atomic weights

[student13]

In my biology textbook there is a short chapter on chemistry, in which it says the mass of 1 proton = the mass of 1 neutron = 1 amu. Hydrogen is made up of 1 proton and 1 electron and has an atomic weight of 1.0079 amu's. Logically, the mass of 1 electron should be .0079 amu's. However, on the same periodic table, it says that helium (2 neutrons, 2 protons, and 2 electrons) has an atomic mass of 4.0026, which means that the mass of 1 electron should be .0013 amu's. I am confused and could not find anything explaining this on google. Is there more subatomic particles than protons, electrons, and neutrons which weigh enough to matter, or is the idea that 1 proton = 1 neutron = 1 amu off?

 

[James R]

Protons and neutrons do not have masses of exactly 1 amu. Both are slightly more than 1 amu, and the neutron mass is slightly higher than the proton mass.

But when protons and neutrons combine to form a nucleus, some of the combined mass is actually lost - converted to energy (called binding energy) according to Einstein's famous equation $$E=mc^2$$. So, you can't arrive at the mass of a nucleus just by adding up the masses of the protons and neutrons.

The electron has a mass that is 1/1836 that of the proton, so electrons don't make much difference to atomic masses.

Atomic masses in chemistry textbooks are even more complicated, because they usually give a kind of average over multiple isotopes of an element.

Take hydrogen, for example. Hydrogen has two stable (non-radioactive) isotopes. One is the normal form of hydrogen, with one proton and one electron. The other, called deuterium has one proton, one neutron and one electron. If you collect some natural hydrogen, you'll find that 99.98% of the atoms are hydrogen 1, and 0.02% are deuterium.

The atomic mass of hydrogen 1 is 1.00794 amu. The atomic mass of deuterium (hydrogen-2) is 2.0136 amu. To calculate the average atomic mass of hydrogen, we do this:

$$\frac{99.98}{100} \times 1.00794 + \frac{0.02}{100} \times 2.0136 = 1.0081$$

The most important point here is that you can't simply add up the masses of the protons, neutrons and electrons to get the total atomic mass, even for just one isotope, because when protons, neutrons and electrons come together to form an atom, some of the mass is converted to energy in the process, meaning that the resulting atom ends up being lighter than its constituents would be if they were not bound together.

 

[Trippy]

In my biology textbook there is a short chapter on chemistry, in which it says the mass of 1 proton = the mass of 1 neutron = 1 amu. Hydrogen is made up of 1 proton and 1 electron and has an atomic weight of 1.0079 amu's. Logically, the mass of 1 electron should be .0079 amu's. However, on the same periodic table, it says that helium (2 neutrons, 2 protons, and 2 electrons) has an atomic mass of 4.0026, which means that the mass of 1 electron should be .0013 amu's. I am confused and could not find anything explaining this on google. Is there more subatomic particles than protons, electrons, and neutrons which weigh enough to matter, or is the idea that 1 proton = 1 neutron = 1 amu off?

Nuclear Binding Energy (among other things).

Binding Energy on Wiki

There's two thing sthat you need to understand.

The first one is that it takes energy to hold a nucleus together, between Hydrogen and Magnesium you get an increase in nuclear binding energy per nucleon. That energy has to come from somewhere, and mass and energy are equivalent, so the mass is reduced a little bit. When you fuse two lighter elements together, you destroy a little bit of mass in each nucleus, and this is released as energy.

Between Magnesium and Xenon, you reach saturation, there isn't a great deal of change in nuclear binding energy. FInally, you get past a certain point, and the nuclei start falling apart, becaus ethe repulsive electrostatic forces become stronger than the attractive strong force.

The second thing you need to understand is that the atomic weights your textbook sites are averages.

Essentially, if you consider Hydrogen, it's stable forms in the environment are H-1 and H-2.

Naturally occuring Hydrogen is 99.985% H-1 and 0.015% H-2, so the average weight of a mole of natural hydrogen weighs (0.9985*(1.00782+.000549))+(0.0015*(2.015995+.000549)) + or 1.00988, where it actually weighs in at 1.00794 with the difference - .00194 amu, or 1.8 MeV being within rounding errors of the binding energy for the nucleus (according to Wiki being 2.2 MeV).

 

[fellowtraveler]

Protons and neutrons do not have masses of exactly 1 amu. Both are slightly more than 1 amu, and the neutron mass is slightly higher than the proton mass.

But when protons and neutrons combine to form a nucleus, some of the combined mass is actually lost - converted to energy (called binding energy) according to Einstein's famous equation $$E=mc^2$$. So, you can't arrive at the mass of a nucleus just by adding up the masses of the protons and neutrons.

The electron has a mass that is 1/1836 that of the proton, so electrons don't make much difference to atomic masses.

Atomic masses in chemistry textbooks are even more complicated, because they usually give a kind of average over multiple isotopes of an element.

Take hydrogen, for example. Hydrogen has two stable (non-radioactive) isotopes. One is the normal form of hydrogen, with one proton and one electron. The other, called deuterium has one proton, one neutron and one electron. If you collect some natural hydrogen, you'll find that 99.98% of the atoms are hydrogen 1, and 0.02% are deuterium.

The atomic mass of hydrogen 1 is 1.00794 amu. The atomic mass of deuterium (hydrogen-2) is 2.0136 amu. To calculate the average atomic mass of hydrogen, we do this:

$$\frac{99.98}{100} \times 1.00794 + \frac{0.02}{100} \times 2.0136 = 1.0081$$

The most important point here is that you can't simply add up the masses of the protons, neutrons and electrons to get the total atomic mass, even for just one isotope, because when protons, neutrons and electrons come together to form an atom, some of the mass is converted to energy in the process, meaning that the resulting atom ends up being lighter than its constituents would be if they were not bound together.

REPLY: I have this desire to actually understand these things. I get very confused about it all. I will limit my questions to two in hopes of my being able to understand the answers. 1. Why doesn`t the binding energy required to hold nucleons [ protons and neutrons ]together ADD TO THE MASS ? 2. I always thought a neutron WAS A PROTON BONDED TO AN ELECTRON in some way. And that this is the reason that: during radioactive decay when a beta particle [ an electron ] is emitted during radioactive decay, that element gains a PROTON AND MOVES TO THE RIGHT ONE PLACE on the periodic table. That when that electron is emitted, WHAT WAS A NEUTRON IS NOW A PROTON. Is this true or not ? ...traveler

 

[Trippy]

REPLY: I have this desire to actually understand these things. I get very confused about it all. I will limit my questions to two in hopes of my being able to understand the answers. 1. Why doesn`t the binding energy required to hold nucleons [ protons and neutrons ]together ADD TO THE MASS ?

Because total energy is conserved.

If, as an example, you consider a deuterium nucleus that is at rest, one proton, and one neutron, and compare this to a proton and neutron that are very far apart, and at rest. The proton at rest has a mass energy of 938 MeV, and the neutron has a mass energy of 939 MeV, which gives us a total energy of (roughly) 1877 MeV. Now, if, for a minute we consider the Deuterium nucleus, then the total energy contained within that nucleus has to be the total energy of the proton, the total energy of the neutron, AND the energy that it takes to stick them together. But, if we treat it as a closed system, then all of the energy that's available in the nucleus is the 1877 MeV that we had to begin with, so, the energy that we used to stick the proton and neutron together to form the nucleus of deuterium has to come out of the mass energy of the proton and the neutron.

2. I always thought a neutron WAS A PROTON BONDED TO AN ELECTRON in some way. And that this is the reason that: during radioactive decay when a beta particle [ an electron ] is emitted during radioactive decay, that element gains a PROTON AND MOVES TO THE RIGHT ONE PLACE on the periodic table. That when that electron is emitted, WHAT WAS A NEUTRON IS NOW A PROTON. Is this true or not ? ...traveler

Firstly, Protons and neutrons are composed of quarks, which come in flavours and colours. Different flavours have different charges, and different masses.

Secondly, there's three different kinds of beta decay, but the one you're thinking of involves an up quark changing to a down quark by emission of a W[sup]-[/sup] Boson, which then decays into an electron and an anti neutrino.

So the neutron decays into a proton, an electron, and an anti neutrino, because one of the particles that makes up the Neutron changes into one of the particles that makes up a proton, which has the net effect of changing the neutron into a proton, because their component particles only differ by one thing. In the process of doing so, it emits a particle, that travels a short distance before decaying into two other particles.

Proton on Wiki
Neutron on Wiki
Quark on Wiki
Beta Decay on Wiki
Q and Z bosons on Wiki

 

[fellowtraveler]

Because total energy is conserved.

If, as an example, you consider a deuterium nucleus that is at rest, one proton, and one neutron, and compare this to a proton and neutron that are very far apart, and at rest. The proton at rest has a mass energy of 938 MeV, and the neutron has a mass energy of 939 MeV, which gives us a total energy of (roughly) 1877 MeV. Now, if, for a minute we consider the Deuterium nucleus, then the total energy contained within that nucleus has to be the total energy of the proton, the total energy of the neutron, AND the energy that it takes to stick them together. But, if we treat it as a closed system, then all of the energy that's available in the nucleus is the 1877 MeV that we had to begin with, so, the energy that we used to stick the proton and neutron together to form the nucleus of deuterium has to come out of the mass energy of the proton and the neutron.



Firstly, Protons and neutrons are composed of quarks, which come in flavours and colours. Different flavours have different charges, and different masses.

Secondly, there's three different kinds of beta decay, but the one you're thinking of involves an up quark changing to a down quark by emission of a W[sup]-[/sup] Boson, which then decays into an electron and an anti neutrino.

So the neutron decays into a proton, an electron, and an anti neutrino, because one of the particles that makes up the Neutron changes into one of the particles that makes up a proton, which has the net effect of changing the neutron into a proton, because their component particles only differ by one thing. In the process of doing so, it emits a particle, that travels a short distance before decaying into two other particles.

Proton on Wiki
Neutron on Wiki
Quark on Wiki
Beta Decay on Wiki
Q and Z bosons on Wiki

REPLY: Dear trippy, thank you for trying. I will investigate the websites you provided. I intend to work on understanding all this. Quite frankly I am as confused as before. I very much admire people such as you who somehow understand these things. I appreciate your providing those websites and will see if I can comprehend at least some of it. Thank you , ...traveler

 

[Walter L. Wagner]

This might help.

Using the references from Wiki we find:

Proton mass = 1.0079 amu
Neutron mass = 1.0086 amu

Deuterium mass = 2.0141 amu (slightly less than the proton + neutron mass)

Since the proton plus the neutron weigh slightly more than the deuterium, the difference is called the 'mass defect'

In essence, when a proton and neutron are brought close together, they fuse into a deuterium. The mass defect is converted into energy. This emits energy in the process (fusion energy) in the form of gamma rays. Fusion energy is why the nuclei are generaly stable (neglecting radioactive decays via the weak force) and don't fall apart back into protons and neutrons from which they were made.

The deuterium can be separated back into a proton and neutron, but it would require an input of energy to separate them. Chemical reactions are far too little energy, so under most circumstances, deuterium is said to be very stable.

So, while protons and neutrons are said to be 1 amu each, this is actually an approximation, useful for chemistry/biology, but not quite accurate for nuclear physics.

A more detailed analysis looks at the quarks which make up the protons and neutrons, since deuterium is actually a combination of quarks, not a proton plus a neutron, which is a loose analogy.

 

[Fraggle Rocker]

Why doesn`t the binding energy required to hold nucleons [protons and neutrons] together ADD TO THE MASS?

That energy had to come from somewhere. It was created by converting of some of the mass of the proton and the neutron into energy, as quantified by Einstein's formula. So mass was decreased and energy was increased. If you look up the value of the binding energy and divide it by the speed of light squared, presumably it will be exactly equal to the missing mass.

 

[Trippy]

Off topic posts moved to SFOG

 

[kurros]

REPLY: Dear trippy, thank you for trying. I will investigate the websites you provided. I intend to work on understanding all this. Quite frankly I am as confused as before. I very much admire people such as you who somehow understand these things. I appreciate your providing those websites and will see if I can comprehend at least some of it. Thank you , ...traveler

I think I understand your confusion, because this always confused me as well. I like to think I understand it a little better now, although I'm a bit confused by what the others have said too, so let me put it the way I see it.

The confusing part is that the binding energy, for light elements, is a negative contribution to the total energy of the system. This is why the bound states weigh less than the unbound states; the binding energy DOES add to the mass of the nucleus, it is just negative for these elements (or at least I like to think of it this way; the usual convention is that these elements have positive binding energy, I think, because this is the energy required to separate all the pieces of the system, but I don't like that convention for thinking of the energy contained in the system)

I.e. Mass(He2) = Mass(p) + Mass(n) + (-binding energy)

Thus, when you combine a proton and neutron to make deuterium, you release some energy which zaps off as photons and the remaining stuff is therefore lighter.

For heavy elements, the binding energy is positive, so the nucleus weighs MORE than its component parts. I.e. you must supply some energy to stick them together, which for some reason is the picture that intuitively comes to mind when I think of binding energy. This energy certainly contributes to the mass of the system, in accordance with what you seem to be thinking of.

Someone correct me if I have screwed this up. I think this is how it goes though.

Ok it just occurred to me that this thread is kind of old, oh well. Helped me clarify this in my own head at least.

 

[rjr6]

Protons and neutrons do not have masses of exactly 1 amu. Both are slightly more than 1 amu, and the neutron mass is slightly higher than the proton mass.

But when protons and neutrons combine to form a nucleus, some of the combined mass is actually lost - converted to energy (called binding energy) according to Einstein's famous equation $$E=mc^2$$. So, you can't arrive at the mass of a nucleus just by adding up the masses of the protons and neutrons.

The electron has a mass that is 1/1836 that of the proton, so electrons don't make much difference to atomic masses.

Atomic masses in chemistry textbooks are even more complicated, because they usually give a kind of average over multiple isotopes of an element.

Take hydrogen, for example. Hydrogen has two stable (non-radioactive) isotopes. One is the normal form of hydrogen, with one proton and one electron. The other, called deuterium has one proton, one neutron and one electron. If you collect some natural hydrogen, you'll find that 99.98% of the atoms are hydrogen 1, and 0.02% are deuterium.

The atomic mass of hydrogen 1 is 1.00794 amu. The atomic mass of deuterium (hydrogen-2) is 2.0136 amu. To calculate the average atomic mass of hydrogen, we do this:

$$\frac{99.98}{100} \times 1.00794 + \frac{0.02}{100} \times 2.0136 = 1.0081$$

The most important point here is that you can't simply add up the masses of the protons, neutrons and electrons to get the total atomic mass, even for just one isotope, because when protons, neutrons and electrons come together to form an atom, some of the mass is converted to energy in the process, meaning that the resulting atom ends up being lighter than its constituents would be if they were not bound together.

Is the mass lost, or is just not accounted for? Isn't this unaccounted for mass the cause for nuclear explosions when man splits the atom? That was my simple understanding.

 

[Fraggle Rocker]

Is the mass lost, or is just not accounted for? Isn't this unaccounted for mass the cause for nuclear explosions when man splits the atom? That was my simple understanding.

It's not really "lost," that may have been an unfortunate choice of words. It's converted to energy, and rather a lot of it: E=mc^2.

That is precisely the energy in a nuclear explosion.

 

[James R]

Is the mass lost, or is just not accounted for?

It's lost - released to the environment when the atom forms.

Isn't this unaccounted for mass the cause for nuclear explosions when man splits the atom? That was my simple understanding.

Splitting the atom involves a similar process.

In that case, you take a large atom like Uranium and split it roughly into two parts. When you add up the combined masses of the resulting fragments (usually two smaller atoms plus a few neutrons), you find that they do not quite equal the mass of the original uranium atom. The "extra" mass was lost when the atom split into the fragments. By "lost" here, I mean converted into energy according to Einstein's equation again.

How does the energy appear? It appears mostly as speed of the fragments (kinetic energy or, approximately, heat), and that energy is what causes the explosion.

 

[rjr6]

Thanks for your answers