# Help me understand a Physics concept

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In our book, Abeka teaches that an atom can have different amounts of neutrons. I have, yet, to come across how you would know up to how many one could have. I've even looked online. I understand they are isotopes. I understand how to figure out how many neutrons are in an atom from the periodic table. What I can't explain is how it is that an atom can have more neutrons than given or how you'd know how many it can have! Thanks for any help. I hope I made sense.

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Not sure about a theoretical limit (it would be tied to nuclear forces - at some point, the Coulomb force would overcome the strong nuclear force, which has a limited effective range), but experimentally, there are very few stable isotopes per element.  The larger the atomic number, the more neutrons are needed per proton to keep an isotope somewhat stable.  You might find some visual clues around half-lives or decay of isotopes.

We do have a more currently practicing physicist here who may be able to expound better than I.

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arrgh, the forum ate my post. No time, gotta run to work, but a quick googling gives a good explanation on wikipedia

https://en.wikipedia.org/wiki/Isotope

Atomic nuclei consist of protons and neutrons bound together by the residual strong force. Because protons are positively charged, they repel each other. Neutrons, which are electrically neutral, stabilize the nucleus in two ways. Their copresence pushes protons slightly apart, reducing the electrostatic repulsion between the protons, and they exert the attractive nuclear force on each other and on protons. For this reason, one or more neutrons are necessary for two or more protons to bind into a nucleus. As the number of protons increases, so does the ratio of neutrons to protons necessary to ensure a stable nucleus (see graph at right). For example, although the neutron:proton ratio of 32He is 1:2, the neutron:proton ratio of 238
92
U
is greater than 3:2. A number of lighter elements have stable nuclides with the ratio 1:1 (Z = N). The nuclide 40 20Ca (calcium-40) is observationally the heaviest stable nuclide with the same number of neutrons and protons; (theoretically, the heaviest stable one is sulfur-32). All stable nuclides heavier than calcium-40 contain more neutrons than protons.

and the graph shows the half life of isotopes. You can see that the the larger the number of protons, the larger the ratio neutron number Z to proton number N for stable isotopes, but it still stays within a narrow range of up to around 1.5. This means you don't get stable isotopes with twice or three times as many neutrons as protons.

Edited by regentrude
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how you'd know how many it can have

In nature, elements are usually found as a mixture of isotopes and scientist knows what percent each of these are.  For practical purposes, that is in lab, Iodine 132I, phosphate 32P, hydrogen 2H isotopes are used most frequently to label compounds so they can visualize it in an experiment and these have relatively short half life.  And of course 14C for carbon-14 dating.  There may be few others but when I worked in lab, those were the ones that were most frequently used.

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arrgh, the forum ate my post. No time, gotta run to work, but a quick googling gives a good explanation on wikipedia

https://en.wikipedia.org/wiki/Isotope

and the graph shows the half life of isotopes. You can see that the the larger the number of protons, the larger the ratio neutron number Z to proton number N for stable isotopes, but it still stays within a narrow range of up to around 1.5. This means you don't get stable isotopes with twice or three times as many neutrons as protons.

I figured that we could count on you for more. :)

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This I get.... What I don't get is statements such as "For example, although a hydrogen atom always has one proton, it may have zero, one, or two neutrons." That is from Abeka. I know the basic formula for figuring out neutrons but that doesn't give me the answer I'm curious about. A hydrogen atom has one proton. How does it have one, two, or three neutrons if its atomic mass is 1.008? How were you able to figure that out?

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This I get.... What I don't get is statements such as "For example, although a hydrogen atom always has one proton, it may have zero, one, or two neutrons." That is from Abeka. I know the basic formula for figuring out neutrons but that doesn't give me the answer I'm curious about. A hydrogen atom has one proton. How does it have one, two, or three neutrons if its atomic mass is 1.008? How were you able to figure that out?

There is a difference between the meanings of atomic mass and mass number. One is the average weight of an element and the other is the total number of nucleons in the atom's nucleus.

Atomic mass is also known as atomic weight. Atomic mass is the weighted average mass of an atom of an element based on the relative natural abundance of that element's isotopes.

Mass number is a count of the total number of protons and neutrons in an atom's nucleus.

Atomic Mass and Mass Number Example

Hydrogen has three natural isotopes: 1H, 2H, and 3H. Each isotope has a different mass number.

1H has 1 proton. Its mass number is 1. 2H has 1 proton and 1 neutron. Its mass number is 2. 3H has 1 proton and 2 neutrons. Its mass number is 3.

99.98% of all hydrogen is 1H

0.018% of all hydrogen is 2H

0.002% of all hydrogen is 3H

Together, they give a value of atomic mass of hydrogen equal to 1.0079 g/mol.

Edited by regentrude
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Yes, I get that, but how did you know that Hydrogen has three isotopes? How would I KNOW how many oxygen has? or carbon? Is there a formula or some way to automatically know what their isotopes are? Maybe I'm missing something here.

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Or how would I know what the isotopes are?

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Yes, I get that, but how did you know that Hydrogen has three isotopes? How would I KNOW how many oxygen has? or carbon? Is there a formula or some way to automatically know what their isotopes are? Maybe I'm missing something here.

I don't think there is a black-and-white theoretical answer - maybe you can find it (please do)?  The experimental evidence is what we have, and it's confined to the testing conditions available to us now.  You can find a list of isotopes identified; you can infer probabilistic likelihoods from the graphs above.  We can assess certain limits due to nuclear forces. electron speed, and the like.  We just don't have mastery of the subatomic yet.

That said, while my math is being forcibly refreshed by my kids, my practice in physics is very outdated.  I still would be surprised if anyone could give you a definitive answer just yet.

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Yes, I get that, but how did you know that Hydrogen has three isotopes? How would I KNOW how many oxygen has? or carbon? Is there a formula or some way to automatically know what their isotopes are? Maybe I'm missing something here.

No, I do not recall there to be a simple formula (but this is not my area of expertise).

Humankind knows that there are three stable H isotopes because they have been observed occurring in nature.

Other unstable isotopes are created in the lab; one can make hydrogen isotopes with more neutrons and they decay within fractions of a second.

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I'm guessing you'd know you have an unstable isotope in your sample if you detect the energy released when it decays?

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Yes, I get that, but how did you know that Hydrogen has three isotopes? How would I KNOW how many oxygen has? or carbon? Is there a formula or some way to automatically know what their isotopes are? Maybe I'm missing something here.

Or how would I know what the isotopes are?

No, I do not recall there to be a simple formula (but this is not my area of expertise).

Humankind knows that there are three stable H isotopes because they have been observed occurring in nature.

Other unstable isotopes are created in the lab; one can make hydrogen isotopes with more neutrons and they decay within fractions of a second.

Agree - regentrude has it.  For example, theoretically, there could be many, many different isotopes of hydrogen - H-1, H-2, H-3, H-4, H-5, H-6, H-7, etc.  The isotopes would be created by adding one more neutron to the hydrogen atom for each successive isotope.  The problem is that only the first three isotopes of H - protium, deuterium, and tritium (H-1, H-2, and H-3, respectively) - are even remotely stable.  H-4 decays within 139 yoctoseconds (1.39 x 10-22 sec) and the larger isotopes get less stable from there.  Since those larger isotopes are so unstable (see Regentrude's diagram above - when the proton:neutron ratio becomes more and more unbalanced, the isotopes get more and more unstable), they don't exist in nature.  When we calculate the atomic mass of an element on the periodic table, we're calculating a weighted average of the masses of the most common naturally occurring isotopes of that element - that's the definition of atomic mass.  We could (and do) have isotopes of each element other than the isotopes used to calculate the atomic mass of a particular element, but we just don't bother worrying about them because they only exist in the lab for tiny, tiny fractions of a second.

As to how we'd know which isotopes were naturally occurring, it would be the ones we detect in nature. :)  There's no formula or quick and easy way for a student to know or calculate this - nuclear chemists (or physicists :) ) would do the detecting and a high school chem student (or physics student) would look up the list of naturally occurring stable isotopes for each element.  Here's a list of naturally occurring isotopes up to element 92 (it's a PDF from Wiley): http://onlinelibrary.wiley.com/doi/10.1002/0470014318.app1/pdf  if anyone is interested. :)

Edited by Dicentra
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In our book, Abeka teaches that an atom can have different amounts of neutrons. I have, yet, to come across how you would know up to how many one could have. I've even looked online. I understand they are isotopes. I understand how to figure out how many neutrons are in an atom from the periodic table. What I can't explain is how it is that an atom can have more neutrons than given or how you'd know how many it can have! Thanks for any help. I hope I made sense.

I HIGHLY recommend Tyler DeWitt's videos on YouTube. He explains a lot of Chemistry concepts, but some of it can roll over into physics.

He's pretty awesome!

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