AMU is defined as 1/12 the mass of Carbon-12. One
> might think from that that one dalton is the average of the mass
> of one proton and one neutron. I'm fine with this so far.
>
> Now comes the difficulty for me.
>
> The mass of Oxygen-16 is given in the periodic table as:
> 15.994914. I presume that this number is derived empirically and
> is accurate.
>
> Oxygen-16 has the exact same ratio of protons, neutrons, and
> electrons as Carbon-12 does. In both cases, the ratios are
> 1:1:1.
>
> So why doesn't the mass of Oxygen-16 = 16.00000... daltons?
Nuclear binding energy.
Not really chemistry though - this is nuclear physics.
>
> Are the protons or neutrons somehow lighter? Is there some
> component of carbon that is not a proton, neutron or electron and
> that is missing or found in a different proportion in oxygen? Is
> there some exotic quantum or relativistic effect that diverts
> mass away from the oxygen atom? Do the masses of protons and
> neutrons differ from each other under certain circumstances?
>
> I've chosen oxygen for comparison with carbon, but the problem
> exists for all of the elements. None of the isotopes of elements
> have masses that form an exact multiple of their numbers of
> protons and neutrons in comparison with the number of protons and
> neutrons of carbon.
>
> How should we understand this?
Try:
http://hyperphysics.phy-astr.gsu.edu/hbase/nucene/nucbin.html
and
http://en.wikipedia.org/wiki/Binding_energy
Regards,
Martin Brown
>
> Thanks.
>
> Alan
David Bostwick
In mass spec, we can separate the isotopes of an element up to a certain
m/z value, which varies with the mass resolution of the analyzer. For
example, we can see both isotopes of Br, and we use 79 as the nominal
(integer) mass of Br, not the average mass of 80. If we're making more
accurate mass measurements, we use the isotopic mass of 79Br, 78.9183, not the
average mass of 79.9. Some students (and others) never quite get the
difference.
When the mass of the ion is large enough that we can't separate the isotopes,
then we use the average mass.
Androcles
Alan Meyer wrote:
> I have a question about the mass of protons and neutrons, and
> about "daltons" or the atomic mass units ("AMU")used to describe
> the mass of atoms.
>
> The Wikipedia gives the masses of protons and neutrons as
> follows:
>
> protons = 1.672621637(83)x10-27 kg
> neutrons = 1.67492729(28)x10-27 kg
>
> One dalton or AMU is defined as 1/12 the mass of Carbon-12. One
> might think from that that one dalton is the average of the mass
> of one proton and one neutron. I'm fine with this so far.
>
> Now comes the difficulty for me.
>
> The mass of Oxygen-16 is given in the periodic table as:
> 15.994914. I presume that this number is derived empirically
Ah...
derive
transitive verb
1 a : to take, receive, or obtain especially from a specified source
b : to obtain (a chemical substance) actually or theoretically from a parent
substance
2 : infer, deduce
Eight figure accuracy with no tolerance...
presume
transitive verb
1 : to undertake without leave or clear justification : dare
2 : to expect or assume especially with confidence
3 : to suppose to be true without proof <presumed innocent until proved
guilty>
4 : to take for granted
Might I suggest that you have a numerical calculation based on a theory
which may be incorrect?
If one presumes the velocity of sound in a vacuum can be derived by
measuring its velocities in ever-decreasing atmospheric pressures then
one can put a number to it... except it becomes meaningless, there is
no sound in a vacuum. Similarly, the volume of a gas at zero kelvin
is zero, except there are no gasses at zero kelvin.
Same with protons, neutrons and electrons: they remain theoretical
constructs and as such are entirely dependent upon integers, so we
have a paradox.
As Martin Brown states, they are not chemistry, they are physics.
Their integer nature was theorised through chemistry and is successful
for that application, but the 8-figure accuracy is rightly questionable.
Martin Brown
Experimentally measured. A magnetic sector mass spec can manage 10^-4 or
so, but bleeding edge ion cyclotrons are now operating at 10^-10. eg
http://www.rle.mit.edu/media/pr143/16a.pdf
>
> Same with protons, neutrons and electrons: they remain theoretical
> constructs and as such are entirely dependent upon integers, so we
> have a paradox.
There is no paradox. E = mc^2
The binding energy is emitted as gamma rays when the nucleus is formed.
> As Martin Brown states, they are not chemistry, they are physics.
> Their integer nature was theorised through chemistry and is successful
> for that application, but the 8-figure accuracy is rightly questionable.
No it isn't questionable. Ion cyclotrons will *measure* to that accuracy.
Using the mass difference to disambiguate interfering species in mass
spectrometry is used in argon plasma Hires ICPMS. It is fairly easy to
separate Fe56+ from Ar40.O16+ for instance.
Regards,
Martin Brown
Androcles
"Martin Brown" <|||newspam|||@nezumi.demon.co.uk> wrote in message
news:tHJBn.146980$gF5.1...@newsfe13.iad...
When you can tell me what matter is we'll discuss it; until then a neutron
and a proton are made of flubber that has a property we call "mass", and
that is nothing more than a measure of the force of gravity acting between
the flubber and the greater flubber called "Earth". The proton has "charge"
as well. E = mc^2 says the force of flubber's gravity vanishes along with
the flubber and becomes two other forces we call electrical and magnetic,
which hurtle away playing leapfrog with each other. Whatever ion cyclotrons
may be doing, they are not nuclear bombs and we are dealing with force
fields, not "stuff" or "flubber" or "matter". The 8-figure accuracy is
rightly
questionable.
You have not and cannot measure m without gravity, F = dp/dt, p = mv.
Might I suggest that you have a numerical calculation based on a theory
which may be incorrect?
>
Alan Meyer
> I have a question about the mass of protons and neutrons, and
> about "daltons" or the atomic mass units ("AMU")used to describe
> the mass of atoms.
Gentlemen,
I thank all of you for enlightening me and, if you'll bear with
me a little longer, perhaps you can help me a little deeper into
this subject. I studied liberal arts lo these many decades ago
and have only recently come to the pursuit of the sciences, at
which I am self-taught and suffering from the many lacunae so
common in the knowledge of men with such ignorant teachers.
Oxygen-16 has a lower relative mass than Carbon-12, in the sense
that the ratio of the mass of Oxygen-16:Carbon-12 is slightly
lower than the ratio of the nuclear particle count of the two
atoms. The difference is accounted for by binding energy - which
is to say that more energy per nucleon was given up in the
formation of Oxygen-16 than in the formation of Carbon-12,
presumably in the center of a star (forgive my presumption
Androcles) in order to get the nuclear particles to bind together
to form the respective atoms. Since mass and energy are the same
thing as explained by Einstein's insight, the loss of that energy
is the same thing as a loss of mass.
So far so good. (If I've got it right that is. If not, I would
love to be corrected.)
Now comes my question.
Does it make any sense to say the mass deficit of the Oxygen-16
atom in comparison with the Carbon-12 atom can be distributed
across the various nuclear particles so that the individual
protons and neutrons of the oxygen atom have less mass than those
of the carbon?
Or is that perhaps a misconception of how one ascribes mass to
protons and neutrons? I'm thinking that a more sensible view of
the matter might be to say that the indvidual protons and neutrons
have no individually measurable mass when bound into an atom, and
to make them individually measurable one must supply the
requisite binding energy to dissociate them from the atom - which
thereby makes them into free standing particles with measurable
mass, and which also restores the mass that was taken away when
the atom was formed. On that view, if one supplies the carbon
atom with the binding energy it needs to dissociate, and one
supplies the oxygen atom with the binding energy it needs to
dissociate, one will be left with protons and neutrons that are
exactly the same mass no matter which atom they came from.
It's possible that I shouldn't be asking these questions at all
since I'm over my head here. But learning about these issues
helps me to feel that, when I study higher level problems in
chemistry, I'm not having to take the underlying nuclear
substrate as some sort of unexplained black box that I just have
to accept without understanding it.
Thanks.
Alan
Alan Meyer
...
> Might I suggest that you have a numerical calculation based on
> a theory which may be incorrect?
Androcles,
I'm confused about where you are going with this. Are you
suggesting that the ratio of mass of Oxygen-16 to Carbon-12 may
*not* be less than 16:12? Are you suggesting that it could be a
measurement error? Or are you merely suggesting that the authors
of the periodic table that I used were using numbers with too
much precision?
The data I used came from:
Click the "Isotopes" tab and hover the mouse cursor on the
element of interest. Known isotopes are displayed as overlapping
tiles. Click one to see the atomic weight assigned to each one.
I don't see a link in the chart to explain how the numbers were
derived.
It's a pretty neat periodic table.
Alan
Androcles
Fusion is at the low end of the period table, fission at the high end.
If we are to obtain energy from mass at both ends then the iron, nickel
and copper in the middle will have the lowest mass per nucleon.
Thus you can ASSUME that as you go through the periodic table
you'll see a mass per nucleon change, with oxygen being lighter per
nucleon than carbon. At least, in theory. The problem today in physics
is that theories are upheld to be "tested", not disproved, and if the test
fails the blame is placed on the experiment. It's been 40 years since
I visited Culham Laboratory when the hope of controlled nuclear fusion
was estimated to be 50 years in the future, and current estimates still
put it 50 years in the future. Seems to me it is time for a radical rethink
about "making sense".
>
> Or is that perhaps a misconception of how one ascribes mass to
> protons and neutrons? I'm thinking that a more sensible view of
> the matter might be to say that the indvidual protons and neutrons
> have no individually measurable mass when bound into an atom, and
> to make them individually measurable one must supply the
> requisite binding energy to dissociate them from the atom - which
> thereby makes them into free standing particles with measurable
> mass, and which also restores the mass that was taken away when
> the atom was formed. On that view, if one supplies the carbon
> atom with the binding energy it needs to dissociate, and one
> supplies the oxygen atom with the binding energy it needs to
> dissociate, one will be left with protons and neutrons that are
> exactly the same mass no matter which atom they came from.
>
> It's possible that I shouldn't be asking these questions at all
> since I'm over my head here. But learning about these issues
> helps me to feel that, when I study higher level problems in
> chemistry, I'm not having to take the underlying nuclear
> substrate as some sort of unexplained black box that I just have
> to accept without understanding it.
>
> Thanks.
>
> Alan
Nothing wrong with asking questions, Alan, it's high time somebody
did. Physics is bogged down with more crackpot theories than pebbles
on a beach.
Einstein had no "great insight":
http://www.androcles01.pwp.blueyonder.co.uk/MC2.htm
A current debate on Einstein's phoney math:
"blackhead" <larry...@softhome.net> wrote in message
news:87aef876-92fc-42bd...@b33g2000yqc.googlegroups.com...
Androcles
I'm saying one cannot "weigh" (i.e. use a balance in a gravitational field)
one
atom. Carbon has an atomic number of 6 (the chemical characteristic that
makes it carbon) and an atomic mass of 12.0107 because there is some
carbon-14 with two extra neutrons mixed in with the carbon-12.
The carbon-14 decays to nitrogen-14 by converting a neutron to a proton,
atomic mass 14.0067, and taking in an electron. But we also have c-13,
another stable isotope.
So we gather up enough equations over the entire range of the periodic
table and include hydrogen, atomic weight 1.00794 and twelve of those
weigh 12.09528 but oxygen is at 15.9994. So we end up with a linear
programming problem and the smallest error in any one isotope can throw
it into a tizzy, we expect to lose some mass as E/c^2 when fizzing lighter
elements into heavier ones. That means we lose some "matter", whatever
the flubber is that a nucleon is made of, and we measure that flubber by
weighing it with a force (gravity).
Sorry, I haven't written that too well, I'm getting tired. Time for bed,
said Zebedee.
Martin Brown
> "Alan Meyer" <ame...@yahoo.com> wrote in message
> news:hr863m$d7c$1...@news.eternal-september.org...
>> On 4/27/2010 10:01 PM, Androcles wrote:
>> ...
>>> Might I suggest that you have a numerical calculation based on
>>> a theory which may be incorrect?
>> ...
>>
>> Androcles,
>>
>> I'm confused about where you are going with this. Are you
>> suggesting that the ratio of mass of Oxygen-16 to Carbon-12 may
>> *not* be less than 16:12? Are you suggesting that it could be a
>> measurement error? Or are you merely suggesting that the authors
>> of the periodic table that I used were using numbers with too
>> much precision?
>>
>> The data I used came from:
>>
>> http://www.ptable.com/
>>
>> Click the "Isotopes" tab and hover the mouse cursor on the
>> element of interest. Known isotopes are displayed as overlapping
>> tiles. Click one to see the atomic weight assigned to each one.
>> I don't see a link in the chart to explain how the numbers were
>> derived.
To about 5 sig figs double focussing magnetic sector instruments will
measure mass to charge ratio of an ion. That is enough to separate a lot
of the important interferences in messy sources like GDMS and GCMS.
Here is an example taken from a JEOL instrument at low mass resolving
the D+ from the H2+ molecular dimer ion of ordinary hydrogen.
They don't allow deep linking so click on the link from
http://www.jeolusa.com/PRODUCTS/AnalyticalInstruments/MassSpectrometers/GCmateII/tabid/231/Default.aspx
It is unusual in being able to go down to mass one - few makers bother.
After that you are into ion cyclotron territory and they can do between
8 and 10 sig fig. I already posted the link but Androcles cannot read.
>>
>> It's a pretty neat periodic table.
>>
>> Alan
>
> I'm saying one cannot "weigh" (i.e. use a balance in a gravitational field)
> one
But you can determine mass by other means - typically by putting a
charge on it and applying electric and/or magnetic fields. That is how
time of flight and quadrupole mass spectrometers work.
Are you really so ignorant of physics?
> atom. Carbon has an atomic number of 6 (the chemical characteristic that
> makes it carbon) and an atomic mass of 12.0107 because there is some
> carbon-14 with two extra neutrons mixed in with the carbon-12.
> The carbon-14 decays to nitrogen-14 by converting a neutron to a proton,
> atomic mass 14.0067, and taking in an electron. But we also have c-13,
> another stable isotope.
> So we gather up enough equations over the entire range of the periodic
> table and include hydrogen, atomic weight 1.00794 and twelve of those
> weigh 12.09528 but oxygen is at 15.9994. So we end up with a linear
> programming problem and the smallest error in any one isotope can throw
> it into a tizzy, we expect to lose some mass as E/c^2 when fizzing lighter
> elements into heavier ones. That means we lose some "matter", whatever
> the flubber is that a nucleon is made of, and we measure that flubber by
> weighing it with a force (gravity).
> Sorry, I haven't written that too well, I'm getting tired. Time for bed,
> said Zebedee.
It is the mass energy relationship that explains the mass difference
when the particles are bound into a atomic nucleus. I doubt if someone
has bothered to measure all the species in the periodic table to full 8
(now 10) digit precision, but efforts are underway to do silicon as a
possible hard line SI standard for mass that is related only to physics.
At present mass is the only SI unit still defined as a reference lump.
For most practical purposes even in high resolution mass spec the value
we have for isotopic masses are good enough. Only research instruments
that are pushing the frontiers of knowledge measure to higher precision.
Regards,
Martin Brown
Martin Brown
In a crude sense when you add an extra particle to N particles you
generate N+1 additional particle particle interactions. Certain magic
numbers of particles which in classical terms close pack exactly are
more stable than they might otherwise be expected to be. A full QM
treatment is needed, but that is the basic principle. Nice symmetric
fully filled shells of nucleons have better stability.
http://en.wikipedia.org/wiki/Island_of_stability
You cannot separate them to measure once they are bound so it is normal
to talk in terms of binding energy per nucleon without distinguishing
between neutrons and protons. The strong nuclear force doesn't care
about the puny charge on a proton at short range.
>
> Or is that perhaps a misconception of how one ascribes mass to
> protons and neutrons? I'm thinking that a more sensible view of
> the matter might be to say that the indvidual protons and neutrons
> have no individually measurable mass when bound into an atom, and
> to make them individually measurable one must supply the
> requisite binding energy to dissociate them from the atom - which
> thereby makes them into free standing particles with measurable
> mass, and which also restores the mass that was taken away when
> the atom was formed. On that view, if one supplies the carbon
> atom with the binding energy it needs to dissociate, and one
> supplies the oxygen atom with the binding energy it needs to
> dissociate, one will be left with protons and neutrons that are
> exactly the same mass no matter which atom they came from.
Stars run out of steam when they have converted most of their fuel into
iron which at mass 56 has the highest binding energy per nucleon. After
that the nuclear reactions for making higher masses are endothermic and
a large star implodes on the timescale of freefall causing a supernova.
>
> It's possible that I shouldn't be asking these questions at all
> since I'm over my head here. But learning about these issues
> helps me to feel that, when I study higher level problems in
> chemistry, I'm not having to take the underlying nuclear
> substrate as some sort of unexplained black box that I just have
> to accept without understanding it.
You might find the illustration on Wolframs demos page interesting:
http://demonstrations.wolfram.com/StellarNucleosynthesis/
Regards,
Martin Brown
Androcles
There you are, see, you've applied a force.
That is how
> time of flight and quadrupole mass spectrometers work.
>
> Are you really so ignorant of physics?
Personal abuse is no argument, but if you want it that way...
Are you really so fuckin' stupidly pompous and arrogant that you think
you can put a charge on a neutron?
Alan Meyer
Thank you.